{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, n: 2, l: 3}. What is the expected number of occurrences of the pattern 'n*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, y: 1, l: 1, g: 1, m: 2}, what is the expected number of times the pattern 'lg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 4, g: 1, y: 1}. What is the expected number of occurrences of the pattern 'g*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, i: 1, s: 1, m: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'i+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, i: 1, w: 1, q: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'iq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, d: 3, r: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, b: 3, p: 1}, what is the expected number of times the pattern 'j.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, m: 4} to form a word, what is the expected number of matches of the pattern 'm*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, a: 1, u: 1, g: 2}, what is the expected number of times the pattern 'a+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, t: 1, u: 1, n: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, f: 1, e: 3, j: 1}, what is the expected number of times the pattern 'eh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, n: 1, b: 4}, what is the expected number of times the pattern 'n*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, k: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'nb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, a: 2, g: 3} to form a word, what is the expected number of matches of the pattern 'a+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, p: 4}. What is the expected number of occurrences of the pattern 'q*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, s: 2, u: 3}, what is the expected number of times the pattern 'x.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, n: 1, g: 1, b: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'jg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, v: 2, m: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'v*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, s: 2, n: 2}, what is the expected number of times the pattern 'nv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, m: 1, f: 2, h: 1}, what is the expected number of times the pattern 'w*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, l: 1, d: 3} to form a word, what is the expected number of matches of the pattern 'od*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, x: 1, w: 2, t: 1, k: 1}, what is the expected number of times the pattern 't+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, i: 1, k: 1, d: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'dm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 3, c: 3}, what is the expected number of times the pattern 's*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, i: 1, f: 3} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, x: 1, u: 3}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, g: 1, v: 2, u: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'uf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, p: 1, g: 1, r: 1, j: 2}. What is the expected number of occurrences of the pattern 'z.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, m: 2, o: 2, i: 1}. What is the expected number of occurrences of the pattern 'i*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, q: 2, m: 3} to form a word, what is the expected number of matches of the pattern 't*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, i: 3, s: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, n: 1, r: 1, o: 1, g: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, y: 3}. What is the expected number of occurrences of the pattern 'ya+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, p: 2, x: 3}. What is the expected number of occurrences of the pattern 'p+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, u: 3}, what is the expected number of times the pattern 'h.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, v: 1, e: 1, o: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'eo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, g: 1, k: 1, i: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'i+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, x: 2, t: 2, a: 1}, what is the expected number of times the pattern 'a+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, z: 1, k: 1, q: 1, h: 2}. What is the expected number of occurrences of the pattern 'cq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, z: 3, r: 1}. What is the expected number of occurrences of the pattern 'z.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, w: 5}. What is the expected number of occurrences of the pattern 'n*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, m: 3}. What is the expected number of occurrences of the pattern 'm.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, y: 1, b: 2, i: 1, m: 1}, what is the expected number of times the pattern 'mb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, o: 5}, what is the expected number of times the pattern 'o*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, g: 1, h: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'yh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 4, o: 2}. What is the expected number of occurrences of the pattern 'p+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, d: 3, o: 2}. What is the expected number of occurrences of the pattern 'l+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, o: 1, u: 2, n: 1, a: 1}. What is the expected number of occurrences of the pattern 'u.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, k: 1, s: 2, o: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'q+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 5, d: 1} to form a word, what is the expected number of matches of the pattern 'dn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, w: 1, h: 1, p: 1, v: 1}. What is the expected number of occurrences of the pattern 'kh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, v: 3}. What is the expected number of occurrences of the pattern 'vf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, f: 2, b: 1, g: 1}. What is the expected number of occurrences of the pattern 'g+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, m: 3}, what is the expected number of times the pattern 'm.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, r: 1, d: 1, l: 1, m: 1}. What is the expected number of occurrences of the pattern 'rt+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, m: 2, z: 2, w: 1}, what is the expected number of times the pattern 'w+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, b: 2, e: 1, r: 2}. What is the expected number of occurrences of the pattern 'p.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 4, b: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, q: 1, k: 1, e: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'i+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, z: 3}. What is the expected number of occurrences of the pattern 'h.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, r: 2, e: 1}, what is the expected number of times the pattern 'e+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, x: 1, h: 2, b: 2}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, s: 3} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'yy+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, h: 1, s: 1, v: 2, x: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, h: 1, x: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'hl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, f: 1, k: 2, z: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'm+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, j: 2, c: 1, u: 1, y: 1}. What is the expected number of occurrences of the pattern 'ug+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, p: 1, f: 1, d: 1, o: 1}, what is the expected number of times the pattern 'dp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, b: 1, n: 1, t: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'q+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, d: 4, s: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, e: 1, c: 1, x: 2}, what is the expected number of times the pattern 'ew*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, o: 3} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, c: 4}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 5, l: 1}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 4, u: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, u: 1, l: 2}. What is the expected number of occurrences of the pattern 'lw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, x: 1, g: 1, p: 1, l: 2}. What is the expected number of occurrences of the pattern 'g.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, k: 1, u: 2, q: 1}. What is the expected number of occurrences of the pattern 'jk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, z: 1, y: 1, o: 2}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, v: 2, o: 1, r: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, k: 1, s: 1, o: 2}, what is the expected number of times the pattern 'yo+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, r: 2, u: 2}. What is the expected number of occurrences of the pattern 'r+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, w: 1, h: 3, i: 1}, what is the expected number of times the pattern 'hu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, u: 1, q: 1, r: 2, a: 1}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, n: 2}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, d: 2, k: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, y: 1, i: 2, t: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'ty+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, l: 2}. What is the expected number of occurrences of the pattern 'ul+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, p: 2, n: 2} to form a word, what is the expected number of matches of the pattern 't*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, i: 1, u: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'u*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, z: 2, b: 1, g: 1, q: 1}, what is the expected number of times the pattern 'ff+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 3, n: 2, d: 1}. What is the expected number of occurrences of the pattern 'np*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, k: 1, i: 1, a: 2, g: 1}, what is the expected number of times the pattern 'd*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, r: 1, i: 1, m: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, r: 1, n: 1, o: 1, d: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, y: 1, l: 1, t: 1, k: 1}. What is the expected number of occurrences of the pattern 'k*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'u.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, a: 2, w: 2} to form a word, what is the expected number of matches of the pattern 'a+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, l: 1, j: 1, b: 1, x: 2}. What is the expected number of occurrences of the pattern 'r+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 4, y: 2}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, a: 2, o: 2}, what is the expected number of times the pattern 'ao+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, r: 1, b: 2}, what is the expected number of times the pattern 'r.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, x: 3, d: 2}, what is the expected number of times the pattern 'md+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, s: 2, e: 1, l: 1, b: 1}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, g: 1, o: 3, m: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, w: 1, y: 1, o: 1, t: 2}, what is the expected number of times the pattern 'o.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, j: 2, s: 1, n: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'q.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, z: 1, f: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'f*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, m: 2, t: 1, b: 2}, what is the expected number of times the pattern 'm*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 4, l: 2}. What is the expected number of occurrences of the pattern 'l*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, l: 1, o: 2, c: 1}, what is the expected number of times the pattern 'c*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, b: 1, q: 1, h: 2, c: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, r: 2, m: 1, f: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, t: 3}. What is the expected number of occurrences of the pattern 'f.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, v: 1, k: 2, t: 1}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, u: 4}, what is the expected number of times the pattern 'z+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, j: 1, a: 1, r: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'i.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 4, r: 2} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, k: 2, t: 2}. What is the expected number of occurrences of the pattern 'h*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, w: 2, l: 2, p: 1}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, y: 4}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, m: 1, c: 1, r: 3}, what is the expected number of times the pattern 'x+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, l: 2, j: 1, f: 1, h: 1}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'v*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, g: 1, p: 1, q: 1}. What is the expected number of occurrences of the pattern 'u*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, b: 1, i: 2, p: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, i: 1, o: 1, t: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'ih+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 5, h: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, u: 4}. What is the expected number of occurrences of the pattern 'ur*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, d: 3}, what is the expected number of times the pattern 'd*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, h: 4} to form a word, what is the expected number of matches of the pattern 'z.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, f: 1, w: 1, s: 1, a: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 4, v: 2}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, t: 1, r: 3}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, s: 2, h: 1}. What is the expected number of occurrences of the pattern 'x*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, h: 2, r: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 4, q: 2} to form a word, what is the expected number of matches of the pattern 'u+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 4, m: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'm.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 4, k: 2}. What is the expected number of occurrences of the pattern 'vk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, u: 1, l: 2, q: 1}. What is the expected number of occurrences of the pattern 'ul*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 5, e: 1}. What is the expected number of occurrences of the pattern 'et+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, n: 1, y: 2}, what is the expected number of times the pattern 'y*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, u: 1, q: 1, f: 2, h: 1}. What is the expected number of occurrences of the pattern 'fu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, k: 1, m: 1, c: 2}. What is the expected number of occurrences of the pattern 'mc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, l: 3, s: 1, t: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, w: 2, o: 1, u: 1, f: 1}, what is the expected number of times the pattern 'r*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, t: 2, o: 2}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, r: 1, h: 1, z: 2, e: 1}, what is the expected number of times the pattern 'q.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, y: 2, k: 2}, what is the expected number of times the pattern 'k.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, q: 1, j: 2, b: 1, h: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, n: 1, x: 2, h: 1, i: 1}. What is the expected number of occurrences of the pattern 'hi*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, l: 1, w: 1, r: 2, x: 1}, what is the expected number of times the pattern 's+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, f: 1, a: 2}, what is the expected number of times the pattern 'af*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, h: 1, t: 1, o: 2, r: 1}, what is the expected number of times the pattern 'r*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, k: 2, m: 2, j: 1}, what is the expected number of times the pattern 'a.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, l: 2, m: 3}, what is the expected number of times the pattern 'lf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, w: 4, k: 1}. What is the expected number of occurrences of the pattern 'w.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, h: 1, f: 2, n: 1}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, p: 2, t: 1, x: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'mx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, y: 2, f: 2, c: 1}. What is the expected number of occurrences of the pattern 'y+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, d: 1, x: 2, j: 1, y: 1}, what is the expected number of times the pattern 'xq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, p: 3} to form a word, what is the expected number of matches of the pattern 'p.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, n: 4} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 4, o: 2} to form a word, what is the expected number of matches of the pattern 't+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, w: 1, u: 2, v: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, l: 2, e: 2} to form a word, what is the expected number of matches of the pattern 'rl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, e: 1, c: 4}. What is the expected number of occurrences of the pattern 'me+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, o: 1, p: 2, s: 1, l: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, b: 2, g: 2, p: 1}. What is the expected number of occurrences of the pattern 'zb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'v.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, l: 2, s: 1, e: 2}. What is the expected number of occurrences of the pattern 'k+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, a: 1, c: 1, j: 1, h: 2}, what is the expected number of times the pattern 'vj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, o: 1, r: 1, i: 1, w: 2}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 4, n: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, e: 3, n: 1} to form a word, what is the expected number of matches of the pattern 'n+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, d: 1, x: 1, n: 3}, what is the expected number of times the pattern 'n*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, i: 1, t: 2, m: 2}. What is the expected number of occurrences of the pattern 't.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, l: 1, u: 2, h: 2}. What is the expected number of occurrences of the pattern 'l*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, e: 1, q: 2, n: 1}, what is the expected number of times the pattern 'eq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 4, r: 2}, what is the expected number of times the pattern 'd*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, o: 3, q: 1, j: 1}. What is the expected number of occurrences of the pattern 'q.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, g: 3, a: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 3, o: 1, b: 1, h: 1}, what is the expected number of times the pattern 'h+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, c: 3, r: 1}. What is the expected number of occurrences of the pattern 'cw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, c: 1, v: 2, l: 2} to form a word, what is the expected number of matches of the pattern 'u.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, g: 1, m: 1, h: 1, r: 1}, what is the expected number of times the pattern 'hr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, z: 1, b: 1, o: 2, t: 1}, what is the expected number of times the pattern 'or*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, k: 1, f: 1, w: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'pl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, u: 1, r: 1, z: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'p+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, d: 4}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, b: 1, v: 1, o: 1, p: 1}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, g: 1, q: 2, i: 2}. What is the expected number of occurrences of the pattern 'qg+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, i: 1, c: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'v+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, h: 2, m: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, p: 3} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, p: 2, b: 1, w: 1, s: 1}. What is the expected number of occurrences of the pattern 'ws*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, i: 1, p: 2, c: 2}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, c: 1, o: 3, v: 1}, what is the expected number of times the pattern 'vc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, r: 3, g: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, v: 4}. What is the expected number of occurrences of the pattern 'v+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, a: 2, q: 1, p: 1, f: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, q: 2, b: 1, k: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'q+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, t: 2, b: 3}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, s: 2, u: 1}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, y: 2, r: 1, c: 1, o: 1}, what is the expected number of times the pattern 'xr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 3, z: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'n+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, p: 1, d: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'pr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, h: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, i: 1, o: 1, x: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, u: 1, m: 1, n: 2, c: 1}, what is the expected number of times the pattern 'om*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, k: 3} to form a word, what is the expected number of matches of the pattern 'ik*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 5, f: 1}, what is the expected number of times the pattern 'ft*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, h: 1, w: 1, s: 1, f: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, h: 1, d: 1, v: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'v*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, r: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, a: 2, y: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'ay*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, a: 1, x: 1, g: 2}. What is the expected number of occurrences of the pattern 'xg*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, u: 2, l: 3} to form a word, what is the expected number of matches of the pattern 'o.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, i: 4}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, e: 2, a: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, i: 1, c: 2, y: 1}. What is the expected number of occurrences of the pattern 'cy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 4, l: 2}, what is the expected number of times the pattern 'c.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, w: 1, d: 3, a: 1}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, w: 4}, what is the expected number of times the pattern 'ws*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, v: 3, a: 1, u: 1}, what is the expected number of times the pattern 'vm+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, e: 3, v: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, s: 1, q: 2, c: 1, f: 1}, what is the expected number of times the pattern 'yf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, p: 1, e: 2, v: 2}. What is the expected number of occurrences of the pattern 'p+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, d: 1, r: 3}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, u: 3}, what is the expected number of times the pattern 'uz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, g: 1, v: 1, z: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'g*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, n: 2, k: 1, o: 2}, what is the expected number of times the pattern 'ek+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, h: 3}, what is the expected number of times the pattern 'h*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 4, h: 2}, what is the expected number of times the pattern 'th*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, a: 1, m: 3} to form a word, what is the expected number of matches of the pattern 'm+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, l: 1, g: 1, p: 1, s: 1}. What is the expected number of occurrences of the pattern 'p*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, k: 2, s: 1, f: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'k.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 3, p: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'n+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, x: 1, k: 2}. What is the expected number of occurrences of the pattern 'h+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, b: 2, j: 1}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, r: 2, y: 2, u: 1}, what is the expected number of times the pattern 'y.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, w: 2, i: 1, z: 1, u: 1}, what is the expected number of times the pattern 'i+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, j: 3}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, h: 1, a: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'h.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, n: 2, g: 1, p: 1, i: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, r: 2, p: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, h: 4}. What is the expected number of occurrences of the pattern 'r.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, h: 1, a: 1, q: 2, g: 1}, what is the expected number of times the pattern 'az+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, s: 4, a: 1}, what is the expected number of times the pattern 'a+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, q: 2, m: 1, a: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'rr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, h: 4}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, m: 3, e: 1}. What is the expected number of occurrences of the pattern 'm+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, w: 1, e: 1, d: 1, y: 2}. What is the expected number of occurrences of the pattern 'dl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, d: 1, y: 1, q: 2}, what is the expected number of times the pattern 'd.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, t: 2, x: 1, w: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, s: 1, d: 1, m: 1, i: 2}, what is the expected number of times the pattern 'mi+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, p: 1, f: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, q: 1, a: 1, w: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'y.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 5, e: 1}. What is the expected number of occurrences of the pattern 'e+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, q: 4} to form a word, what is the expected number of matches of the pattern 'qi*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 4, q: 2}. What is the expected number of occurrences of the pattern 'qo+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, f: 1, c: 1, m: 2, q: 1}. What is the expected number of occurrences of the pattern 'mf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, o: 2, e: 1, s: 1, b: 1} to form a word, what is the expected number of matches of the pattern 's+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, g: 4} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, a: 1, y: 2} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 4, l: 2}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, z: 1, f: 2, b: 1, v: 1}. What is the expected number of occurrences of the pattern 'fv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, e: 1, r: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'r*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, i: 1, n: 1, h: 3}, what is the expected number of times the pattern 'n+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, a: 1, c: 2, b: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, c: 1, j: 2, g: 1, s: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, f: 1, n: 2, s: 1}. What is the expected number of occurrences of the pattern 'a*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, n: 3, t: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'pn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, j: 1, x: 1, o: 1, a: 2}. What is the expected number of occurrences of the pattern 'a+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, x: 2, u: 3}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, s: 1, q: 1, g: 1, i: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, h: 1, x: 3, n: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, q: 2, h: 2}. What is the expected number of occurrences of the pattern 'v*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'jh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, r: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'z+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, t: 4}. What is the expected number of occurrences of the pattern 't+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, h: 1, t: 2}. What is the expected number of occurrences of the pattern 'j.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, i: 2, j: 1, y: 1, l: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, t: 4} to form a word, what is the expected number of matches of the pattern 'qt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, n: 2, z: 1, s: 1}, what is the expected number of times the pattern 'qs+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, z: 3}, what is the expected number of times the pattern 'i*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 3, i: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, k: 2, n: 1, f: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, c: 2, j: 1, h: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'wh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, h: 2, z: 1, u: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'zh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 5, r: 1}. What is the expected number of occurrences of the pattern 'hr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, o: 1, w: 1, k: 1, r: 1}. What is the expected number of occurrences of the pattern 'k+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, c: 2, v: 1, z: 1, p: 1}, what is the expected number of times the pattern 'vl*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, g: 1, s: 1, i: 2, c: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, y: 3}, what is the expected number of times the pattern 'yv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, p: 1, d: 3} to form a word, what is the expected number of matches of the pattern 'ld*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, c: 3}. What is the expected number of occurrences of the pattern 'y*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, s: 1, b: 1, t: 2} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, w: 2, s: 1, l: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'qo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, v: 2, o: 2}. What is the expected number of occurrences of the pattern 'vh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, s: 1, z: 1, o: 1, e: 1}. What is the expected number of occurrences of the pattern 'd.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 4, s: 2} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, g: 2, f: 2}, what is the expected number of times the pattern 'g*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, i: 1, h: 3} to form a word, what is the expected number of matches of the pattern 'h*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 4, o: 2}, what is the expected number of times the pattern 'ok+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, b: 1, n: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, u: 2, j: 1, n: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, n: 2, v: 2, p: 1}. What is the expected number of occurrences of the pattern 'n+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, n: 1, f: 4}, what is the expected number of times the pattern 'g*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, l: 3, m: 1}. What is the expected number of occurrences of the pattern 'n.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, h: 1, x: 1, c: 2, l: 1}, what is the expected number of times the pattern 'h.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 4, i: 1, s: 1}. What is the expected number of occurrences of the pattern 's.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, a: 2, b: 1, k: 1}. What is the expected number of occurrences of the pattern 'af*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, s: 5}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, e: 2, f: 1, o: 1, g: 1}, what is the expected number of times the pattern 'k*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, o: 1, y: 1, f: 2, m: 1}. What is the expected number of occurrences of the pattern 'jo*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, u: 3}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, i: 2, y: 3}. What is the expected number of occurrences of the pattern 'y.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, i: 3} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, s: 1, n: 1, o: 3}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, s: 3, i: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, s: 4} to form a word, what is the expected number of matches of the pattern 'n*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, k: 1, z: 4}. What is the expected number of occurrences of the pattern 'ze+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, r: 1, e: 1, b: 2, w: 1}, what is the expected number of times the pattern 'r.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, r: 2, k: 1}, what is the expected number of times the pattern 'rk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, u: 2, a: 1, v: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'u.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, m: 2, q: 2}, what is the expected number of times the pattern 'q+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, g: 2, b: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, r: 3}. What is the expected number of occurrences of the pattern 'r+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, t: 1, h: 1, o: 2, u: 1}, what is the expected number of times the pattern 'qu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, v: 1, k: 2, c: 2}, what is the expected number of times the pattern 'c.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, h: 2, d: 3}, what is the expected number of times the pattern 'd+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, p: 1, h: 1, r: 1, u: 1}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 4, g: 2}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, g: 3}. What is the expected number of occurrences of the pattern 'g.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, z: 2, c: 1, a: 1, k: 1}. What is the expected number of occurrences of the pattern 'z+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, n: 2, w: 1, d: 1}. What is the expected number of occurrences of the pattern 's.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, v: 3}. What is the expected number of occurrences of the pattern 'yv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, m: 1, f: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'm+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, i: 1, t: 2, y: 2}, what is the expected number of times the pattern 'i.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, i: 1, k: 3, n: 1} to form a word, what is the expected number of matches of the pattern 'kn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, o: 3, w: 2}. What is the expected number of occurrences of the pattern 'wo*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, c: 4}, what is the expected number of times the pattern 'ct+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, v: 2, c: 2} to form a word, what is the expected number of matches of the pattern 'zc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, d: 1, p: 1, l: 1, g: 1}, what is the expected number of times the pattern 'pd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, n: 1, j: 1, y: 1, o: 2}, what is the expected number of times the pattern 'y*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, v: 4, i: 1}. What is the expected number of occurrences of the pattern 'rv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, y: 1, j: 1, t: 3} to form a word, what is the expected number of matches of the pattern 't+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, h: 1, a: 3, z: 1}, what is the expected number of times the pattern 'ga+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 4, l: 1, d: 1}, what is the expected number of times the pattern 'dy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, p: 1, z: 2, y: 2}. What is the expected number of occurrences of the pattern 'y.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, j: 3, n: 2} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, c: 3, a: 1} to form a word, what is the expected number of matches of the pattern 'u*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, f: 3, v: 2} to form a word, what is the expected number of matches of the pattern 'fv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, z: 1, g: 1, x: 1, s: 2}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, q: 3, b: 1, s: 1}. What is the expected number of occurrences of the pattern 's+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 3, d: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'kd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, l: 3}. What is the expected number of occurrences of the pattern 'kl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, m: 1, v: 1, g: 1, c: 2}, what is the expected number of times the pattern 'c*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, q: 1, m: 1, c: 1, o: 2}, what is the expected number of times the pattern 'o*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 3, c: 1, e: 1, i: 1}, what is the expected number of times the pattern 'e.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 4, k: 2}, what is the expected number of times the pattern 'ku*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, d: 2, t: 1, i: 1, y: 1}. What is the expected number of occurrences of the pattern 't.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, z: 2, j: 1, v: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'zv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, h: 1, d: 1, j: 2, a: 1}. What is the expected number of occurrences of the pattern 'ra+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, p: 1, e: 3}. What is the expected number of occurrences of the pattern 'p*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, i: 3, o: 1, j: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, r: 2, q: 1, v: 1}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, z: 1, w: 3} to form a word, what is the expected number of matches of the pattern 's+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, j: 1, o: 1, f: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'q+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, v: 1, e: 1, c: 2, u: 1}, what is the expected number of times the pattern 'u.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, s: 2, k: 1, v: 2}. What is the expected number of occurrences of the pattern 's+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 4, t: 2}. What is the expected number of occurrences of the pattern 't.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, r: 2, a: 1, k: 1, h: 1}, what is the expected number of times the pattern 'a*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, k: 2, o: 3} to form a word, what is the expected number of matches of the pattern 'o.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, p: 2, s: 1, b: 2} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, s: 3}, what is the expected number of times the pattern 'sc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, n: 1, r: 1, i: 1, w: 1}. What is the expected number of occurrences of the pattern 'is+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, f: 1, o: 2, g: 1}, what is the expected number of times the pattern 'f*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, m: 2, i: 3}, what is the expected number of times the pattern 'gi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, h: 2, q: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, c: 1, i: 1, n: 1, j: 1}. What is the expected number of occurrences of the pattern 'ix+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, b: 1, y: 1, u: 1, g: 1}, what is the expected number of times the pattern 'uv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, g: 3, f: 2}, what is the expected number of times the pattern 'gv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, o: 1, g: 2, p: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, d: 2, c: 1, s: 1, g: 1}, what is the expected number of times the pattern 'v.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, r: 1, j: 3, m: 1}, what is the expected number of times the pattern 'm*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, y: 4}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, v: 3, m: 2}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, u: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'yx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 4, l: 2} to form a word, what is the expected number of matches of the pattern 'h+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, y: 1, z: 2, r: 2} to form a word, what is the expected number of matches of the pattern 'p*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, n: 1, m: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'ms+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, f: 2, c: 1, w: 2}. What is the expected number of occurrences of the pattern 'cj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, w: 3, p: 2}. What is the expected number of occurrences of the pattern 'vp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, y: 1, k: 1, s: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'sk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, o: 2, t: 1, y: 1, s: 1}, what is the expected number of times the pattern 'j.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 4, m: 2} to form a word, what is the expected number of matches of the pattern 'gm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, l: 1, h: 2, m: 2}. What is the expected number of occurrences of the pattern 'm*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, m: 1, i: 1, g: 1, a: 1}, what is the expected number of times the pattern 'i+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, l: 1, b: 2, i: 1}, what is the expected number of times the pattern 'ii+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, m: 2}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, u: 1, k: 1, q: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, p: 5} to form a word, what is the expected number of matches of the pattern 'p*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, y: 2, q: 1, p: 1, o: 1}. What is the expected number of occurrences of the pattern 'y.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, w: 3, k: 1} to form a word, what is the expected number of matches of the pattern 'ww+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, t: 2, j: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'jx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, e: 1, x: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'a*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, k: 2, u: 2}, what is the expected number of times the pattern 'dk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, j: 1, m: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'k.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, q: 1, o: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, f: 1, n: 1, i: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'n.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, v: 2, l: 1, d: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, k: 1, d: 2, w: 1}. What is the expected number of occurrences of the pattern 'di+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, r: 1, l: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, p: 1, c: 2}, what is the expected number of times the pattern 'c*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, g: 3, k: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, r: 1, d: 2, x: 1}. What is the expected number of occurrences of the pattern 'x.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, s: 1, r: 1, k: 1, m: 2} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, e: 4}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, a: 2, w: 2}. What is the expected number of occurrences of the pattern 'a*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 4, q: 2}, what is the expected number of times the pattern 'qj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, q: 1, s: 1, k: 1}. What is the expected number of occurrences of the pattern 'ss*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, a: 2, z: 1, f: 1, e: 1}, what is the expected number of times the pattern 'za+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, u: 5} to form a word, what is the expected number of matches of the pattern 'l.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, k: 1, g: 3}. What is the expected number of occurrences of the pattern 'g+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, r: 2, x: 2, u: 1}. What is the expected number of occurrences of the pattern 'r+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, k: 1, r: 2, z: 1, t: 1}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, o: 2, x: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'x*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, b: 2, k: 2, n: 1}, what is the expected number of times the pattern 'k.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, p: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'p+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, u: 1, y: 1, l: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'u.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 4, n: 2}, what is the expected number of times the pattern 'n*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, t: 4}. What is the expected number of occurrences of the pattern 't+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, h: 4}. What is the expected number of occurrences of the pattern 'uh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, e: 1, m: 1, f: 2, o: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, c: 1, x: 1, h: 1, a: 1}. What is the expected number of occurrences of the pattern 'xa*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, e: 4}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, a: 3, p: 2} to form a word, what is the expected number of matches of the pattern 'wp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, i: 1, g: 1, x: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, e: 2, j: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, u: 5}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, v: 1, l: 2, x: 2}, what is the expected number of times the pattern 'c*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, e: 3, p: 1} to form a word, what is the expected number of matches of the pattern 'ap*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, v: 5} to form a word, what is the expected number of matches of the pattern 'tv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, a: 2, r: 1, q: 2}. What is the expected number of occurrences of the pattern 'a*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, t: 1, q: 1, b: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'qh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, o: 1, h: 1, c: 2, b: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 3, h: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'h.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, d: 4}. What is the expected number of occurrences of the pattern 'd.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, t: 1, l: 1, n: 2} to form a word, what is the expected number of matches of the pattern 't+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, d: 3} to form a word, what is the expected number of matches of the pattern 'u.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, t: 3, b: 1} to form a word, what is the expected number of matches of the pattern 't+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, w: 1, u: 1, y: 1}, what is the expected number of times the pattern 'w*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, k: 2, i: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'ki*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, o: 1, y: 3, x: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, c: 1, r: 1, d: 1, e: 1}. What is the expected number of occurrences of the pattern 'o.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, t: 1, v: 2, q: 1}, what is the expected number of times the pattern 'tv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, i: 1, x: 2, e: 1}. What is the expected number of occurrences of the pattern 'if*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, n: 1, i: 1, r: 3}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, p: 1, u: 4}, what is the expected number of times the pattern 'j.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, h: 4} to form a word, what is the expected number of matches of the pattern 'h*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, m: 1, j: 2, a: 2}, what is the expected number of times the pattern 'ml*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, w: 1, e: 1, k: 1, h: 2}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, p: 1, a: 1, k: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'j.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, l: 2, z: 1, i: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, j: 4}. What is the expected number of occurrences of the pattern 'k*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, r: 1, t: 1, i: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, x: 1, j: 1, k: 1, m: 1}. What is the expected number of occurrences of the pattern 'm.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, f: 3, h: 2} to form a word, what is the expected number of matches of the pattern 'fn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, p: 4}, what is the expected number of times the pattern 'pr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, i: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'i+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, v: 1, p: 2, w: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'wh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, i: 2, y: 2, z: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, e: 1, z: 4}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, o: 1, g: 1, b: 2, t: 1}. What is the expected number of occurrences of the pattern 'g*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, q: 2, m: 2}, what is the expected number of times the pattern 'q+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, k: 1, n: 1, g: 1, m: 1}. What is the expected number of occurrences of the pattern 'k+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, z: 1, w: 1, j: 1, o: 1}. What is the expected number of occurrences of the pattern 'ow+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, m: 1, a: 2, d: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, t: 2, x: 1, i: 1, z: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, w: 4, t: 1}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, l: 2, a: 1, k: 2}, what is the expected number of times the pattern 'p+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 4, t: 2} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, v: 2, w: 2, t: 1}, what is the expected number of times the pattern 't.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 5, f: 1}. What is the expected number of occurrences of the pattern 'cf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, g: 1, h: 2, u: 1, c: 1}. What is the expected number of occurrences of the pattern 'm.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, o: 2, l: 1, v: 1}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, t: 1, x: 4} to form a word, what is the expected number of matches of the pattern 'x*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, w: 3}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, j: 2, m: 1, a: 1, n: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, v: 3}. What is the expected number of occurrences of the pattern 'vy*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, f: 1, h: 1, p: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, v: 2, h: 3} to form a word, what is the expected number of matches of the pattern 'h*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, b: 1, z: 1, x: 3}. What is the expected number of occurrences of the pattern 'yx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, u: 1, b: 2, s: 2}, what is the expected number of times the pattern 'e+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, b: 4}. What is the expected number of occurrences of the pattern 'cb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, y: 2, j: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, q: 3, s: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, q: 1, i: 2, u: 1, n: 1}. What is the expected number of occurrences of the pattern 'in+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 4, k: 2} to form a word, what is the expected number of matches of the pattern 'h+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, m: 1, n: 2, f: 2} to form a word, what is the expected number of matches of the pattern 'f+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, q: 1, d: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, i: 3, n: 1} to form a word, what is the expected number of matches of the pattern 'n+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, s: 3}. What is the expected number of occurrences of the pattern 'sd+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, x: 1, h: 1, f: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'xh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, l: 1, e: 2, f: 1, i: 1}. What is the expected number of occurrences of the pattern 'iv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, y: 3} to form a word, what is the expected number of matches of the pattern 'y*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 4, d: 2} to form a word, what is the expected number of matches of the pattern 'ud*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, f: 4}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 4, b: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'x.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, y: 3}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 4, g: 2}. What is the expected number of occurrences of the pattern 'g*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, c: 3}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, n: 3}. What is the expected number of occurrences of the pattern 'ne*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, c: 2, n: 3}. What is the expected number of occurrences of the pattern 'n*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, y: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, z: 1, g: 1, u: 1, e: 1}, what is the expected number of times the pattern 'z.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, z: 1, p: 1, x: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'zp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, j: 2, d: 1, i: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, s: 4} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, p: 1, l: 2, g: 1, u: 1}, what is the expected number of times the pattern 'gl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, l: 3}, what is the expected number of times the pattern 'lk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, m: 1, q: 1, g: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'gq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, u: 1, e: 1, z: 1}, what is the expected number of times the pattern 'ew+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, i: 3, t: 1}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, j: 3}, what is the expected number of times the pattern 'ju+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, n: 3}. What is the expected number of occurrences of the pattern 'gn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, i: 2, n: 1, t: 1, a: 1}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, g: 2, o: 1, r: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'oc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, h: 1, b: 2}, what is the expected number of times the pattern 'zb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, z: 3, k: 1, h: 1}, what is the expected number of times the pattern 'kz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, d: 3} to form a word, what is the expected number of matches of the pattern 'wd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, m: 1, x: 3}. What is the expected number of occurrences of the pattern 'xb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, k: 1, d: 2, g: 2}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, o: 1, a: 2, j: 1}. What is the expected number of occurrences of the pattern 'o*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, d: 3}, what is the expected number of times the pattern 'g.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, j: 1, i: 2, k: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'a*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, d: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, x: 1, s: 1, t: 1, i: 1} to form a word, what is the expected number of matches of the pattern 't+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'x+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, h: 1, c: 1, w: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, u: 1, g: 3}, what is the expected number of times the pattern 'gu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, f: 1, q: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, v: 2, h: 1, y: 2}, what is the expected number of times the pattern 'c.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'x*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, l: 2, x: 2}. What is the expected number of occurrences of the pattern 'x.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, q: 1, j: 2, x: 1} to form a word, what is the expected number of matches of the pattern 'x*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, g: 1, b: 1, z: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'dg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, h: 1, q: 2, m: 1}. What is the expected number of occurrences of the pattern 'q.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, h: 1, a: 1, g: 3} to form a word, what is the expected number of matches of the pattern 'g+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, l: 2, p: 1, v: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, v: 2, g: 1}. What is the expected number of occurrences of the pattern 'g*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, h: 1, f: 2, t: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'fp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, m: 2, d: 1}, what is the expected number of times the pattern 'dg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, i: 2, l: 3}, what is the expected number of times the pattern 'l*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, k: 2, x: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'x*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, u: 3}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, d: 1, y: 2, r: 1, o: 1}, what is the expected number of times the pattern 'd*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, n: 2, c: 1, b: 1, q: 1}. What is the expected number of occurrences of the pattern 'q+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, w: 1, e: 1, k: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, c: 2, e: 1, v: 1, s: 1}. What is the expected number of occurrences of the pattern 'ce*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, u: 2, p: 1, b: 2}, what is the expected number of times the pattern 'p+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, d: 1, x: 2}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, c: 1, s: 2, i: 1, y: 1}. What is the expected number of occurrences of the pattern 'y+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, c: 2, w: 2}, what is the expected number of times the pattern 'w.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, f: 1, l: 1, w: 2}. What is the expected number of occurrences of the pattern 'wn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 4, h: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, v: 1, p: 1, h: 2}, what is the expected number of times the pattern 'h.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, y: 1, m: 1, g: 2, e: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, q: 1, s: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'sh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, o: 2, c: 2}. What is the expected number of occurrences of the pattern 'c*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, k: 3, v: 2} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, b: 1, w: 1, l: 1, s: 1}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, d: 4, x: 1} to form a word, what is the expected number of matches of the pattern 'x+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 4, i: 1, c: 1}, what is the expected number of times the pattern 'cd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, u: 2, z: 2}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, u: 3}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 4, b: 2}, what is the expected number of times the pattern 'zz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, i: 2, v: 1, j: 1, h: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, q: 2, m: 1}, what is the expected number of times the pattern 'mq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, b: 4}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, s: 3}, what is the expected number of times the pattern 'x+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, a: 1, h: 2, q: 1, r: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, e: 3}. What is the expected number of occurrences of the pattern 'ze+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, h: 4}. What is the expected number of occurrences of the pattern 's*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, p: 1, a: 1, k: 1, s: 1}. What is the expected number of occurrences of the pattern 'as*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, p: 2, u: 1}. What is the expected number of occurrences of the pattern 'm+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, w: 2, a: 1, j: 1}. What is the expected number of occurrences of the pattern 'j.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, s: 3, x: 1} to form a word, what is the expected number of matches of the pattern 'y+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, r: 1, x: 1, b: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'l+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, j: 1, w: 2, n: 1}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, j: 1, i: 1, q: 1, c: 2}, what is the expected number of times the pattern 'jq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, n: 1, c: 1, k: 1, o: 2}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, d: 4}, what is the expected number of times the pattern 'yd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, m: 1, w: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'yo+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 4, h: 2}. What is the expected number of occurrences of the pattern 'h*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, a: 1, y: 1, g: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, n: 3, j: 2} to form a word, what is the expected number of matches of the pattern 'nf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, h: 1, s: 1, n: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'q+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, p: 3, q: 1} to form a word, what is the expected number of matches of the pattern 'qp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, l: 1, s: 2, x: 1, v: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, p: 3}, what is the expected number of times the pattern 'g*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, t: 3, d: 1, u: 1}. What is the expected number of occurrences of the pattern 't.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, a: 1, x: 2, y: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, q: 1, f: 1, e: 2, n: 1}. What is the expected number of occurrences of the pattern 'fe*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, x: 1, k: 1, d: 1, l: 2}, what is the expected number of times the pattern 'l*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, e: 2, l: 3}, what is the expected number of times the pattern 'ge+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, j: 2, t: 1, x: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, l: 3}. What is the expected number of occurrences of the pattern 'lu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 3, g: 1, f: 2}, what is the expected number of times the pattern 'yg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, e: 3, y: 2} to form a word, what is the expected number of matches of the pattern 'y.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, g: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'xg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, n: 4} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, g: 3, t: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, u: 2, m: 2}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, u: 1, d: 2, r: 2}, what is the expected number of times the pattern 'h+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'eh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, m: 4, n: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, f: 1, d: 1, v: 3}, what is the expected number of times the pattern 'r+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, e: 1, k: 1, g: 1, q: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, t: 1, d: 2, e: 1}. What is the expected number of occurrences of the pattern 'g*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, x: 1, b: 2, l: 2}. What is the expected number of occurrences of the pattern 'a.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, h: 1, x: 2, w: 2}, what is the expected number of times the pattern 'h+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, j: 2, z: 2}, what is the expected number of times the pattern 'pj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, p: 2, z: 1}. What is the expected number of occurrences of the pattern 'pz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, x: 2, u: 1, w: 1, n: 1}. What is the expected number of occurrences of the pattern 't+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, r: 1, b: 3} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, o: 3, x: 2}, what is the expected number of times the pattern 'o+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, x: 2, e: 2}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, v: 2, a: 1, o: 1}, what is the expected number of times the pattern 'ov+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, s: 1, q: 1, k: 3}. What is the expected number of occurrences of the pattern 'k+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, p: 1, f: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'n+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, f: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'xy*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, c: 1, f: 1, i: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'dc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, n: 1, y: 1, z: 1, e: 2}. What is the expected number of occurrences of the pattern 'yg+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, e: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, x: 1, p: 3}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, o: 1, k: 2, c: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'kh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, w: 3} to form a word, what is the expected number of matches of the pattern 'wv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, x: 1, n: 1, j: 2, t: 1} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, s: 1, i: 2, x: 1, y: 1}. What is the expected number of occurrences of the pattern 'x*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, r: 1, y: 2, z: 2}. What is the expected number of occurrences of the pattern 'z+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, f: 2, z: 1, k: 1}, what is the expected number of times the pattern 'z*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 5, w: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, x: 1, r: 3, h: 1}. What is the expected number of occurrences of the pattern 'q.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, x: 2, y: 1, j: 1, n: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, w: 3, j: 1}, what is the expected number of times the pattern 'w+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, r: 1, o: 4} to form a word, what is the expected number of matches of the pattern 'm.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, b: 2, z: 3}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, y: 1, b: 3}. What is the expected number of occurrences of the pattern 'mm*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, z: 1, g: 1, n: 1}. What is the expected number of occurrences of the pattern 'mg*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, d: 1, t: 1, v: 1, a: 1}. What is the expected number of occurrences of the pattern 'v*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, y: 1, c: 2, l: 1, d: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 4, l: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, l: 3} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, v: 3}. What is the expected number of occurrences of the pattern 's*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, c: 1, q: 1, e: 3}, what is the expected number of times the pattern 'g*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, r: 1, s: 1, i: 2, e: 1}, what is the expected number of times the pattern 'o+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, i: 2, w: 2}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, w: 1, f: 1, i: 3}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, i: 1, b: 3}, what is the expected number of times the pattern 'i.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, p: 1, i: 3}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, v: 2, r: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'wm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, k: 4} to form a word, what is the expected number of matches of the pattern 'ak+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 4, j: 1, o: 1}, what is the expected number of times the pattern 'oj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, r: 5}. What is the expected number of occurrences of the pattern 'm.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, a: 1, s: 2, i: 1, v: 1}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, c: 2, b: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, l: 1, t: 3}, what is the expected number of times the pattern 'l.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, p: 1, e: 1, j: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, d: 1, f: 3, s: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, x: 2, a: 2, e: 1}, what is the expected number of times the pattern 'xz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, i: 3, w: 1, k: 1}, what is the expected number of times the pattern 'q*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, m: 5} to form a word, what is the expected number of matches of the pattern 'm*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, a: 4} to form a word, what is the expected number of matches of the pattern 'a+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, j: 3}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, i: 1, c: 2}. What is the expected number of occurrences of the pattern 'ci*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, e: 1, d: 2, v: 2}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, n: 1, l: 1, u: 1}. What is the expected number of occurrences of the pattern 'un+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, l: 2, o: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, q: 2, n: 1, u: 1, f: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, j: 1, f: 1, u: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'fu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, m: 1, c: 2}. What is the expected number of occurrences of the pattern 'a+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, o: 1, b: 1, h: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'pp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, o: 1, x: 2}, what is the expected number of times the pattern 'x.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, t: 2, k: 1, x: 1} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, l: 1, j: 1, v: 1, a: 1}, what is the expected number of times the pattern 'a*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, l: 3} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, s: 2, v: 1, m: 2}, what is the expected number of times the pattern 'vy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, o: 3}, what is the expected number of times the pattern 'o*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, r: 1, b: 1}. What is the expected number of occurrences of the pattern 'tt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, i: 1, v: 2, z: 1, b: 1} to form a word, what is the expected number of matches of the pattern 't.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, q: 1, d: 1, s: 2, i: 1}. What is the expected number of occurrences of the pattern 'd+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, s: 1, m: 1, l: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 4, v: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'wv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, z: 1, q: 1, i: 2, c: 1} to form a word, what is the expected number of matches of the pattern 'i+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 4, f: 2} to form a word, what is the expected number of matches of the pattern 'fq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, s: 1, v: 4}, what is the expected number of times the pattern 'v+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, a: 1, n: 3}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, w: 1, t: 2, a: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'r*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, p: 1, k: 4}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, w: 5} to form a word, what is the expected number of matches of the pattern 'uw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 4, p: 2}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, j: 1, c: 1, l: 1, s: 2}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, s: 3}. What is the expected number of occurrences of the pattern 's+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, f: 3, c: 1}. What is the expected number of occurrences of the pattern 'cn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 5, g: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, j: 1, w: 1, q: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'w.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, h: 4}, what is the expected number of times the pattern 't*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, k: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'k*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, a: 1, m: 1, z: 2}, what is the expected number of times the pattern 'am+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, v: 1, r: 1, a: 2, q: 1}, what is the expected number of times the pattern 'vq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, z: 4}, what is the expected number of times the pattern 'p+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, a: 2, c: 1, e: 1}. What is the expected number of occurrences of the pattern 'ae+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, b: 1, w: 4} to form a word, what is the expected number of matches of the pattern 'w.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, f: 2, k: 2, u: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, u: 2, a: 1, v: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, w: 1, y: 1, u: 1, g: 2} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, t: 2, f: 2}. What is the expected number of occurrences of the pattern 'q.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, i: 3, m: 2}, what is the expected number of times the pattern 'm*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, u: 1, r: 1, j: 2, c: 1} to form a word, what is the expected number of matches of the pattern 'qr+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, w: 1, k: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'lk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, i: 1, q: 1, u: 2, y: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, u: 4}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, d: 3}, what is the expected number of times the pattern 'do*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 4, t: 2} to form a word, what is the expected number of matches of the pattern 'a.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, x: 3, f: 1, u: 1}. What is the expected number of occurrences of the pattern 'x.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, d: 1, o: 1, m: 1, l: 1}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 4, q: 2}. What is the expected number of occurrences of the pattern 'qx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, e: 1, x: 1, b: 2, t: 1}. What is the expected number of occurrences of the pattern 't.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, d: 1, q: 2, k: 2}. What is the expected number of occurrences of the pattern 'q.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, t: 2, s: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'xh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, k: 2, s: 2}. What is the expected number of occurrences of the pattern 's.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, g: 1, b: 4} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, j: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, t: 1, w: 1, z: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'w+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, h: 3, r: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'w.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, f: 2, j: 1, e: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, r: 1, t: 1, w: 1, m: 1}, what is the expected number of times the pattern 'wt+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, x: 2, d: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, e: 2, v: 1, x: 1, h: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, l: 2, c: 3}, what is the expected number of times the pattern 'c.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, l: 1, g: 1, i: 2, h: 1}, what is the expected number of times the pattern 'gl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 3, b: 3}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 4, e: 2}, what is the expected number of times the pattern 'e*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, o: 1, n: 2, d: 1, v: 1}. What is the expected number of occurrences of the pattern 'i.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, d: 1, r: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'r*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, a: 2, m: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'am*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, p: 1, m: 3, v: 1} to form a word, what is the expected number of matches of the pattern 'm+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, m: 4}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, c: 1, e: 1, z: 2, l: 1}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, i: 1, z: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'i+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, k: 2, m: 1, h: 2}, what is the expected number of times the pattern 'hm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, g: 1, o: 3}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, m: 1, l: 1, r: 1, g: 1}, what is the expected number of times the pattern 'l+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, n: 3, x: 2}. What is the expected number of occurrences of the pattern 'xw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'n+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, n: 1, e: 1, w: 1}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, v: 2, l: 1, a: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'vr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, v: 1, e: 1, i: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'ie+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, k: 2, a: 1, s: 2}, what is the expected number of times the pattern 'm+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, j: 3, r: 2} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, h: 2, r: 1, g: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, h: 3}, what is the expected number of times the pattern 'x*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, z: 2, y: 2}. What is the expected number of occurrences of the pattern 'p.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, r: 1, n: 2, q: 2} to form a word, what is the expected number of matches of the pattern 'r+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, z: 1, q: 1, k: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'kq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, m: 1, c: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'm.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, f: 2, l: 3} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, n: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, h: 1, p: 1, l: 1, t: 1}, what is the expected number of times the pattern 'lp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, r: 1, d: 1, c: 1, e: 2}. What is the expected number of occurrences of the pattern 'd*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 4, z: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, i: 4} to form a word, what is the expected number of matches of the pattern 'oi+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, x: 1, m: 1, f: 1, g: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, z: 1, t: 2, d: 1, s: 1}. What is the expected number of occurrences of the pattern 'd+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, j: 2, e: 2} to form a word, what is the expected number of matches of the pattern 'js*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, o: 2, a: 1, x: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'ax+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, j: 1, x: 2, e: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, y: 2, u: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, n: 3, z: 1}. What is the expected number of occurrences of the pattern 'n*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, b: 3, k: 1}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, v: 3, l: 1, n: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, l: 2, g: 1, o: 2}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 4, a: 2}. What is the expected number of occurrences of the pattern 'y.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, e: 3} to form a word, what is the expected number of matches of the pattern 'e*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, d: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'dx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 4, t: 1, e: 1}. What is the expected number of occurrences of the pattern 'te+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, t: 2, f: 1, o: 1, c: 1}, what is the expected number of times the pattern 't.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, d: 2, l: 3}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, a: 1, x: 1, d: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'a*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, j: 1, x: 3, e: 1}, what is the expected number of times the pattern 'pj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, h: 2, f: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'rh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, d: 1, b: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, t: 1, n: 1, b: 2, a: 1}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 5, v: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, p: 3, r: 1} to form a word, what is the expected number of matches of the pattern 'f+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, y: 1, q: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'y+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, g: 1, e: 1, s: 1}. What is the expected number of occurrences of the pattern 'v.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, z: 2, f: 1, s: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, x: 1, w: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, m: 1, z: 3}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, r: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'j+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, j: 2, z: 1, b: 1, y: 1}. What is the expected number of occurrences of the pattern 'j+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, y: 2, g: 2}, what is the expected number of times the pattern 'q.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, l: 2, n: 1, z: 1}. What is the expected number of occurrences of the pattern 'cl+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, m: 1, t: 3}. What is the expected number of occurrences of the pattern 'dt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, f: 2, y: 1, k: 1, j: 1}. What is the expected number of occurrences of the pattern 'y.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, l: 1, j: 2, q: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'jq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, q: 3} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, p: 3}, what is the expected number of times the pattern 'p+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, a: 2, v: 1, n: 1}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, u: 2, d: 3}. What is the expected number of occurrences of the pattern 'm*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 4, d: 2}. What is the expected number of occurrences of the pattern 'd+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, m: 4}. What is the expected number of occurrences of the pattern 'm+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, x: 2, w: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, f: 2, g: 1, p: 1}. What is the expected number of occurrences of the pattern 'g*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, s: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'v+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, d: 3, z: 2}. What is the expected number of occurrences of the pattern 'd+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, y: 1, t: 2, g: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, j: 1, m: 1, i: 2, l: 1}, what is the expected number of times the pattern 'yi+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 4, g: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'v*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 4, y: 2}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, n: 2, i: 1, j: 1, y: 1}. What is the expected number of occurrences of the pattern 'jn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, p: 1, t: 2, j: 2}. What is the expected number of occurrences of the pattern 'j.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, f: 1, h: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, g: 4}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, g: 2, k: 3}. What is the expected number of occurrences of the pattern 'kg*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, z: 1, v: 1, m: 3}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, i: 1, o: 1, b: 2, v: 1}. What is the expected number of occurrences of the pattern 'i.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, b: 2, o: 2, y: 1}. What is the expected number of occurrences of the pattern 'y+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, n: 4}, what is the expected number of times the pattern 'q+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 4, n: 2}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, s: 1, a: 3}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, b: 2, a: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'g+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, l: 2, i: 1, h: 1}. What is the expected number of occurrences of the pattern 'l.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, w: 2, z: 1}. What is the expected number of occurrences of the pattern 'cz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, i: 1, e: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'iz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, c: 1, g: 2, p: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'r.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 4, z: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, q: 1, n: 1, i: 1, b: 2}, what is the expected number of times the pattern 'ti*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 4, g: 2}, what is the expected number of times the pattern 'u.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, c: 2, n: 1, a: 1, v: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, s: 2, f: 1, r: 1}. What is the expected number of occurrences of the pattern 'rs+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, h: 1, x: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'xe+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, b: 2, z: 1, k: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'k+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, g: 2, l: 2}. What is the expected number of occurrences of the pattern 'lg*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, k: 2, g: 3} to form a word, what is the expected number of matches of the pattern 'gk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, s: 5}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, m: 1, w: 1, o: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, r: 1, c: 1, v: 3}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, t: 3} to form a word, what is the expected number of matches of the pattern 'v.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, i: 1, a: 3, z: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, j: 3, l: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, n: 1, q: 1, m: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'n*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, x: 1, m: 2}. What is the expected number of occurrences of the pattern 'e+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, k: 2, t: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'ky+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 4, c: 2}. What is the expected number of occurrences of the pattern 'c*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, q: 3, w: 2}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, i: 1, s: 1, t: 1, u: 2}. What is the expected number of occurrences of the pattern 'it+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, k: 3, p: 1, d: 1}. What is the expected number of occurrences of the pattern 'do*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, g: 5}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, m: 1, p: 1, w: 1, l: 1}. What is the expected number of occurrences of the pattern 'w.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, f: 1, g: 2, z: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, k: 2, w: 1}. What is the expected number of occurrences of the pattern 'wy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, v: 5} to form a word, what is the expected number of matches of the pattern 'f*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, h: 1, t: 1, k: 2, n: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, b: 4} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, c: 2, x: 2}, what is the expected number of times the pattern 'c*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, y: 4}. What is the expected number of occurrences of the pattern 'y.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, o: 2, r: 1, j: 1}, what is the expected number of times the pattern 'o+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, p: 1, x: 3, m: 1}, what is the expected number of times the pattern 'pd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, i: 2, r: 2} to form a word, what is the expected number of matches of the pattern 'a*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, j: 4} to form a word, what is the expected number of matches of the pattern 'fj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, p: 1, n: 2, r: 1, t: 1}, what is the expected number of times the pattern 'ft+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 3, e: 3}, what is the expected number of times the pattern 'ea*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, y: 2, c: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, z: 1, t: 1, g: 2, v: 1}. What is the expected number of occurrences of the pattern 'kz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, q: 1, m: 2, t: 1, b: 1} to form a word, what is the expected number of matches of the pattern 's.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, o: 4}. What is the expected number of occurrences of the pattern 'ko+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, l: 2, n: 1, q: 2}. What is the expected number of occurrences of the pattern 'n+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, q: 1, x: 3}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 4, x: 2}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, r: 2, p: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, m: 3}. What is the expected number of occurrences of the pattern 'mv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, x: 1, s: 2, e: 1}. What is the expected number of occurrences of the pattern 'j*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, k: 1, t: 2}, what is the expected number of times the pattern 'q*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, k: 2, z: 2, m: 1}. What is the expected number of occurrences of the pattern 'g.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, u: 2, l: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, o: 2, f: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 4, u: 1, z: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, q: 3, z: 1, g: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, v: 1, x: 2}. What is the expected number of occurrences of the pattern 'x+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, c: 3}, what is the expected number of times the pattern 'c.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, r: 1, m: 2, y: 2} to form a word, what is the expected number of matches of the pattern 's+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, b: 3}. What is the expected number of occurrences of the pattern 'rr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, r: 2, k: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'rb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, c: 1, d: 2, z: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'd*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, f: 2, j: 3} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, s: 1, w: 2, l: 2} to form a word, what is the expected number of matches of the pattern 'l+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, x: 1, m: 1, q: 1, w: 1}. What is the expected number of occurrences of the pattern 't+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, t: 2, u: 2, o: 1}. What is the expected number of occurrences of the pattern 'ou*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, t: 1, q: 2, l: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, d: 1, q: 3, x: 1}. What is the expected number of occurrences of the pattern 'h+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, k: 1, e: 1, y: 1, a: 1}, what is the expected number of times the pattern 'ky*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, o: 3, q: 2} to form a word, what is the expected number of matches of the pattern 'm+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, a: 1, i: 2, f: 1, g: 1}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, j: 1, k: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'c+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, k: 3}. What is the expected number of occurrences of the pattern 'w.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, d: 1, h: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'p.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, x: 1, o: 1, d: 2}. What is the expected number of occurrences of the pattern 'od+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, p: 1, n: 1, a: 1, v: 1}. What is the expected number of occurrences of the pattern 'nu+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, y: 3}, what is the expected number of times the pattern 'g*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, w: 1, x: 1, p: 1, q: 2} to form a word, what is the expected number of matches of the pattern 'xw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, d: 2, z: 2}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, h: 2, p: 2, c: 1}, what is the expected number of times the pattern 'pr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, x: 4} to form a word, what is the expected number of matches of the pattern 'x+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 4, g: 2} to form a word, what is the expected number of matches of the pattern 'g.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, a: 3, c: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, a: 1, f: 1, n: 1, p: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, x: 3, j: 2}. What is the expected number of occurrences of the pattern 'w.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, j: 1, p: 2, v: 1, k: 1}. What is the expected number of occurrences of the pattern 'oj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, g: 1, h: 2, o: 1, v: 1}. What is the expected number of occurrences of the pattern 'd.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, s: 2, d: 2, o: 1}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, s: 2, l: 2, e: 1}, what is the expected number of times the pattern 'tl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, m: 2, u: 2, g: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 4, q: 2} to form a word, what is the expected number of matches of the pattern 'qd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, o: 1, p: 1, c: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, b: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'w.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, b: 2, n: 2}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, z: 1, b: 1, a: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'z*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, u: 1, q: 2}. What is the expected number of occurrences of the pattern 'uc+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, h: 2, l: 3} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, x: 2, s: 1, r: 1, f: 1}, what is the expected number of times the pattern 'fp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, e: 4}. What is the expected number of occurrences of the pattern 'ae*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, e: 3, q: 2} to form a word, what is the expected number of matches of the pattern 'iq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, c: 1, a: 1, n: 2, p: 1}, what is the expected number of times the pattern 'a.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'v*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, c: 2, r: 1, o: 1, s: 1}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, u: 1, t: 2}, what is the expected number of times the pattern 'pu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, u: 4}. What is the expected number of occurrences of the pattern 'ju+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, d: 3, v: 2} to form a word, what is the expected number of matches of the pattern 'a+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, a: 1, z: 2, r: 1}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, b: 2, p: 1, y: 1}. What is the expected number of occurrences of the pattern 'y*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, k: 3}. What is the expected number of occurrences of the pattern 'yk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, y: 2, f: 2, j: 1}. What is the expected number of occurrences of the pattern 'y+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, a: 1, x: 3}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, x: 1, d: 1, l: 1, a: 1}. What is the expected number of occurrences of the pattern 'a*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, v: 2, p: 1, h: 1, z: 1}. What is the expected number of occurrences of the pattern 'pv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, o: 4, e: 1}, what is the expected number of times the pattern 'e+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, l: 1, n: 2, o: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'ln*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, j: 3, w: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, w: 1, v: 2, q: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'wq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, p: 1, z: 2, m: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'p*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, a: 1, d: 1, y: 1}. What is the expected number of occurrences of the pattern 'q.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, s: 1, m: 1, y: 1, n: 1}, what is the expected number of times the pattern 'm*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, x: 3}, what is the expected number of times the pattern 'vx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, q: 3} to form a word, what is the expected number of matches of the pattern 'qv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, d: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'pg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, b: 2, l: 2, c: 1}, what is the expected number of times the pattern 'ee+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, r: 2, g: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, m: 1, i: 1, v: 1, s: 2}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, e: 1, x: 1, c: 1}. What is the expected number of occurrences of the pattern 'd*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, b: 1, h: 1, v: 2}. What is the expected number of occurrences of the pattern 'v*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, t: 1, u: 1, d: 1, x: 2}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, c: 4}, what is the expected number of times the pattern 'c+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, d: 1, e: 2, r: 1, v: 1}. What is the expected number of occurrences of the pattern 'l.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, y: 1, u: 2, v: 1, x: 1}, what is the expected number of times the pattern 'y*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, w: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'c+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, t: 1, z: 2, j: 1, p: 1}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, h: 1, v: 1, l: 2}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, o: 3, d: 1}, what is the expected number of times the pattern 'do*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, a: 1, n: 3, t: 1}, what is the expected number of times the pattern 'n*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, w: 1, s: 3} to form a word, what is the expected number of matches of the pattern 'h+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, i: 3, w: 1} to form a word, what is the expected number of matches of the pattern 'c+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, c: 2, n: 2, v: 1}, what is the expected number of times the pattern 'v*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, m: 1, g: 3}, what is the expected number of times the pattern 'fg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, l: 1, o: 2, k: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'lp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, l: 3}, what is the expected number of times the pattern 'lg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, q: 1, r: 1, v: 2, s: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, d: 2, f: 2}. What is the expected number of occurrences of the pattern 'd+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, s: 4} to form a word, what is the expected number of matches of the pattern 'd.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, f: 3} to form a word, what is the expected number of matches of the pattern 'tf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, l: 1, i: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'd+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, j: 1, k: 1, n: 2, x: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, p: 2, n: 1, f: 2}. What is the expected number of occurrences of the pattern 'p+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, j: 1, k: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'k.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, x: 2, d: 1, c: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'd+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, t: 2, r: 1, k: 1}. What is the expected number of occurrences of the pattern 'k.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, w: 1, v: 1, h: 1, f: 2}. What is the expected number of occurrences of the pattern 'f.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, d: 3}. What is the expected number of occurrences of the pattern 'id*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, z: 2, h: 1, m: 1, k: 1}. What is the expected number of occurrences of the pattern 'h*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, f: 1, i: 1, p: 1, x: 1}, what is the expected number of times the pattern 'p+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, i: 5} to form a word, what is the expected number of matches of the pattern 'm.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, e: 1, u: 3} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, t: 4}. What is the expected number of occurrences of the pattern 'f+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, k: 1, f: 2, j: 2} to form a word, what is the expected number of matches of the pattern 'k*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 4, c: 2}, what is the expected number of times the pattern 'c+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, v: 1, u: 1, h: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'to+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 4, u: 2}, what is the expected number of times the pattern 'uk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, m: 1, d: 2, z: 1, g: 1}. What is the expected number of occurrences of the pattern 'z*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 4, s: 1, t: 1}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, a: 2, t: 1, n: 1}, what is the expected number of times the pattern 'c+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, f: 1, d: 1, s: 1, h: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, b: 1, k: 2, c: 1}, what is the expected number of times the pattern 'c+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, w: 1, q: 3} to form a word, what is the expected number of matches of the pattern 'ww*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, m: 1, x: 1, y: 1, i: 2}, what is the expected number of times the pattern 'iu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, p: 1, q: 1, f: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'f+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, x: 2, u: 1, i: 1, g: 1}. What is the expected number of occurrences of the pattern 'u+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, u: 1, y: 1, w: 1, f: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, n: 4} to form a word, what is the expected number of matches of the pattern 'ln*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, v: 2, g: 1, f: 2}, what is the expected number of times the pattern 'x*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, c: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, p: 5}, what is the expected number of times the pattern 'u.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, g: 3} to form a word, what is the expected number of matches of the pattern 'v+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, g: 2, a: 3}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, z: 2, o: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, h: 1, n: 2, r: 1}. What is the expected number of occurrences of the pattern 'r+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, m: 4} to form a word, what is the expected number of matches of the pattern 'm+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, b: 3, n: 1, k: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, p: 1, g: 1, k: 1, u: 2}, what is the expected number of times the pattern 'p+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, c: 1, v: 2}. What is the expected number of occurrences of the pattern 'vu+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, r: 2, h: 2}. What is the expected number of occurrences of the pattern 'c*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, b: 2, d: 1, y: 1, j: 1}, what is the expected number of times the pattern 'y+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, b: 1, v: 1, t: 1, f: 2}. What is the expected number of occurrences of the pattern 'f*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, v: 2, e: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'e*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, z: 1, y: 2, w: 1, j: 1}. What is the expected number of occurrences of the pattern 'w.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, l: 2, p: 2}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, p: 3, w: 1}. What is the expected number of occurrences of the pattern 'fp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 5, e: 1}, what is the expected number of times the pattern 'we*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, b: 1, s: 1, v: 2}, what is the expected number of times the pattern 'd+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, m: 4}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, w: 1, n: 1, d: 1, q: 1}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, g: 2, h: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'h*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, x: 3}, what is the expected number of times the pattern 'xw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, u: 3}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, h: 1, s: 2, q: 2} to form a word, what is the expected number of matches of the pattern 'q+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, z: 4, g: 1}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, y: 1, a: 1, c: 2, m: 1} to form a word, what is the expected number of matches of the pattern 'm*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, m: 2, e: 2} to form a word, what is the expected number of matches of the pattern 'e*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, i: 2, s: 2} to form a word, what is the expected number of matches of the pattern 'i*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, s: 3}. What is the expected number of occurrences of the pattern 'l*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, a: 3, b: 2}. What is the expected number of occurrences of the pattern 'v*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 4, f: 2}, what is the expected number of times the pattern 'fo+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, w: 1, o: 1, t: 2, k: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, s: 4}. What is the expected number of occurrences of the pattern 'sh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, h: 2, y: 2}. What is the expected number of occurrences of the pattern 's*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, h: 4}, what is the expected number of times the pattern 'hg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, b: 4}, what is the expected number of times the pattern 'kk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 4, v: 2} to form a word, what is the expected number of matches of the pattern 'o.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, d: 2, s: 2} to form a word, what is the expected number of matches of the pattern 's+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, y: 1, c: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'c*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, r: 3, k: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'n*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, r: 3}, what is the expected number of times the pattern 're*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, n: 3}, what is the expected number of times the pattern 'dn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, v: 4}. What is the expected number of occurrences of the pattern 'vk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, c: 1, q: 2}. What is the expected number of occurrences of the pattern 'qc+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, l: 1, b: 2, n: 2}, what is the expected number of times the pattern 'n+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, d: 2, y: 3}, what is the expected number of times the pattern 'd.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 4, y: 2} to form a word, what is the expected number of matches of the pattern 'yc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, m: 3, d: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, h: 1, w: 1, t: 1, f: 1}. What is the expected number of occurrences of the pattern 'ft+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, p: 3}, what is the expected number of times the pattern 'p.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, h: 3, a: 1}, what is the expected number of times the pattern 'a+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, g: 1, o: 1, j: 1, q: 2}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, c: 2, d: 1, f: 2}, what is the expected number of times the pattern 'c.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, q: 3}. What is the expected number of occurrences of the pattern 'sq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, j: 2, k: 3} to form a word, what is the expected number of matches of the pattern 'jk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, d: 4}. What is the expected number of occurrences of the pattern 'dv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, b: 1, p: 1, n: 1, c: 1}. What is the expected number of occurrences of the pattern 'p+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, s: 3}, what is the expected number of times the pattern 'sg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, p: 1, u: 2, s: 1, l: 1}. What is the expected number of occurrences of the pattern 's*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, n: 2, i: 1, z: 1, p: 1}. What is the expected number of occurrences of the pattern 'pa*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, o: 1, w: 2, l: 1, c: 1}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, i: 3}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, k: 4}, what is the expected number of times the pattern 'v*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, b: 3} to form a word, what is the expected number of matches of the pattern 's+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, y: 3, g: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'g+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, u: 1, r: 1, g: 1, e: 1}, what is the expected number of times the pattern 'c*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, n: 3}, what is the expected number of times the pattern 'nf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, y: 4}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, i: 3, g: 1}. What is the expected number of occurrences of the pattern 'g*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, z: 3} to form a word, what is the expected number of matches of the pattern 'l.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'h*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, g: 2, h: 1, q: 2}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, f: 2, p: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'fw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, s: 2, a: 2, l: 1}. What is the expected number of occurrences of the pattern 'a+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, l: 2, j: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'f+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, e: 1, b: 2, w: 2} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, n: 2, v: 1, c: 1, p: 1}, what is the expected number of times the pattern 'nc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, l: 3, k: 2}. What is the expected number of occurrences of the pattern 'l.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, i: 4}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 4, l: 2}. What is the expected number of occurrences of the pattern 'ls*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, m: 1, n: 2, p: 1}, what is the expected number of times the pattern 'n.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, n: 3} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, a: 4}, what is the expected number of times the pattern 'ad*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, o: 2, e: 1, y: 2}. What is the expected number of occurrences of the pattern 'e*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, u: 1, k: 2, w: 2}. What is the expected number of occurrences of the pattern 'uw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, p: 2, f: 1, u: 2}. What is the expected number of occurrences of the pattern 'f+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, y: 1, r: 1, m: 2}. What is the expected number of occurrences of the pattern 'my+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, w: 1, s: 1, o: 2, b: 1}, what is the expected number of times the pattern 'c.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 5, p: 1}, what is the expected number of times the pattern 'pd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, b: 2, d: 3}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, i: 1, r: 3, p: 1}. What is the expected number of occurrences of the pattern 'p.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, m: 2, o: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'mb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, o: 1, v: 2, r: 2}, what is the expected number of times the pattern 'rv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, q: 3, o: 1} to form a word, what is the expected number of matches of the pattern 'w.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, x: 2, p: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'x.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, q: 1, p: 2, c: 2} to form a word, what is the expected number of matches of the pattern 'py*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, z: 1, h: 2}, what is the expected number of times the pattern 'z+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, t: 4}. What is the expected number of occurrences of the pattern 'lt+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, z: 2, b: 2}. What is the expected number of occurrences of the pattern 'kb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, j: 4} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, i: 2, d: 2}, what is the expected number of times the pattern 'id*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, e: 3, b: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, j: 1, o: 3, d: 1} to form a word, what is the expected number of matches of the pattern 'o*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, r: 1, k: 2, o: 2}. What is the expected number of occurrences of the pattern 'o+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, q: 1, v: 1, z: 1, y: 1}, what is the expected number of times the pattern 'r.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, o: 2, d: 1, n: 2}, what is the expected number of times the pattern 'n.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, h: 2, f: 2, j: 1}, what is the expected number of times the pattern 'h.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, c: 2, x: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'ix*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, s: 1, u: 2, c: 2}. What is the expected number of occurrences of the pattern 'su+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, f: 2, u: 1, y: 2}. What is the expected number of occurrences of the pattern 'y*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, h: 1, i: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'ha+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, n: 1, u: 1, g: 1, w: 1}. What is the expected number of occurrences of the pattern 'u.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, i: 1, h: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, a: 1, c: 1, p: 2, u: 1}. What is the expected number of occurrences of the pattern 'u+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, c: 2, f: 1, x: 1, k: 1}, what is the expected number of times the pattern 'a+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, h: 1, z: 1, g: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'e*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, z: 5} to form a word, what is the expected number of matches of the pattern 'j*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, m: 1, y: 2, i: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, o: 1, m: 1, y: 1, u: 1}. What is the expected number of occurrences of the pattern 'm*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 4, r: 1, s: 1} to form a word, what is the expected number of matches of the pattern 's.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, u: 2, x: 1, f: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, a: 5} to form a word, what is the expected number of matches of the pattern 'm.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 4, z: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 4, k: 1, n: 1}, what is the expected number of times the pattern 'i+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, z: 1, e: 4}. What is the expected number of occurrences of the pattern 'e.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, e: 3}, what is the expected number of times the pattern 'g.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, i: 2, l: 1, s: 2}, what is the expected number of times the pattern 'al+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 4, t: 2}, what is the expected number of times the pattern 'tj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, r: 1, w: 1, b: 2}, what is the expected number of times the pattern 'rr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, k: 1, b: 1, h: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'ka*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, c: 4}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, g: 1, y: 1, w: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'y.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, h: 1, t: 2, b: 1, q: 1}, what is the expected number of times the pattern 'q+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, d: 1, z: 3, x: 1}. What is the expected number of occurrences of the pattern 'v+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, u: 5}, what is the expected number of times the pattern 'eu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, w: 1, c: 1, u: 2, m: 1} to form a word, what is the expected number of matches of the pattern 'u.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, d: 2, e: 2, y: 1}, what is the expected number of times the pattern 'e.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, w: 2, m: 1, i: 2}. What is the expected number of occurrences of the pattern 'w+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, k: 2, v: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'p+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 4, y: 2}. What is the expected number of occurrences of the pattern 'y.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, g: 1, k: 1, f: 1, j: 2}, what is the expected number of times the pattern 'j*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 4, c: 2}. What is the expected number of occurrences of the pattern 's+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, z: 1, d: 2, y: 1, r: 1}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, s: 3}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, t: 2, s: 2}. What is the expected number of occurrences of the pattern 'i.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, f: 2, a: 1, j: 1, y: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, h: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'w*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, m: 2, k: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'm+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, j: 1, b: 1, k: 1, o: 1}, what is the expected number of times the pattern 'o*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, v: 1, s: 1, u: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'u*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, f: 1, k: 1, h: 1, i: 2}. What is the expected number of occurrences of the pattern 'k*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, n: 1, g: 1, k: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'm+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, p: 2, z: 2, a: 1}. What is the expected number of occurrences of the pattern 'p+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, o: 1, n: 1, w: 1}, what is the expected number of times the pattern 'n.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, i: 3, k: 1} to form a word, what is the expected number of matches of the pattern 'i+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 4, k: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, c: 3}. What is the expected number of occurrences of the pattern 'm*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, z: 1, i: 2, e: 2} to form a word, what is the expected number of matches of the pattern 'is*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, v: 1, d: 2, a: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'd+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, c: 3, b: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'cb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 4, y: 1, b: 1}, what is the expected number of times the pattern 'y+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, c: 1, x: 1, y: 2}. What is the expected number of occurrences of the pattern 'u+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, g: 5}, what is the expected number of times the pattern 'dg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, r: 1, p: 1, o: 2}, what is the expected number of times the pattern 'po*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, u: 1, r: 1, e: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, j: 4}. What is the expected number of occurrences of the pattern 'j.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, i: 1, t: 3, q: 1}. What is the expected number of occurrences of the pattern 'a+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, h: 2, p: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'h*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, o: 1, r: 1, y: 3} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 3, l: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'l+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 4, n: 2} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, i: 4} to form a word, what is the expected number of matches of the pattern 'w*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, u: 2, i: 1, z: 1}. What is the expected number of occurrences of the pattern 'z+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, l: 2, k: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'k*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, z: 2, h: 2}, what is the expected number of times the pattern 'th+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, s: 1, g: 1, b: 1, t: 1}, what is the expected number of times the pattern 'tg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, m: 3, k: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, t: 1, e: 1, f: 1, k: 1}, what is the expected number of times the pattern 'k*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, l: 4} to form a word, what is the expected number of matches of the pattern 'x.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, m: 2, i: 1, x: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, z: 3}. What is the expected number of occurrences of the pattern 'z*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, r: 2, u: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, x: 2, h: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'hq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, n: 5}, what is the expected number of times the pattern 'jn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, e: 2, w: 1, y: 1, l: 1}. What is the expected number of occurrences of the pattern 'r.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, q: 3} to form a word, what is the expected number of matches of the pattern 't+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, x: 1, v: 1, s: 1, u: 1}, what is the expected number of times the pattern 'x.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, i: 1, u: 1, e: 2}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, n: 1, a: 1, s: 1}. What is the expected number of occurrences of the pattern 'sa+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, l: 2, u: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'u+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, h: 1, t: 1, v: 2, z: 1}, what is the expected number of times the pattern 'hz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, u: 1, l: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'l*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, n: 1, m: 1, p: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, w: 2, y: 3} to form a word, what is the expected number of matches of the pattern 'q.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, j: 1, t: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'j+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, f: 1, k: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'f.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, a: 3, q: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 4, o: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, u: 1, d: 1, v: 1, f: 1}, what is the expected number of times the pattern 'p*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, b: 1, x: 1, m: 1, t: 2}. What is the expected number of occurrences of the pattern 'xx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, c: 1, h: 1, p: 1}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, x: 1, d: 1, f: 1, r: 2}. What is the expected number of occurrences of the pattern 'y.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, r: 5}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, c: 4}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, r: 1, n: 1, h: 1, f: 2}, what is the expected number of times the pattern 'rh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, z: 2, e: 1, s: 2} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, c: 1, r: 2, w: 2}. What is the expected number of occurrences of the pattern 'rx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, h: 1, l: 1, i: 1, x: 1}, what is the expected number of times the pattern 'c*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, v: 2, m: 1, w: 1}. What is the expected number of occurrences of the pattern 'wv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, r: 3}, what is the expected number of times the pattern 'r+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, j: 4}, what is the expected number of times the pattern 'jx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, d: 2, u: 1, c: 1, s: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, d: 2, e: 1, h: 2}. What is the expected number of occurrences of the pattern 'f.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, f: 2, g: 1, z: 1}, what is the expected number of times the pattern 'f*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 4, w: 2}, what is the expected number of times the pattern 'ew+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, z: 1, d: 2, s: 1, y: 1}. What is the expected number of occurrences of the pattern 'l+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, z: 2, n: 2, t: 1}, what is the expected number of times the pattern 'ng+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, j: 1, g: 1, m: 1, c: 1}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, v: 1, r: 2, w: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, a: 1, f: 2, v: 2}, what is the expected number of times the pattern 'fj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, t: 1, h: 1, v: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, f: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, e: 2, r: 1, s: 1, h: 1}, what is the expected number of times the pattern 'e.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, o: 1, j: 1, f: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'f.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, t: 3}, what is the expected number of times the pattern 'o+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, j: 4} to form a word, what is the expected number of matches of the pattern 'jg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, e: 1, k: 2, j: 2}, what is the expected number of times the pattern 'jk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, i: 2, v: 3}. What is the expected number of occurrences of the pattern 'v.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, q: 1, m: 2, f: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, h: 2, x: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, n: 1, t: 1, p: 1, s: 2} to form a word, what is the expected number of matches of the pattern 't*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, g: 3, i: 2} to form a word, what is the expected number of matches of the pattern 'g*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, v: 2, u: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'j.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, d: 2, c: 2}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, a: 2, b: 1}, what is the expected number of times the pattern 'a*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, y: 1, c: 2}. What is the expected number of occurrences of the pattern 'c+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, v: 4}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, j: 1, r: 1, m: 3} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, s: 1, b: 1, e: 1}, what is the expected number of times the pattern 'e.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, b: 1, x: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'xx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, g: 4} to form a word, what is the expected number of matches of the pattern 'eg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, j: 1, c: 1, m: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'sm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, z: 3, s: 2} to form a word, what is the expected number of matches of the pattern 'z.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 4, i: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'di*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, j: 4}. What is the expected number of occurrences of the pattern 'j+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, p: 2, m: 3}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, h: 1, c: 2, x: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'u.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, c: 3}, what is the expected number of times the pattern 'u.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, i: 2, e: 2} to form a word, what is the expected number of matches of the pattern 'ei*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, f: 2, v: 1, h: 1, p: 1}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 4, n: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, d: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'xd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 4, y: 2}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, o: 1, y: 1, b: 2, a: 1}, what is the expected number of times the pattern 'a.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 4, t: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, c: 4}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, k: 3}, what is the expected number of times the pattern 'vk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, n: 1, g: 1, b: 2, s: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, t: 3, h: 2}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, s: 2}. What is the expected number of occurrences of the pattern 't+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, z: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'nz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, e: 2, x: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, s: 2, v: 3}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, z: 1, t: 1, l: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'al+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, q: 1, g: 1, n: 1, p: 1}, what is the expected number of times the pattern 'qr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, y: 1, c: 1, a: 1, p: 2}, what is the expected number of times the pattern 'za*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, l: 1, o: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'w.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, o: 2, i: 1, y: 1, h: 1}, what is the expected number of times the pattern 'i*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, r: 1, i: 1, w: 2, m: 1}. What is the expected number of occurrences of the pattern 'w.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, m: 2, t: 1, p: 1}, what is the expected number of times the pattern 'p.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, w: 2, k: 1, s: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, u: 1, i: 2, t: 1}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, g: 2, w: 1, p: 1, r: 1}, what is the expected number of times the pattern 'w+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, r: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'rl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, m: 2, y: 2, a: 1}, what is the expected number of times the pattern 'ka+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, o: 2, r: 2}. What is the expected number of occurrences of the pattern 'r+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, m: 1, i: 1, o: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, t: 3} to form a word, what is the expected number of matches of the pattern 'ot+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, o: 2, a: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, s: 5} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, g: 1, n: 1, v: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, d: 1, z: 2}. What is the expected number of occurrences of the pattern 'du*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, y: 1, i: 1, l: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, n: 1, l: 1, a: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, n: 1, f: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 5, r: 1}. What is the expected number of occurrences of the pattern 'r+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, a: 3, q: 1}. What is the expected number of occurrences of the pattern 'qa+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, i: 1, g: 2, s: 1, c: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, e: 3}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, v: 1, g: 1, h: 2, p: 1}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, v: 2, l: 1, a: 1, d: 1}, what is the expected number of times the pattern 'vd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, d: 2, x: 2}, what is the expected number of times the pattern 'j.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, i: 1, y: 2, x: 1, p: 1}, what is the expected number of times the pattern 'iy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, q: 2, a: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, p: 2, w: 1, x: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, y: 2, f: 2, v: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 5, q: 1}, what is the expected number of times the pattern 'k*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 4, w: 2}, what is the expected number of times the pattern 'wl*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, f: 1, w: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'of+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, h: 5}, what is the expected number of times the pattern 'th+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 4, i: 2}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, p: 3, j: 2} to form a word, what is the expected number of matches of the pattern 'g.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, q: 1, y: 1, v: 1}. What is the expected number of occurrences of the pattern 'vr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, z: 2, y: 3}. What is the expected number of occurrences of the pattern 'zy*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, x: 4}. What is the expected number of occurrences of the pattern 'sx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, d: 3}. What is the expected number of occurrences of the pattern 'd*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, h: 2, n: 1}. What is the expected number of occurrences of the pattern 'vn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, s: 1, t: 2, n: 2} to form a word, what is the expected number of matches of the pattern 't.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, b: 2, a: 1, g: 1}, what is the expected number of times the pattern 'i+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, d: 3} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, k: 1, z: 1, q: 1, c: 1}. What is the expected number of occurrences of the pattern 't*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, g: 2, v: 1, r: 2}, what is the expected number of times the pattern 'g.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, q: 1, a: 1, u: 2, i: 1}. What is the expected number of occurrences of the pattern 'ue+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, a: 2, s: 1, g: 1}, what is the expected number of times the pattern 'g+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 4, g: 2}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 4, k: 2}, what is the expected number of times the pattern 'kz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, p: 1, b: 1, k: 2}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, f: 1, j: 1, d: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'cr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, n: 2, c: 1, k: 1, p: 1}, what is the expected number of times the pattern 'cp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, n: 3, p: 1}. What is the expected number of occurrences of the pattern 'p+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, k: 3, u: 2} to form a word, what is the expected number of matches of the pattern 'k.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, n: 1, v: 2}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, i: 2, x: 1}, what is the expected number of times the pattern 'x+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, g: 1, q: 2}. What is the expected number of occurrences of the pattern 'lg*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, n: 2, m: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'wn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, u: 1, j: 2, v: 2}. What is the expected number of occurrences of the pattern 'uj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, q: 4}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, s: 1, i: 3} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 4, m: 2} to form a word, what is the expected number of matches of the pattern 'mp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, q: 2, s: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'rs*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 4, p: 2}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, x: 1, y: 1, c: 1, a: 1}. What is the expected number of occurrences of the pattern 'x*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, q: 3, x: 1} to form a word, what is the expected number of matches of the pattern 'xq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, a: 1, v: 2} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, u: 1, s: 1, m: 2}. What is the expected number of occurrences of the pattern 'uh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, t: 2, g: 2}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, r: 1, n: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'r.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, i: 1, u: 2, m: 1} to form a word, what is the expected number of matches of the pattern 'ms+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, t: 1, l: 1, u: 1, o: 1}. What is the expected number of occurrences of the pattern 'tv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, h: 2, v: 1, y: 1, p: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, v: 2, p: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'k*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 3, q: 3} to form a word, what is the expected number of matches of the pattern 'fq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, x: 2, k: 1, l: 2}, what is the expected number of times the pattern 'c*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, r: 1, l: 1, j: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'j*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, v: 4}. What is the expected number of occurrences of the pattern 'vo*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, u: 3, w: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, f: 1, g: 1, z: 2, v: 1}. What is the expected number of occurrences of the pattern 'f.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, n: 2, h: 2, v: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 4, e: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, a: 1, v: 1, t: 3} to form a word, what is the expected number of matches of the pattern 't.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, m: 1, q: 2}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, f: 3, h: 2}. What is the expected number of occurrences of the pattern 'fa+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, a: 1, y: 1, c: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 4, a: 1, b: 1}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, h: 4}, what is the expected number of times the pattern 'g+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, b: 2, w: 1}. What is the expected number of occurrences of the pattern 'e*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, k: 4}. What is the expected number of occurrences of the pattern 'kl+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, y: 2, q: 2} to form a word, what is the expected number of matches of the pattern 'j+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, l: 1, m: 1, z: 2, o: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, s: 2, f: 1, a: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'f.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, d: 1, p: 2, t: 1, o: 1}, what is the expected number of times the pattern 'pz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, w: 1, t: 1, d: 2}. What is the expected number of occurrences of the pattern 'id*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, c: 3, u: 2}, what is the expected number of times the pattern 'm*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, h: 3}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 3, r: 2, x: 1} to form a word, what is the expected number of matches of the pattern 'fr+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 4, g: 2} to form a word, what is the expected number of matches of the pattern 'w.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, a: 1, r: 1, t: 3} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 4, q: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, x: 4}, what is the expected number of times the pattern 'nx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, r: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'r.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, r: 1, f: 1, g: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, c: 1, t: 3} to form a word, what is the expected number of matches of the pattern 'jc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 4, c: 2}, what is the expected number of times the pattern 'c.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, m: 4}, what is the expected number of times the pattern 'm+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, g: 1, x: 1, e: 2}. What is the expected number of occurrences of the pattern 'e*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, v: 1, g: 3}. What is the expected number of occurrences of the pattern 'vd+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, q: 2, k: 1}. What is the expected number of occurrences of the pattern 'kk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, y: 1, k: 3}. What is the expected number of occurrences of the pattern 'yk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, q: 3} to form a word, what is the expected number of matches of the pattern 'vq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, z: 3}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, t: 3, y: 1, i: 1}, what is the expected number of times the pattern 'ty+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, p: 4, u: 1}. What is the expected number of occurrences of the pattern 'p+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, t: 2, w: 1, j: 1, d: 1}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, s: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'gs*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, e: 1, h: 2, c: 2}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, j: 3}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, l: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'kl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, s: 4}. What is the expected number of occurrences of the pattern 'cs*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, e: 2, y: 1, n: 1, c: 1}, what is the expected number of times the pattern 'c.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, r: 3, f: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, w: 4}. What is the expected number of occurrences of the pattern 'w.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 3, e: 3}, what is the expected number of times the pattern 'se*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, n: 2, z: 1, r: 1, j: 1}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, a: 1, n: 1, y: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'n.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, j: 3}. What is the expected number of occurrences of the pattern 's.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 4, x: 2} to form a word, what is the expected number of matches of the pattern 'p*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, b: 2, e: 1, g: 1, s: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, h: 2, f: 1, s: 1, x: 1}, what is the expected number of times the pattern 's+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 3, e: 2, u: 1}, what is the expected number of times the pattern 'ue*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, z: 3, i: 1} to form a word, what is the expected number of matches of the pattern 'j+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, t: 1, v: 1, i: 1}. What is the expected number of occurrences of the pattern 'v*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 4, y: 2}, what is the expected number of times the pattern 'y+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, x: 1, o: 2, l: 1, t: 1}, what is the expected number of times the pattern 'lt+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, o: 2, m: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, q: 1, y: 3}, what is the expected number of times the pattern 'yq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, g: 1, k: 2, t: 1} to form a word, what is the expected number of matches of the pattern 'k.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, t: 5} to form a word, what is the expected number of matches of the pattern 'zt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, s: 2, k: 1, d: 2}, what is the expected number of times the pattern 'sd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, c: 2, r: 2}. What is the expected number of occurrences of the pattern 'rn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 5, s: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, c: 1, q: 4} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, v: 1, o: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'ov+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, v: 1, d: 1, k: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, d: 2, t: 3}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, n: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'yv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, p: 1, o: 3} to form a word, what is the expected number of matches of the pattern 'p+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, x: 2, t: 1, f: 1, d: 1}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, u: 1, g: 1, x: 2, v: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, j: 1, r: 1, v: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'g*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, d: 3, z: 1}, what is the expected number of times the pattern 'a.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, f: 3} to form a word, what is the expected number of matches of the pattern 'f*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, x: 1, q: 1, a: 3}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, t: 2, l: 1, b: 1, u: 1}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, w: 1, x: 3, h: 1}. What is the expected number of occurrences of the pattern 'd*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, f: 1, g: 1, p: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, w: 2, n: 1, y: 1, i: 1}. What is the expected number of occurrences of the pattern 'i*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, e: 2, t: 1, u: 1}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, f: 4} to form a word, what is the expected number of matches of the pattern 'f*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, c: 1, d: 2, p: 1, z: 1}. What is the expected number of occurrences of the pattern 'a+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, h: 1, l: 1, y: 2, m: 1}. What is the expected number of occurrences of the pattern 'ly+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, d: 1, t: 2, p: 2}. What is the expected number of occurrences of the pattern 'd.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, p: 1, z: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'mf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 4, v: 2}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, q: 2, s: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, b: 1, k: 1, w: 2, t: 1} to form a word, what is the expected number of matches of the pattern 'aw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, n: 1, s: 3}. What is the expected number of occurrences of the pattern 'as+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, i: 1, x: 1, o: 2, j: 1}, what is the expected number of times the pattern 'j+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 4, d: 2} to form a word, what is the expected number of matches of the pattern 'd*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, e: 5}. What is the expected number of occurrences of the pattern 'e+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, i: 2, o: 1, d: 1, k: 1}. What is the expected number of occurrences of the pattern 'o+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, h: 1, c: 1, u: 2}, what is the expected number of times the pattern 'u.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, q: 1, z: 1, u: 1, m: 1}, what is the expected number of times the pattern 'q*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, l: 4, i: 1}. What is the expected number of occurrences of the pattern 'i+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, j: 1, g: 2}, what is the expected number of times the pattern 'o*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, o: 2, n: 1, p: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, v: 1, m: 1, h: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'm*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, r: 1, z: 1, j: 1, p: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 4, n: 2}, what is the expected number of times the pattern 'n*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, p: 1, y: 1, q: 2, u: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, q: 1, y: 3}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, y: 1, a: 1, n: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'i+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, o: 1, t: 2, n: 2}. What is the expected number of occurrences of the pattern 'mo+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, f: 3}, what is the expected number of times the pattern 'nf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, w: 1, c: 1, x: 1, u: 2}. What is the expected number of occurrences of the pattern 'e*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, c: 2, r: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, i: 2, j: 2, g: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, i: 1, g: 1, v: 1, u: 1}. What is the expected number of occurrences of the pattern 'ig+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 4, x: 2}, what is the expected number of times the pattern 'v*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, s: 2, l: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'cs*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, e: 2, t: 2} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 4, s: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, h: 2, f: 1, s: 2}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, c: 2, w: 2}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, x: 1, z: 1, h: 2}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, h: 2, y: 2}, what is the expected number of times the pattern 'hy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, d: 1, z: 2, u: 1}, what is the expected number of times the pattern 'u*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, q: 1, u: 1, o: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'o*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 3, d: 1, q: 1, j: 1}, what is the expected number of times the pattern 'dj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, e: 2, y: 2}. What is the expected number of occurrences of the pattern 'y*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, h: 2, x: 1, q: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'r*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, c: 1, i: 3, t: 1}. What is the expected number of occurrences of the pattern 't+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, r: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'g.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 4, i: 2}, what is the expected number of times the pattern 'di*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 4, t: 2}. What is the expected number of occurrences of the pattern 'ct+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, c: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'ct+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, i: 1, h: 1, y: 1, r: 2}. What is the expected number of occurrences of the pattern 'h+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, n: 2, d: 1}. What is the expected number of occurrences of the pattern 's+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 4, j: 1, w: 1}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, q: 2, w: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'w+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, f: 1, i: 2, t: 1, m: 1}, what is the expected number of times the pattern 'of+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, p: 1, o: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'i.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, c: 1, t: 1, q: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, s: 1, a: 2, h: 2}, what is the expected number of times the pattern 'a.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, g: 1, j: 1, z: 2, y: 1}, what is the expected number of times the pattern 'gw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, a: 2, y: 1, i: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, p: 3} to form a word, what is the expected number of matches of the pattern 'w.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, e: 2, y: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, k: 1, g: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, h: 1, e: 1, g: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'hg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, g: 1, j: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'jt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, u: 1, v: 1, f: 3} to form a word, what is the expected number of matches of the pattern 'w*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, d: 1, z: 1, g: 2, w: 1}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, k: 2, h: 1, z: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'hh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, w: 1, b: 3}, what is the expected number of times the pattern 'gw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, e: 2, p: 3} to form a word, what is the expected number of matches of the pattern 'e.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, v: 1, n: 1, m: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, s: 1, j: 2, i: 1, k: 1} to form a word, what is the expected number of matches of the pattern 's+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, c: 1, p: 2, m: 1, l: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, p: 1, e: 2}, what is the expected number of times the pattern 'p.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, z: 2, b: 1, r: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, l: 2, p: 3}. What is the expected number of occurrences of the pattern 'p*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, z: 3, c: 2}. What is the expected number of occurrences of the pattern 'rz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, w: 1, k: 1, n: 2, m: 1}. What is the expected number of occurrences of the pattern 'k.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, c: 3, h: 2} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, s: 1, x: 1, p: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'y*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 4, k: 2} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, e: 2, c: 2}. What is the expected number of occurrences of the pattern 'qe*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, k: 1, z: 1, q: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'z.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, r: 1, e: 2, g: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'ue*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, k: 1, o: 3}. What is the expected number of occurrences of the pattern 'ot+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, n: 3} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, h: 4, u: 1}. What is the expected number of occurrences of the pattern 'ui+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, y: 2, c: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'u.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, a: 1, s: 1, h: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'e*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, w: 2, o: 1, r: 2}, what is the expected number of times the pattern 'ow+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, g: 1, e: 1, v: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'sg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, b: 1, z: 1, w: 2, a: 1}. What is the expected number of occurrences of the pattern 'wz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, q: 4}, what is the expected number of times the pattern 'x.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 3, e: 3}. What is the expected number of occurrences of the pattern 'p+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, h: 2, k: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, w: 2, m: 1, l: 1, n: 1}. What is the expected number of occurrences of the pattern 'w+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, m: 2, b: 3}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, u: 5} to form a word, what is the expected number of matches of the pattern 'uy*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, o: 1, r: 1, x: 1, v: 2}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, f: 1, i: 1, y: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'o*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, q: 3, n: 2}, what is the expected number of times the pattern 'n*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, t: 1, m: 2, e: 2}. What is the expected number of occurrences of the pattern 'e*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, l: 2, x: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'o+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, b: 2, k: 3} to form a word, what is the expected number of matches of the pattern 'kk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 4, m: 2}. What is the expected number of occurrences of the pattern 'm+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, y: 1, g: 1, n: 2}. What is the expected number of occurrences of the pattern 'n+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, q: 1, m: 1, k: 1, v: 1}, what is the expected number of times the pattern 'q*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, u: 2, t: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, n: 2, u: 2}, what is the expected number of times the pattern 'a*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, q: 1, n: 3} to form a word, what is the expected number of matches of the pattern 'qe*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, f: 4, b: 1} to form a word, what is the expected number of matches of the pattern 'fp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, a: 1, y: 1, c: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'cs+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, j: 5} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, r: 3}. What is the expected number of occurrences of the pattern 'd*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, z: 1, w: 2, g: 1}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, e: 1, w: 1, k: 2}, what is the expected number of times the pattern 'kx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, o: 1, r: 4}. What is the expected number of occurrences of the pattern 'ro+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, t: 3, u: 2}. What is the expected number of occurrences of the pattern 'h+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, g: 1, v: 1, r: 1, a: 1}. What is the expected number of occurrences of the pattern 'pv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, x: 1, g: 2, d: 1}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, h: 2, n: 1, w: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, y: 3, h: 2}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, c: 2, a: 1, n: 2}. What is the expected number of occurrences of the pattern 'aa+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, p: 1, x: 2, f: 1, z: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, a: 1, w: 1, j: 2}. What is the expected number of occurrences of the pattern 'j.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, j: 4} to form a word, what is the expected number of matches of the pattern 'ej+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 5, b: 1} to form a word, what is the expected number of matches of the pattern 'k+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.83", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, r: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'v+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, t: 2, h: 2} to form a word, what is the expected number of matches of the pattern 't+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, n: 2, e: 3}, what is the expected number of times the pattern 'e+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, s: 5}, what is the expected number of times the pattern 'sg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, h: 1, t: 1, y: 2, c: 1}, what is the expected number of times the pattern 'yt*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, v: 2, g: 3}, what is the expected number of times the pattern 'x+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, r: 1, v: 2}, what is the expected number of times the pattern 'r*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, t: 2, j: 1}. What is the expected number of occurrences of the pattern 'tj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 4, i: 2}. What is the expected number of occurrences of the pattern 'i*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, e: 1, u: 1, p: 1, r: 1}. What is the expected number of occurrences of the pattern 'a.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, j: 1, r: 1, e: 1, a: 1}, what is the expected number of times the pattern 'ra+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, c: 1, f: 1, w: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'gv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, s: 1, z: 1, h: 1, c: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, f: 1, l: 1, v: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'fr+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, i: 2, z: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'k.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, r: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 4, d: 2} to form a word, what is the expected number of matches of the pattern 'd+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, n: 1, h: 1, c: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'c+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 4, q: 2}. What is the expected number of occurrences of the pattern 'q*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, c: 1, d: 2, h: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, f: 1, d: 1, w: 2, l: 1}, what is the expected number of times the pattern 'dw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, z: 2, a: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'z*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, f: 4} to form a word, what is the expected number of matches of the pattern 'r+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, u: 2, l: 1}, what is the expected number of times the pattern 'u+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, s: 2, o: 1, t: 1}. What is the expected number of occurrences of the pattern 'o.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, n: 2, f: 1, r: 1}. What is the expected number of occurrences of the pattern 'fs+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, u: 2, n: 1, v: 1, m: 1}, what is the expected number of times the pattern 'n.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, z: 1, o: 1, s: 3} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, t: 2, n: 2}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, m: 3}, what is the expected number of times the pattern 'mn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, j: 2, h: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'j*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, q: 4, e: 1}, what is the expected number of times the pattern 'e.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, x: 1, r: 1, f: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, r: 3}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, v: 3}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, e: 1, w: 3}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, x: 1, t: 1, k: 2, a: 1}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'kb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, l: 1, q: 2, y: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'cl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, k: 3}, what is the expected number of times the pattern 'x.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, h: 4} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, g: 3}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, i: 2, z: 1, h: 2}. What is the expected number of occurrences of the pattern 'hw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, h: 1, k: 2, a: 2}. What is the expected number of occurrences of the pattern 'ag*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, x: 1, o: 1, v: 1, c: 1}, what is the expected number of times the pattern 'vo+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, x: 1, o: 1, v: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'yz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, n: 2, i: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, m: 1, i: 1, x: 3}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, y: 2, a: 1, f: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'y+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, j: 1, n: 1, b: 3}. What is the expected number of occurrences of the pattern 'j.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, o: 1, a: 1, l: 1}. What is the expected number of occurrences of the pattern 'o*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, k: 2, p: 1, e: 1, g: 1}, what is the expected number of times the pattern 'k.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, f: 1, s: 4}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, z: 1, o: 2, p: 1}. What is the expected number of occurrences of the pattern 'po+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, t: 1, r: 1, d: 1, c: 2} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, d: 2, l: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'z.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, d: 2, s: 2} to form a word, what is the expected number of matches of the pattern 's+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, s: 3} to form a word, what is the expected number of matches of the pattern 's+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, d: 1, t: 1, j: 2}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 4, c: 2}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, k: 2, y: 1, e: 2}. What is the expected number of occurrences of the pattern 'e*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, i: 2, o: 2, l: 1}, what is the expected number of times the pattern 'li*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, n: 1, q: 2}. What is the expected number of occurrences of the pattern 'q*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, u: 4}. What is the expected number of occurrences of the pattern 'v.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, x: 1, p: 2, n: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 4, t: 2}. What is the expected number of occurrences of the pattern 'dt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, i: 1, m: 1, t: 2, f: 1}. What is the expected number of occurrences of the pattern 'ft+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, b: 2, t: 1, z: 1}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, l: 3}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, y: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'oy*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 4, m: 2}, what is the expected number of times the pattern 'km+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, j: 1, q: 3, k: 1}. What is the expected number of occurrences of the pattern 'j+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, z: 4} to form a word, what is the expected number of matches of the pattern 'zl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, u: 2, e: 1}. What is the expected number of occurrences of the pattern 've*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, k: 1, m: 1, u: 3} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, h: 2, l: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'ha*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, y: 1, a: 1, p: 1, r: 1}. What is the expected number of occurrences of the pattern 'a+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, d: 1, u: 1, c: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'c+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, t: 1, f: 1, d: 1, v: 2}, what is the expected number of times the pattern 'd*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, t: 1, e: 1, o: 2, b: 1}, what is the expected number of times the pattern 'ob*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 4, x: 2}. What is the expected number of occurrences of the pattern 'a+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, q: 3}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, g: 3}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 3, y: 3} to form a word, what is the expected number of matches of the pattern 'r+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, k: 2, h: 1, t: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'ft+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, l: 2, s: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'xc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 4, m: 2} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 4, x: 2}, what is the expected number of times the pattern 'rx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'a.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, q: 2, p: 2}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, v: 2, w: 3}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, e: 3}. What is the expected number of occurrences of the pattern 'z.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, n: 2, m: 1, s: 1}. What is the expected number of occurrences of the pattern 'ms+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, w: 2, j: 1, m: 2}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, k: 1, n: 1, b: 1, w: 1}. What is the expected number of occurrences of the pattern 'w.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, j: 1, w: 1, q: 2, l: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, t: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'n.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, d: 2, e: 2, b: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, h: 2, p: 1, y: 1}, what is the expected number of times the pattern 'h+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, n: 1, y: 1, q: 1, o: 2}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, x: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, r: 1, a: 1, o: 1}, what is the expected number of times the pattern 'or+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, x: 3}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, r: 1, z: 1, i: 2, k: 1}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, j: 3, q: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'cq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, q: 1, p: 1, u: 2}. What is the expected number of occurrences of the pattern 'ua+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, w: 1, i: 2, g: 1, h: 1}. What is the expected number of occurrences of the pattern 'w*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, t: 1, d: 2, f: 1, n: 1}, what is the expected number of times the pattern 'n+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, x: 1, l: 1, e: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'p*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, t: 1, w: 2, l: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, s: 1, n: 1, r: 2}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, x: 1, c: 2, a: 1}, what is the expected number of times the pattern 'c.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, t: 2, o: 3} to form a word, what is the expected number of matches of the pattern 'ot+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, s: 1, z: 1, f: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'cf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 4, a: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 4, o: 2}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, t: 1, v: 2, w: 1, p: 1}. What is the expected number of occurrences of the pattern 't.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, j: 1, i: 1, w: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'q.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, h: 3, q: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, d: 2, c: 1, v: 2}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, q: 1, p: 1, x: 2, z: 1}, what is the expected number of times the pattern 'z.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, c: 1, j: 2, t: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 5, i: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, a: 1, x: 1, n: 1, t: 2}. What is the expected number of occurrences of the pattern 'xt+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, e: 1, a: 1, i: 2, o: 1}. What is the expected number of occurrences of the pattern 'oa*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, v: 2, k: 2}, what is the expected number of times the pattern 'vi+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, m: 1, x: 3, f: 1} to form a word, what is the expected number of matches of the pattern 'xm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, t: 1, f: 1, g: 1}, what is the expected number of times the pattern 'g*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, b: 1, i: 2, f: 1, u: 1}. What is the expected number of occurrences of the pattern 'ij*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, t: 4}. What is the expected number of occurrences of the pattern 't.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, z: 1, j: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, y: 1, a: 1, f: 2, t: 1}. What is the expected number of occurrences of the pattern 'f.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, o: 2, i: 1, b: 1, c: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, p: 2, q: 1, r: 1, c: 1}, what is the expected number of times the pattern 'c.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, w: 1, z: 2, q: 1}. What is the expected number of occurrences of the pattern 'q.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, n: 1, v: 2}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, e: 2, s: 1, g: 2}, what is the expected number of times the pattern 'pe*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, i: 3, z: 1} to form a word, what is the expected number of matches of the pattern 'iz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, b: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'td*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, b: 1, q: 2, y: 1}, what is the expected number of times the pattern 'q*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, y: 1, i: 3} to form a word, what is the expected number of matches of the pattern 'l.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, w: 1, o: 1, m: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, r: 1, z: 1, a: 3}. What is the expected number of occurrences of the pattern 'z.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, o: 4}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, a: 2, m: 2}, what is the expected number of times the pattern 'a.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, n: 2, j: 1, y: 2}. What is the expected number of occurrences of the pattern 'fn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 4, w: 2}, what is the expected number of times the pattern 'wr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, b: 4}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, k: 1, j: 2, x: 1, s: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, e: 1, g: 1, j: 2, k: 1}. What is the expected number of occurrences of the pattern 'j*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, o: 1, b: 1, y: 3}. What is the expected number of occurrences of the pattern 'c.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, k: 3}, what is the expected number of times the pattern 'm.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, t: 3}, what is the expected number of times the pattern 'm+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, a: 2, q: 1, s: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'q.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, f: 1, h: 1, j: 2, p: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, r: 3, c: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'l.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, t: 5}. What is the expected number of occurrences of the pattern 'ts+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, r: 1, l: 1, m: 2}, what is the expected number of times the pattern 'kr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, a: 1, v: 2, k: 1, p: 1}, what is the expected number of times the pattern 'a*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, h: 1, x: 2, g: 2}. What is the expected number of occurrences of the pattern 'wh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, o: 2, l: 1, m: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, q: 2, l: 3}, what is the expected number of times the pattern 'qu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, w: 1, m: 2, k: 1}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, b: 3}, what is the expected number of times the pattern 'rr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 4, y: 2}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, m: 2, k: 1, o: 2}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 4, s: 2} to form a word, what is the expected number of matches of the pattern 's.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, d: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'hb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, q: 4}. What is the expected number of occurrences of the pattern 'q*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, j: 1, n: 2, k: 1, c: 1}. What is the expected number of occurrences of the pattern 'a+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, s: 1, x: 1, m: 1, k: 2} to form a word, what is the expected number of matches of the pattern 's.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, m: 4}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, j: 4}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, a: 1, y: 1, v: 2}. What is the expected number of occurrences of the pattern 'ay+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, d: 1, m: 2, a: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'd*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, w: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'w.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, y: 1, c: 2}. What is the expected number of occurrences of the pattern 'ct*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 4, q: 2}, what is the expected number of times the pattern 'qu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, s: 1, f: 1, a: 2}, what is the expected number of times the pattern 'as*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, d: 3, f: 2}, what is the expected number of times the pattern 'f.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 4, y: 2}, what is the expected number of times the pattern 'u*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'x.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 4, a: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, e: 1, t: 2, p: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'e*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, x: 1, a: 2, d: 2}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, y: 2, h: 1}. What is the expected number of occurrences of the pattern 'yh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, p: 3}, what is the expected number of times the pattern 'rp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, y: 1, q: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, u: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'p.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, o: 1, i: 1, r: 1, p: 2}. What is the expected number of occurrences of the pattern 'ir+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, v: 4}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, w: 1, q: 2, t: 1}, what is the expected number of times the pattern 'tw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, k: 3}. What is the expected number of occurrences of the pattern 'k.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, p: 1, n: 1, s: 2} to form a word, what is the expected number of matches of the pattern 's.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, d: 2, v: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 4, d: 2}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, r: 1, d: 1, c: 1, z: 2}, what is the expected number of times the pattern 'o.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 4, e: 2}. What is the expected number of occurrences of the pattern 'oe*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, p: 1, f: 2, t: 1}. What is the expected number of occurrences of the pattern 'f+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, w: 3}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 4, e: 2} to form a word, what is the expected number of matches of the pattern 'l*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, i: 1, d: 1, n: 2, s: 1}, what is the expected number of times the pattern 'in+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 4, a: 2} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, m: 1, c: 1, f: 2, n: 1}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, b: 1, e: 1, l: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, f: 4}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, b: 3}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, e: 4}. What is the expected number of occurrences of the pattern 'ei+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, i: 3}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, x: 2, g: 2, s: 1}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 4, t: 2} to form a word, what is the expected number of matches of the pattern 'nt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 5, k: 1}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, u: 1, b: 1, w: 1, p: 2}, what is the expected number of times the pattern 'u.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, g: 2, w: 3} to form a word, what is the expected number of matches of the pattern 'h*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, o: 1, w: 2, y: 1, u: 1}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, t: 1, v: 1, p: 2}, what is the expected number of times the pattern 'g*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, q: 2, d: 2}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, e: 3} to form a word, what is the expected number of matches of the pattern 'es*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, i: 4} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, q: 3, u: 2}, what is the expected number of times the pattern 'q.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, t: 4} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, w: 1, y: 1, s: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'vs+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 4, l: 2}, what is the expected number of times the pattern 'ld*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, a: 1, j: 3}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, v: 1, x: 4}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, i: 1, w: 1, j: 1, g: 2}, what is the expected number of times the pattern 'jw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, d: 1, h: 1, a: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, u: 3}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, m: 3}, what is the expected number of times the pattern 'm.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, v: 3, y: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, f: 4} to form a word, what is the expected number of matches of the pattern 'f+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, s: 1, d: 2}. What is the expected number of occurrences of the pattern 'l*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, u: 1, i: 3}, what is the expected number of times the pattern 'ui*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, j: 2, x: 1, o: 1, u: 1}, what is the expected number of times the pattern 'x.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, i: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'i.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, r: 1, m: 2, z: 1}, what is the expected number of times the pattern 'y.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, p: 3}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, n: 1, j: 2}, what is the expected number of times the pattern 'nf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, y: 4} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, f: 1, s: 1, c: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'c*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, g: 2, q: 1, y: 1}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, i: 1, l: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 5, l: 1} to form a word, what is the expected number of matches of the pattern 'v+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, q: 5}, what is the expected number of times the pattern 'q+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, v: 3}, what is the expected number of times the pattern 'i+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, c: 2, h: 2}. What is the expected number of occurrences of the pattern 'cz*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, r: 1, w: 2, v: 1}, what is the expected number of times the pattern 'wr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, d: 2, t: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'd*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, b: 1, z: 1, p: 3}. What is the expected number of occurrences of the pattern 'pz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 5, y: 1}. What is the expected number of occurrences of the pattern 'xy*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, t: 2, e: 2, o: 1}. What is the expected number of occurrences of the pattern 'o+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 5, m: 1} to form a word, what is the expected number of matches of the pattern 'xm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, i: 4}, what is the expected number of times the pattern 'q.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 4, p: 2} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, a: 2, u: 3} to form a word, what is the expected number of matches of the pattern 'uo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, d: 2, u: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 4, l: 2}. What is the expected number of occurrences of the pattern 'l.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, l: 1, q: 1, t: 1, x: 2}. What is the expected number of occurrences of the pattern 'x+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, h: 2, v: 2, m: 1}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, b: 2, f: 1}. What is the expected number of occurrences of the pattern 'vb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, w: 2, s: 1, g: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, x: 1, w: 1, u: 1, q: 2}. What is the expected number of occurrences of the pattern 'rq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, h: 2, m: 1, p: 1, a: 1}. What is the expected number of occurrences of the pattern 'q*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, q: 3, w: 1}. What is the expected number of occurrences of the pattern 'w+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, z: 3}, what is the expected number of times the pattern 'fz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, w: 2, r: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'm+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, h: 1, a: 2, n: 1, t: 1}, what is the expected number of times the pattern 'n.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, k: 1, i: 1, j: 2}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, p: 5} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, y: 3}. What is the expected number of occurrences of the pattern 'yx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, q: 1, b: 1, j: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, c: 1, u: 1, q: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'ul*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, r: 1, w: 1, k: 1}. What is the expected number of occurrences of the pattern 'k*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, z: 1, v: 1, e: 2}, what is the expected number of times the pattern 'z+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, p: 1, q: 1, r: 1, l: 1}. What is the expected number of occurrences of the pattern 'hp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, i: 1, u: 1, j: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'nu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, s: 1, n: 2, u: 1, e: 1}. What is the expected number of occurrences of the pattern 'u.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, j: 1, z: 3}, what is the expected number of times the pattern 'z+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 4, b: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, f: 1, y: 1, e: 1, d: 2}. What is the expected number of occurrences of the pattern 'd.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, i: 1, y: 1, s: 2, e: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, s: 1, k: 1, p: 1, v: 2} to form a word, what is the expected number of matches of the pattern 's.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, j: 3} to form a word, what is the expected number of matches of the pattern 'j*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, w: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'kc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, l: 3, x: 1}. What is the expected number of occurrences of the pattern 'lr+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, z: 1, t: 1, x: 2} to form a word, what is the expected number of matches of the pattern 't*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, k: 1, t: 1, y: 1, c: 1}. What is the expected number of occurrences of the pattern 'yk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, f: 1, y: 1, z: 1, h: 2}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, x: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, a: 1, n: 1, t: 2}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 4, q: 2} to form a word, what is the expected number of matches of the pattern 'q*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, l: 1, w: 1, c: 2, x: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, m: 1, q: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'x*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, n: 1, v: 1, d: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 4, q: 2}. What is the expected number of occurrences of the pattern 'j+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, m: 1, y: 2, k: 1, f: 1}. What is the expected number of occurrences of the pattern 'f.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, o: 1, c: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, d: 3} to form a word, what is the expected number of matches of the pattern 'w*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, e: 2, a: 1, x: 1}, what is the expected number of times the pattern 'ma*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, p: 1, d: 1, q: 2}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, w: 3}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, c: 2, g: 1}, what is the expected number of times the pattern 'i.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, n: 1, j: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, y: 1, n: 1, f: 1, i: 2}, what is the expected number of times the pattern 'y*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, g: 1, o: 2, e: 1, r: 1}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, k: 2, f: 1, u: 1, m: 1}, what is the expected number of times the pattern 'pk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, j: 1, s: 2, m: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'sm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, m: 4} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, u: 1, h: 2, b: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'm.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, w: 1, r: 1, d: 2, x: 1}, what is the expected number of times the pattern 'dr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, c: 1, g: 1, s: 1, y: 2}, what is the expected number of times the pattern 'c*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, i: 2, h: 2}, what is the expected number of times the pattern 'ih*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, a: 1, q: 3, t: 1}, what is the expected number of times the pattern 'ag*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, j: 1, z: 2}. What is the expected number of occurrences of the pattern 'z*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, u: 1, n: 2}, what is the expected number of times the pattern 'n+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, l: 2, t: 3} to form a word, what is the expected number of matches of the pattern 't.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, z: 1, o: 2, h: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'uo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, o: 1, a: 2, s: 1}, what is the expected number of times the pattern 's+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, k: 1, c: 2, x: 1}, what is the expected number of times the pattern 'c.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, k: 2, y: 3}. What is the expected number of occurrences of the pattern 'yh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, x: 1, j: 2, t: 2} to form a word, what is the expected number of matches of the pattern 'nj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, w: 2, r: 1}. What is the expected number of occurrences of the pattern 'qr+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 3, q: 1, h: 2}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, q: 1, s: 1, p: 2, b: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, s: 2, k: 3} to form a word, what is the expected number of matches of the pattern 'sk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, a: 1, f: 2, k: 1, i: 1}, what is the expected number of times the pattern 'k+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, a: 3, x: 1, r: 1}, what is the expected number of times the pattern 'ax*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 4, g: 2}. What is the expected number of occurrences of the pattern 'e.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, x: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'lz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, p: 2, y: 1}, what is the expected number of times the pattern 'yw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, q: 2, n: 2}. What is the expected number of occurrences of the pattern 'nq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, q: 3}, what is the expected number of times the pattern 'qg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, h: 1, j: 3, x: 1}. What is the expected number of occurrences of the pattern 'h.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, p: 3, w: 1}. What is the expected number of occurrences of the pattern 'f+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, a: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, y: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'n+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, v: 2, b: 1, e: 1, y: 1}, what is the expected number of times the pattern 'vv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, g: 2, w: 1, r: 1, t: 1}. What is the expected number of occurrences of the pattern 'g+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, j: 1, g: 1, e: 1, c: 1}. What is the expected number of occurrences of the pattern 'z.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'c.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, h: 5}, what is the expected number of times the pattern 'ha+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, k: 3} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, l: 1, y: 2, x: 2}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, s: 1, o: 1, n: 2, p: 1}, what is the expected number of times the pattern 'n+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, s: 1, h: 1, z: 1, y: 2}. What is the expected number of occurrences of the pattern 'ys+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, m: 1, f: 1, x: 1, j: 2}, what is the expected number of times the pattern 'h+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, b: 1, n: 3}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, i: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'i*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, m: 3}. What is the expected number of occurrences of the pattern 'm.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 4, l: 2} to form a word, what is the expected number of matches of the pattern 'k*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, d: 3}, what is the expected number of times the pattern 'n*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, x: 2, j: 2} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, f: 1, b: 2, u: 1}. What is the expected number of occurrences of the pattern 'k.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, l: 1, i: 1, p: 1, q: 1}. What is the expected number of occurrences of the pattern 'pt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, t: 3}. What is the expected number of occurrences of the pattern 'to*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, b: 2, a: 2}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, f: 2, p: 1, z: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, w: 1, g: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'dw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, g: 1, r: 4}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, s: 4} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, w: 2, n: 1, u: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, m: 1, f: 1, w: 2}. What is the expected number of occurrences of the pattern 'k.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, r: 2, v: 2}. What is the expected number of occurrences of the pattern 'kv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, z: 3}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, u: 2, i: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'uu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, c: 1, g: 1, u: 1, y: 2}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, i: 2, w: 1}, what is the expected number of times the pattern 'w.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, k: 3, l: 1, n: 1}. What is the expected number of occurrences of the pattern 'l+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, p: 4} to form a word, what is the expected number of matches of the pattern 'p*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, j: 4} to form a word, what is the expected number of matches of the pattern 'j+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, k: 4}. What is the expected number of occurrences of the pattern 'kg+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 4, o: 2}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, i: 1, r: 3, p: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, p: 2, u: 1}, what is the expected number of times the pattern 'u.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, l: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'x+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, i: 3, f: 2}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, h: 1, q: 2, o: 1, x: 1}. What is the expected number of occurrences of the pattern 'qo*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, p: 2, c: 1, w: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'cf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, f: 4}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, j: 2, q: 3}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, v: 1, h: 1}. What is the expected number of occurrences of the pattern 'uh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, d: 1, m: 1, l: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'j*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, t: 2, v: 1, i: 1, k: 1}. What is the expected number of occurrences of the pattern 'q+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, s: 3}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, x: 2, p: 1, s: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, z: 4} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 4, w: 2}, what is the expected number of times the pattern 'w.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, p: 1, i: 1, r: 2}, what is the expected number of times the pattern 'ib*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 4, i: 2}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, x: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'lx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, j: 4}. What is the expected number of occurrences of the pattern 'k*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, q: 1, a: 1, x: 1, n: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, j: 2, r: 2} to form a word, what is the expected number of matches of the pattern 'd*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 4, u: 2}, what is the expected number of times the pattern 'j*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, p: 2, w: 1, j: 1, t: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, q: 2, g: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, n: 2, z: 1, d: 2}. What is the expected number of occurrences of the pattern 'z+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, z: 3}, what is the expected number of times the pattern 'z+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, c: 2, w: 2, y: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, i: 1, z: 2, p: 1, c: 1}. What is the expected number of occurrences of the pattern 'w+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 3, p: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'f*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 4, l: 2} to form a word, what is the expected number of matches of the pattern 'lh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, r: 3, q: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, l: 1, e: 1, j: 2, a: 1}, what is the expected number of times the pattern 'cl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, s: 1, t: 2, r: 1, c: 1}, what is the expected number of times the pattern 'tc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, v: 1, y: 2, m: 2}. What is the expected number of occurrences of the pattern 'y+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 4, n: 2}. What is the expected number of occurrences of the pattern 'j*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 4, m: 2} to form a word, what is the expected number of matches of the pattern 'g+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, w: 1, t: 2, y: 1}, what is the expected number of times the pattern 'y.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, h: 1, y: 1, d: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 5, s: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, a: 1, o: 1, y: 2, v: 1}. What is the expected number of occurrences of the pattern 'oy*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, f: 3}. What is the expected number of occurrences of the pattern 'fc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, i: 1, h: 1, z: 1, q: 2}, what is the expected number of times the pattern 'z.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'h+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, g: 2, j: 2, c: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, y: 1, s: 1, t: 1, w: 1}. What is the expected number of occurrences of the pattern 'w.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, z: 1, p: 1, y: 1, q: 1}, what is the expected number of times the pattern 'pq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, e: 1, y: 1, f: 2, a: 1}. What is the expected number of occurrences of the pattern 'a+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, t: 4}, what is the expected number of times the pattern 't*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, e: 2, h: 2}. What is the expected number of occurrences of the pattern 'h+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, r: 4} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 5, t: 1}, what is the expected number of times the pattern 't+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, t: 2, l: 1, w: 1}, what is the expected number of times the pattern 'vw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, i: 2, k: 1, r: 1, m: 1}, what is the expected number of times the pattern 'i.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, r: 1, v: 1, g: 1, z: 1}, what is the expected number of times the pattern 'vx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, c: 1, a: 1, w: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'rw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, j: 1, v: 1, t: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, b: 1, s: 1, w: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'dw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, w: 2, o: 3}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 4, k: 2}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, o: 1, z: 1, i: 1, p: 2}. What is the expected number of occurrences of the pattern 'r.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, g: 4}. What is the expected number of occurrences of the pattern 'g+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, e: 1, p: 2, b: 1}, what is the expected number of times the pattern 'e*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, z: 2, e: 1, p: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'x+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 4, t: 2}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, v: 2, x: 1, k: 2}. What is the expected number of occurrences of the pattern 'k.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, p: 3, t: 1}. What is the expected number of occurrences of the pattern 'p*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, g: 3, t: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, h: 1, z: 1, m: 1}. What is the expected number of occurrences of the pattern 'g.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, m: 2, w: 1, c: 2}, what is the expected number of times the pattern 'cd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, x: 3, q: 1, j: 1}. What is the expected number of occurrences of the pattern 'xq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, s: 1, j: 1, m: 1, h: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, h: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, k: 1, x: 2}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'v.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, b: 2, y: 2, z: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, t: 1, g: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'v*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, v: 2, w: 2, b: 1} to form a word, what is the expected number of matches of the pattern 'v.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, r: 2, w: 1, k: 2}, what is the expected number of times the pattern 'k.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, c: 3}. What is the expected number of occurrences of the pattern 'cw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 4, o: 2}, what is the expected number of times the pattern 'o*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, k: 1, r: 1, f: 1, v: 1}, what is the expected number of times the pattern 'f+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, s: 2, b: 2} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, u: 2, b: 3} to form a word, what is the expected number of matches of the pattern 'u*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, m: 1, t: 1, d: 1, c: 1}. What is the expected number of occurrences of the pattern 'ds*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 4, r: 2}. What is the expected number of occurrences of the pattern 'h.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, z: 4, l: 1}, what is the expected number of times the pattern 'l.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, w: 3, j: 1, f: 1}, what is the expected number of times the pattern 'jf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, t: 1, c: 1, f: 1, g: 2}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 5, n: 1} to form a word, what is the expected number of matches of the pattern 'd*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, o: 1, q: 3, y: 1}. What is the expected number of occurrences of the pattern 'y+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, w: 2, a: 1, c: 1}, what is the expected number of times the pattern 'k+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, o: 1, k: 1, s: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'ds+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, w: 3, c: 1, n: 1}, what is the expected number of times the pattern 'wr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, z: 5} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, t: 1, f: 2, e: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'zf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, y: 1, r: 1, m: 2}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, k: 4, f: 1}. What is the expected number of occurrences of the pattern 'nk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, t: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'nt+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, g: 1, s: 3, h: 1}. What is the expected number of occurrences of the pattern 'sh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, n: 3}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, w: 2, e: 3}. What is the expected number of occurrences of the pattern 'w.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, p: 1, v: 1, n: 1, l: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, p: 4} to form a word, what is the expected number of matches of the pattern 'pq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, y: 1, c: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'e*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, r: 1, d: 2, a: 2}. What is the expected number of occurrences of the pattern 'r+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, g: 2, u: 3} to form a word, what is the expected number of matches of the pattern 'u*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, a: 2, i: 1, m: 2}. What is the expected number of occurrences of the pattern 'r*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, h: 1, f: 2, s: 1, z: 1}. What is the expected number of occurrences of the pattern 'sz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, i: 5}, what is the expected number of times the pattern 'r.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, k: 1, f: 1, i: 1, e: 1}. What is the expected number of occurrences of the pattern 'tf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, k: 2, s: 1, t: 1}. What is the expected number of occurrences of the pattern 'ti*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, x: 3, w: 2}. What is the expected number of occurrences of the pattern 'x+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, w: 1, x: 1, u: 2, h: 1}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, b: 2, h: 1, c: 1, w: 1}, what is the expected number of times the pattern 'ha+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, d: 1, j: 2, f: 1}. What is the expected number of occurrences of the pattern 'df*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, f: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'd+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, o: 1, t: 1, r: 2}. What is the expected number of occurrences of the pattern 'te*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, l: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'lz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, i: 3} to form a word, what is the expected number of matches of the pattern 's*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, a: 2, z: 2}, what is the expected number of times the pattern 'a.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, r: 2, y: 2, t: 1}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, m: 3, q: 1, n: 1}. What is the expected number of occurrences of the pattern 'on+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, o: 1, i: 1, n: 1, l: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, g: 1, w: 1, h: 1, s: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, y: 1, v: 1, t: 2, c: 1}, what is the expected number of times the pattern 'vt+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 4, b: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, k: 4}, what is the expected number of times the pattern 'k.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, j: 3, d: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, n: 3, i: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, u: 1, x: 2, b: 1, n: 1}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 4, i: 2}. What is the expected number of occurrences of the pattern 'd+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, u: 4} to form a word, what is the expected number of matches of the pattern 'g+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, v: 1, m: 1, k: 2}. What is the expected number of occurrences of the pattern 'v*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, j: 1, l: 1, b: 1, n: 2}, what is the expected number of times the pattern 'f.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, v: 1, a: 2, c: 1}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, f: 1, s: 3, v: 1}. What is the expected number of occurrences of the pattern 'qf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, d: 2, r: 1, m: 1, w: 1}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, a: 2, x: 1, j: 1}. What is the expected number of occurrences of the pattern 'jx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, c: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'im+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, h: 2, e: 2}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, p: 1, f: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'p.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, s: 1, t: 1, m: 2}, what is the expected number of times the pattern 'd.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, a: 1, f: 3}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, c: 3, h: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 4, c: 2} to form a word, what is the expected number of matches of the pattern 'z*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, h: 1, j: 1, u: 1, i: 1}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, l: 1, t: 2, g: 2}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, x: 1, t: 1, e: 2, z: 1}. What is the expected number of occurrences of the pattern 'ew+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, a: 3, q: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'h+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, e: 3, m: 1, j: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, c: 2, z: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'u*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, k: 2, s: 1, r: 2}, what is the expected number of times the pattern 'ps*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, o: 2, u: 1, x: 1, m: 1}, what is the expected number of times the pattern 'o.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 4, t: 2}, what is the expected number of times the pattern 'at+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, l: 1, u: 1, c: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, n: 3}. What is the expected number of occurrences of the pattern 'na+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, u: 3}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, f: 1, n: 2, y: 1, k: 1}. What is the expected number of occurrences of the pattern 'y+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, d: 2, l: 1, b: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, v: 1, d: 2, r: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, m: 2, t: 2}, what is the expected number of times the pattern 'm+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, k: 1, y: 2, t: 1} to form a word, what is the expected number of matches of the pattern 'o+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 4, e: 2}. What is the expected number of occurrences of the pattern 'ey+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, t: 4}, what is the expected number of times the pattern 'l*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 4, w: 2} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 4, v: 2}, what is the expected number of times the pattern 'k+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, s: 1, x: 1, m: 1, a: 1}, what is the expected number of times the pattern 'ax+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, m: 1, l: 1, d: 1, y: 1}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, q: 3} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, x: 3}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, u: 2, m: 3}, what is the expected number of times the pattern 'cm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, p: 2, u: 1, a: 1, h: 1}. What is the expected number of occurrences of the pattern 'ha*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 4, j: 2}, what is the expected number of times the pattern 'xj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, v: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'vx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, t: 3, q: 1}. What is the expected number of occurrences of the pattern 'q+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, x: 1, o: 1, g: 2}, what is the expected number of times the pattern 'x.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, l: 2, k: 1, e: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'ke*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, m: 1, e: 1, g: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'gq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, l: 2, m: 1, z: 1}, what is the expected number of times the pattern 'za*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, q: 1, a: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, r: 1, t: 1, u: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'g*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, m: 3, e: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, a: 4}. What is the expected number of occurrences of the pattern 'ya+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, t: 3}. What is the expected number of occurrences of the pattern 'k.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, e: 1, j: 1, p: 1, z: 1}, what is the expected number of times the pattern 'p*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, r: 1, h: 1, s: 2, j: 1}. What is the expected number of occurrences of the pattern 'gh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, q: 4}. What is the expected number of occurrences of the pattern 'q+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, v: 1, e: 1, w: 2, k: 1}. What is the expected number of occurrences of the pattern 'w.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, c: 1, h: 1, a: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'e+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 4, q: 2} to form a word, what is the expected number of matches of the pattern 'd*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 4, o: 2}. What is the expected number of occurrences of the pattern 'k.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, g: 1, q: 1, i: 1, t: 2}. What is the expected number of occurrences of the pattern 'gq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, r: 3}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, m: 4}, what is the expected number of times the pattern 'm*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, j: 1, v: 2}. What is the expected number of occurrences of the pattern 'va+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, v: 3}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, c: 4} to form a word, what is the expected number of matches of the pattern 'mc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, d: 2, v: 1, b: 2}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, d: 2, l: 2}. What is the expected number of occurrences of the pattern 'd*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, p: 1, c: 2, z: 1}, what is the expected number of times the pattern 'c+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, v: 1, l: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'm+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, h: 2, i: 3} to form a word, what is the expected number of matches of the pattern 'zh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, l: 2, t: 2, y: 1}, what is the expected number of times the pattern 'ya+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 4, f: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, d: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'dc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, r: 4}. What is the expected number of occurrences of the pattern 'r*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, q: 1, a: 1, r: 1, v: 1}. What is the expected number of occurrences of the pattern 'av+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 4, y: 2} to form a word, what is the expected number of matches of the pattern 'yd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, w: 5}, what is the expected number of times the pattern 'wl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, i: 2, f: 1, p: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'ff+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, y: 1, q: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, p: 2, d: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, v: 2}. What is the expected number of occurrences of the pattern 'vu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, h: 2, p: 1}, what is the expected number of times the pattern 'px+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, g: 1, q: 4}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, m: 3}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, j: 1, l: 2, s: 1, v: 1}. What is the expected number of occurrences of the pattern 'lt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, k: 3}, what is the expected number of times the pattern 'k.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, k: 5}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, w: 4} to form a word, what is the expected number of matches of the pattern 'w+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, p: 1, m: 1, x: 1, q: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, z: 2, b: 2}. What is the expected number of occurrences of the pattern 'jj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, b: 1, v: 2, x: 2}, what is the expected number of times the pattern 'x*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, t: 3, c: 1}. What is the expected number of occurrences of the pattern 't.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, d: 2, y: 1, h: 1, m: 1}. What is the expected number of occurrences of the pattern 'v*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, p: 3} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, s: 1, g: 1, o: 2, h: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, b: 4}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 5, n: 1}, what is the expected number of times the pattern 'cn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, q: 4, p: 1}. What is the expected number of occurrences of the pattern 'q+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, b: 5}, what is the expected number of times the pattern 'f+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, c: 5} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, p: 3, q: 1} to form a word, what is the expected number of matches of the pattern 'q*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, u: 1, x: 1, y: 3}, what is the expected number of times the pattern 'x*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, e: 1, r: 3, d: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 3, z: 3} to form a word, what is the expected number of matches of the pattern 'r+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, n: 2, r: 1, i: 1, j: 1}. What is the expected number of occurrences of the pattern 'ij*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, a: 1, m: 2}, what is the expected number of times the pattern 'ma+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, j: 3} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 4, u: 2} to form a word, what is the expected number of matches of the pattern 'u+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, r: 1, v: 3, u: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, p: 1, m: 1, r: 1}, what is the expected number of times the pattern 'hm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 4, d: 2} to form a word, what is the expected number of matches of the pattern 'w+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, q: 3, y: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, k: 3}, what is the expected number of times the pattern 'k.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, v: 3, s: 1, n: 1}. What is the expected number of occurrences of the pattern 'ns+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 4, s: 2}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, s: 1, h: 2, i: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, w: 1, b: 1, i: 1, y: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, e: 4}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, c: 3, m: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, n: 1, y: 1, h: 1, k: 1}, what is the expected number of times the pattern 'k.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, e: 1, d: 1, a: 1, n: 2}, what is the expected number of times the pattern 'on*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, h: 3}. What is the expected number of occurrences of the pattern 'h.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, s: 4} to form a word, what is the expected number of matches of the pattern 's+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, o: 4}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, j: 3} to form a word, what is the expected number of matches of the pattern 't.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, d: 3}. What is the expected number of occurrences of the pattern 'ds*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, z: 1, m: 1, r: 2}. What is the expected number of occurrences of the pattern 'zt+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, y: 3} to form a word, what is the expected number of matches of the pattern 'wy+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, j: 1, u: 3}. What is the expected number of occurrences of the pattern 'jb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, f: 4}, what is the expected number of times the pattern 'f.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, b: 1, n: 1, g: 2, c: 1}. What is the expected number of occurrences of the pattern 'nc+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, t: 4}. What is the expected number of occurrences of the pattern 't+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, p: 2, s: 1}. What is the expected number of occurrences of the pattern 'y.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, h: 3, r: 1}. What is the expected number of occurrences of the pattern 'h.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, j: 1, s: 1, g: 1, c: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, u: 1, h: 2, s: 2}, what is the expected number of times the pattern 'u*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, l: 1, m: 1, i: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'm.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, h: 3}. What is the expected number of occurrences of the pattern 'h.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, x: 3, p: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, j: 1, v: 1, h: 2, r: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, r: 3, v: 2} to form a word, what is the expected number of matches of the pattern 'v.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, s: 3}. What is the expected number of occurrences of the pattern 's*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, b: 1, w: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'w+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, h: 2, k: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, c: 2, p: 3}. What is the expected number of occurrences of the pattern 'm+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, b: 1, w: 1, j: 1, i: 2}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, w: 1, h: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'n.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, h: 1, c: 2, u: 1, d: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, s: 1, u: 2, d: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'dj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, a: 4}, what is the expected number of times the pattern 'a.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, p: 3, b: 2}, what is the expected number of times the pattern 'ff*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, s: 4} to form a word, what is the expected number of matches of the pattern 'rs*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, q: 1, h: 2, j: 2}. What is the expected number of occurrences of the pattern 'jj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, b: 1, o: 2, s: 2}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, i: 5}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, q: 1, b: 2, o: 2}. What is the expected number of occurrences of the pattern 'k*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, u: 4} to form a word, what is the expected number of matches of the pattern 'uo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, o: 2, z: 1, i: 1, y: 1}. What is the expected number of occurrences of the pattern 'yb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, k: 2, z: 1, s: 1, o: 1}. What is the expected number of occurrences of the pattern 'sm*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, w: 3}. What is the expected number of occurrences of the pattern 'c+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 4, q: 2}. What is the expected number of occurrences of the pattern 'dq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, c: 4, i: 1}, what is the expected number of times the pattern 'c*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, z: 1, f: 4} to form a word, what is the expected number of matches of the pattern 'f+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 4, x: 2}, what is the expected number of times the pattern 'h*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, j: 1, v: 3} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, d: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, b: 3}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, k: 4}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, z: 1, n: 1, e: 1, d: 2}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, g: 3}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, a: 3}, what is the expected number of times the pattern 'va*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, e: 3}. What is the expected number of occurrences of the pattern 'e+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, z: 3} to form a word, what is the expected number of matches of the pattern 'c.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, e: 2, f: 1, n: 2}. What is the expected number of occurrences of the pattern 'nf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, u: 3}. What is the expected number of occurrences of the pattern 'u*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, b: 2, x: 1, m: 2}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, g: 3}. What is the expected number of occurrences of the pattern 'og+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, i: 2, o: 2, c: 1} to form a word, what is the expected number of matches of the pattern 'c+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, b: 3, x: 1} to form a word, what is the expected number of matches of the pattern 'ob+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, g: 1, d: 1, m: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, x: 4} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, g: 1, e: 2, q: 1}. What is the expected number of occurrences of the pattern 'u.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, o: 4}, what is the expected number of times the pattern 'oy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, q: 1, p: 1, i: 3}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, s: 2, g: 2, c: 1} to form a word, what is the expected number of matches of the pattern 'fs+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, m: 1, c: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'fm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, n: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, i: 2, k: 2}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, q: 1, g: 3, v: 1}, what is the expected number of times the pattern 'v+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, q: 3, n: 2} to form a word, what is the expected number of matches of the pattern 'v*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, d: 1, z: 1, v: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'nv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, k: 2, g: 1}, what is the expected number of times the pattern 'ki+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, u: 2, r: 1, z: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, s: 1, d: 2, t: 1}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, v: 1, h: 1, f: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 4, w: 2}. What is the expected number of occurrences of the pattern 'wi+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, e: 3} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, h: 1, c: 1, w: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'c.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, z: 1, w: 3, q: 1} to form a word, what is the expected number of matches of the pattern 'w*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, a: 1, l: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'ae+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, b: 3, u: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, d: 2, f: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'f*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, z: 4}, what is the expected number of times the pattern 'd*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, e: 1, v: 2, k: 1, s: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, i: 2, y: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'ij+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, x: 3}, what is the expected number of times the pattern 'xk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, p: 1, x: 2}. What is the expected number of occurrences of the pattern 'xp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, a: 3, q: 1}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, l: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'l+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, m: 4} to form a word, what is the expected number of matches of the pattern 'mj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, h: 2, o: 2}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, j: 4} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, q: 2, c: 1, a: 1, p: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, n: 1, r: 1, l: 3} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, q: 3, s: 2}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, d: 2, y: 2, w: 1}, what is the expected number of times the pattern 'yd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, j: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'a+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, s: 1, z: 2, r: 2}. What is the expected number of occurrences of the pattern 's.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, k: 2, r: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'e.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, w: 1, t: 1, u: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'tu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, m: 1, n: 1, q: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'um+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 4, l: 2} to form a word, what is the expected number of matches of the pattern 'l+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, f: 1, a: 1, q: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, p: 2, l: 1, d: 1}, what is the expected number of times the pattern 'p.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, u: 5}. What is the expected number of occurrences of the pattern 'u+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, o: 2, w: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, k: 1, r: 2, p: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, x: 3}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, a: 3}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, b: 4, i: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, h: 1, j: 2}, what is the expected number of times the pattern 'p+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, v: 1, e: 2, p: 1, c: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 4, a: 1, x: 1}. What is the expected number of occurrences of the pattern 'x.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, c: 2, z: 2}. What is the expected number of occurrences of the pattern 'za*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, j: 1, q: 1, h: 1, v: 1}, what is the expected number of times the pattern 'kq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, j: 1, k: 3}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, s: 2, l: 1, c: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 3, f: 2, p: 1}. What is the expected number of occurrences of the pattern 'f+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, l: 2, w: 1}, what is the expected number of times the pattern 'r+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, l: 2, o: 2}, what is the expected number of times the pattern 'o.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, d: 1, s: 1, t: 2, l: 1}. What is the expected number of occurrences of the pattern 'dt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, s: 1, z: 1, r: 1, k: 2}, what is the expected number of times the pattern 'sc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, l: 1, g: 2, x: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'l*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, f: 1, v: 3, y: 1}, what is the expected number of times the pattern 'fv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, p: 3, v: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'g*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, s: 1, z: 2, w: 2}, what is the expected number of times the pattern 'sz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, p: 1, e: 1, z: 2, o: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, m: 4}, what is the expected number of times the pattern 'e.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, m: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'mp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, k: 1, r: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'i*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 4, x: 2}. What is the expected number of occurrences of the pattern 'xf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, y: 2, j: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'j*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, j: 1, s: 2, m: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'm*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, r: 1, d: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'd+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, d: 1, g: 1, v: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, u: 2, y: 2, k: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 4, j: 2}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, u: 4, i: 1}, what is the expected number of times the pattern 'u+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, v: 2, c: 2, b: 1}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, y: 1, e: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'e.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, d: 1, n: 2, m: 2}. What is the expected number of occurrences of the pattern 'r+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, r: 2, z: 1, u: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'r+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, r: 3, c: 1, v: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, h: 1, k: 3, q: 1} to form a word, what is the expected number of matches of the pattern 'hq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, p: 1, u: 1, c: 1, x: 1}, what is the expected number of times the pattern 'c.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 4, g: 2}. What is the expected number of occurrences of the pattern 'g+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, h: 1, o: 1, t: 2, i: 1}. What is the expected number of occurrences of the pattern 'lo+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, d: 1, n: 2, q: 1, i: 1}, what is the expected number of times the pattern 'yn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, j: 3} to form a word, what is the expected number of matches of the pattern 'aj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, w: 1, l: 2, v: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'x.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 4, l: 2}, what is the expected number of times the pattern 'l+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, l: 1, v: 1, t: 1, i: 1}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 4, q: 2}, what is the expected number of times the pattern 'qs*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, y: 3}, what is the expected number of times the pattern 'y+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, l: 2, t: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'tv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, z: 2, i: 1, f: 1}, what is the expected number of times the pattern 'z*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, r: 3}, what is the expected number of times the pattern 'jr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, a: 3}. What is the expected number of occurrences of the pattern 'xa+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, i: 3} to form a word, what is the expected number of matches of the pattern 'ci+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, g: 2, f: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'vg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, c: 2, v: 2, z: 1}, what is the expected number of times the pattern 'h+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, w: 1, j: 1, c: 1, h: 2}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, x: 1, f: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, s: 1, b: 3} to form a word, what is the expected number of matches of the pattern 's+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, v: 4}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, w: 1, z: 1, k: 2}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, f: 3, y: 1, j: 1}. What is the expected number of occurrences of the pattern 'y*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, l: 1, r: 4}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, r: 3}, what is the expected number of times the pattern 'u+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, b: 2, h: 2}, what is the expected number of times the pattern 'h*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, p: 1, o: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'l*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, n: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, d: 3}, what is the expected number of times the pattern 'd+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, s: 2, t: 1, h: 1}, what is the expected number of times the pattern 'h.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, g: 1, n: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'p+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, o: 1, w: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, k: 2, a: 1}. What is the expected number of occurrences of the pattern 'ay*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, q: 4}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, t: 1, g: 2}. What is the expected number of occurrences of the pattern 't*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, p: 1, n: 1, c: 1, r: 2}, what is the expected number of times the pattern 'p+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, t: 1, z: 3, k: 1} to form a word, what is the expected number of matches of the pattern 'km+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, z: 3, n: 2}. What is the expected number of occurrences of the pattern 'z*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 4, h: 2}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, f: 2, y: 1, e: 1, h: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, p: 1, x: 2}, what is the expected number of times the pattern 'xn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, r: 2, t: 1, v: 1}. What is the expected number of occurrences of the pattern 'o.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, v: 2, t: 2}, what is the expected number of times the pattern 'tv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, h: 2, c: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'l+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, w: 1, q: 1, c: 2, o: 1}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, u: 2, c: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, d: 3, c: 1} to form a word, what is the expected number of matches of the pattern 'cd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, z: 1, o: 1, r: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'l.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, m: 2, k: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'cm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, c: 2, t: 1, k: 1}, what is the expected number of times the pattern 'pc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 4, n: 2} to form a word, what is the expected number of matches of the pattern 'n+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, e: 1, y: 1, v: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, q: 2, k: 3}. What is the expected number of occurrences of the pattern 'kr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, q: 2, g: 2, s: 1}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, g: 1, i: 1, k: 2, s: 1}, what is the expected number of times the pattern 's+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, t: 4} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, y: 1, t: 3, u: 1}. What is the expected number of occurrences of the pattern 'tj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, k: 3}. What is the expected number of occurrences of the pattern 'q.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, c: 3, u: 1}. What is the expected number of occurrences of the pattern 'c*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, a: 2, z: 2, g: 1}, what is the expected number of times the pattern 'z*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, a: 1, u: 1, j: 2, d: 1}, what is the expected number of times the pattern 'u*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, b: 2, c: 1, w: 1, p: 1}, what is the expected number of times the pattern 'w.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, z: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'h+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, e: 2, o: 1, g: 1}. What is the expected number of occurrences of the pattern 'e+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 4, f: 2}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, w: 1, k: 1, i: 2, f: 1}, what is the expected number of times the pattern 'k+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, j: 3, p: 1, n: 1}. What is the expected number of occurrences of the pattern 'n*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, p: 1, m: 1, e: 1, t: 1}, what is the expected number of times the pattern 'tm+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, z: 4} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, l: 1, w: 1, m: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, i: 3, h: 1}. What is the expected number of occurrences of the pattern 'hi+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, x: 1, e: 2}, what is the expected number of times the pattern 'e+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, c: 2}. What is the expected number of occurrences of the pattern 'c*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 4, c: 2}. What is the expected number of occurrences of the pattern 'm*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 4, q: 2}. What is the expected number of occurrences of the pattern 'qb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, c: 3, f: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, q: 1, h: 2, o: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'u*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, y: 2, b: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'yl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, h: 1, v: 3}. What is the expected number of occurrences of the pattern 'v*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, k: 2, n: 1, w: 1}. What is the expected number of occurrences of the pattern 'vw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, z: 3}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, i: 1, c: 3, n: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 4, a: 2} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, m: 1, h: 1, k: 1}. What is the expected number of occurrences of the pattern 'm.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, a: 1, d: 1, c: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'd*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, d: 2, c: 1, b: 1, l: 1}. What is the expected number of occurrences of the pattern 'tt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, v: 1, j: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, a: 3, t: 2}, what is the expected number of times the pattern 'd+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 4, s: 2} to form a word, what is the expected number of matches of the pattern 's*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, u: 4}, what is the expected number of times the pattern 'e*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 4, z: 1, q: 1}, what is the expected number of times the pattern 'zq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, l: 1, g: 2, r: 1, a: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, u: 3, k: 2}, what is the expected number of times the pattern 'k.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, h: 1, m: 2, f: 2}. What is the expected number of occurrences of the pattern 'h.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, b: 1, n: 3} to form a word, what is the expected number of matches of the pattern 'n*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, m: 1, u: 2, d: 1, q: 1}, what is the expected number of times the pattern 'md*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, o: 3}, what is the expected number of times the pattern 'g+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, n: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'n.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, c: 1, o: 3} to form a word, what is the expected number of matches of the pattern 'xc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, v: 1, s: 1, d: 2}, what is the expected number of times the pattern 'd.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, h: 3, c: 2} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, p: 1, t: 1, k: 1, m: 1} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, f: 1, z: 1, m: 2, x: 1}. What is the expected number of occurrences of the pattern 'f.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, r: 1, v: 1, z: 2}, what is the expected number of times the pattern 'z+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, a: 3}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, w: 2, y: 1, p: 2}. What is the expected number of occurrences of the pattern 'y.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, s: 1, t: 2}, what is the expected number of times the pattern 's*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, h: 1, r: 2, y: 1}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, z: 1, c: 1, t: 1}. What is the expected number of occurrences of the pattern 'tb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, f: 3}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, t: 2, f: 3} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, u: 2, v: 1}. What is the expected number of occurrences of the pattern 'v*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, c: 5} to form a word, what is the expected number of matches of the pattern 'c.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, e: 1, h: 1, z: 1, m: 1}, what is the expected number of times the pattern 'm*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, s: 1, r: 2, y: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, a: 3} to form a word, what is the expected number of matches of the pattern 'qa*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, y: 1, g: 1, c: 1, j: 2} to form a word, what is the expected number of matches of the pattern 'y*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, p: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'pz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, r: 1, j: 1, y: 2, k: 1}. What is the expected number of occurrences of the pattern 'dk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 4, l: 2} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, z: 1, s: 1, b: 2}, what is the expected number of times the pattern 's+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, y: 2, f: 1, k: 1, t: 1}. What is the expected number of occurrences of the pattern 'k+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, z: 1, x: 1, n: 1}. What is the expected number of occurrences of the pattern 'cn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, c: 1, p: 2, x: 1} to form a word, what is the expected number of matches of the pattern 'pc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, u: 2, h: 2, n: 1}. What is the expected number of occurrences of the pattern 'h*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, b: 1, w: 1, v: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'uu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, x: 2, d: 1}, what is the expected number of times the pattern 'dx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, z: 3}, what is the expected number of times the pattern 'h.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, i: 3, g: 2} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, s: 2, t: 1, y: 1}, what is the expected number of times the pattern 'ya*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, a: 5}, what is the expected number of times the pattern 'ma+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, n: 2, l: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, v: 3, p: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, r: 2, g: 1, a: 1, f: 1}. What is the expected number of occurrences of the pattern 'a.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, h: 2, w: 2, s: 1}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 4, j: 2}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, y: 2, u: 1, f: 1}, what is the expected number of times the pattern 'n+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, u: 2, f: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'u+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, n: 4}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, d: 3}. What is the expected number of occurrences of the pattern 'dw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 4, x: 2}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, i: 2, k: 2}. What is the expected number of occurrences of the pattern 'ui+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, s: 1, o: 3, r: 1}, what is the expected number of times the pattern 'ro+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, k: 1, c: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'kt+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, v: 4}, what is the expected number of times the pattern 'v.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, u: 3}. What is the expected number of occurrences of the pattern 'ug+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 4, p: 1, v: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, b: 3}, what is the expected number of times the pattern 'dd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, w: 3}. What is the expected number of occurrences of the pattern 'wk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, m: 3}. What is the expected number of occurrences of the pattern 'r+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, j: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'x.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, x: 1, u: 1, e: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'a+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'x.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, g: 3} to form a word, what is the expected number of matches of the pattern 'gl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, f: 3}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 3, z: 3}. What is the expected number of occurrences of the pattern 'zp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, z: 2, f: 2, w: 1}, what is the expected number of times the pattern 'z.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, p: 1, b: 1, j: 2}. What is the expected number of occurrences of the pattern 'pp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, d: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'dl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, x: 1, s: 4}. What is the expected number of occurrences of the pattern 'w.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, a: 1, d: 2, j: 2} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 4, v: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, t: 2, m: 2, i: 1}, what is the expected number of times the pattern 'im*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 5, z: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, l: 4}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, i: 1, x: 1, o: 1, k: 1}. What is the expected number of occurrences of the pattern 'x+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, a: 1, m: 3}. What is the expected number of occurrences of the pattern 'o*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, z: 3, g: 2}, what is the expected number of times the pattern 'gz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, x: 1, w: 1, p: 1, s: 1}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, o: 2, d: 1, b: 2}, what is the expected number of times the pattern 'd*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, q: 1, z: 1, c: 2}, what is the expected number of times the pattern 'kq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, y: 1, h: 2}, what is the expected number of times the pattern 'e+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, i: 4}. What is the expected number of occurrences of the pattern 'x.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, z: 1, b: 1, s: 3} to form a word, what is the expected number of matches of the pattern 'zb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, a: 3, h: 1}. What is the expected number of occurrences of the pattern 'h+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, y: 1, n: 2, x: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, t: 1, x: 1, p: 3}, what is the expected number of times the pattern 't.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, c: 1, i: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'e.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, x: 1, k: 2, c: 2} to form a word, what is the expected number of matches of the pattern 'cr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, s: 2, b: 1} to form a word, what is the expected number of matches of the pattern 'xx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, i: 1, x: 1, m: 1}, what is the expected number of times the pattern 'fi+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 4, j: 2}. What is the expected number of occurrences of the pattern 'g*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, d: 2, n: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'm*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, s: 1, n: 1, d: 1, c: 2}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, w: 1, s: 2, z: 1, b: 1}, what is the expected number of times the pattern 's+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, n: 1, f: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, o: 2, r: 2}. What is the expected number of occurrences of the pattern 'og*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, t: 3, v: 2}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, e: 3} to form a word, what is the expected number of matches of the pattern 'eb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, a: 1, e: 1, q: 1, d: 1}. What is the expected number of occurrences of the pattern 'q.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, t: 1, h: 2, n: 1, p: 1}. What is the expected number of occurrences of the pattern 'pb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, n: 2, u: 3} to form a word, what is the expected number of matches of the pattern 'n+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, n: 3, i: 1, p: 1}, what is the expected number of times the pattern 'i+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, n: 2, g: 1, q: 1, o: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, x: 2, f: 2, g: 1}, what is the expected number of times the pattern 'f+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, e: 2, c: 1, o: 1, q: 1}. What is the expected number of occurrences of the pattern 'ch+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, q: 4}, what is the expected number of times the pattern 'qp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 4, x: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, t: 1, y: 1, g: 3}, what is the expected number of times the pattern 'gg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, m: 1, f: 3}, what is the expected number of times the pattern 'mb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, q: 1, b: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, k: 1, b: 1, a: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'aa+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, g: 1, q: 1, h: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'a.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, s: 1, o: 2, c: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, e: 1, z: 2, s: 1}, what is the expected number of times the pattern 'e*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, o: 1, e: 1, f: 2, x: 1}, what is the expected number of times the pattern 't*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, g: 3}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, q: 2, u: 2}, what is the expected number of times the pattern 'u+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, i: 2, u: 2, j: 1}, what is the expected number of times the pattern 'in*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, u: 4}. What is the expected number of occurrences of the pattern 'd*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, w: 1, j: 1, b: 3}, what is the expected number of times the pattern 'jb+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, g: 3} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, r: 1, m: 1, w: 1, k: 2}, what is the expected number of times the pattern 'm.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, c: 2, e: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, u: 1, h: 1, n: 3} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, i: 1, h: 2}. What is the expected number of occurrences of the pattern 'h.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, x: 2, o: 1, u: 1}, what is the expected number of times the pattern 'o*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, o: 1, p: 3}, what is the expected number of times the pattern 'o+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, m: 2, o: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'm+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, j: 3, e: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, m: 2, l: 3} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, n: 2, c: 3} to form a word, what is the expected number of matches of the pattern 'zn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, l: 3, y: 1}. What is the expected number of occurrences of the pattern 'lj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, d: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, d: 3}. What is the expected number of occurrences of the pattern 'd.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, b: 2, v: 1, a: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, d: 2, x: 1, i: 1, q: 1}, what is the expected number of times the pattern 'if*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, w: 1, v: 1, y: 2, z: 1}, what is the expected number of times the pattern 'v+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, p: 1, l: 1, z: 2, h: 1}, what is the expected number of times the pattern 'p+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, u: 1, z: 1, m: 2, s: 1}. What is the expected number of occurrences of the pattern 'rs+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, n: 2, d: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'dc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, i: 1, e: 2, s: 2}, what is the expected number of times the pattern 'i.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 3, v: 1, d: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'e.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, m: 1, g: 1, o: 2, r: 1}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, p: 1, b: 3} to form a word, what is the expected number of matches of the pattern 'pp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, y: 1, b: 1, a: 1, e: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, x: 1, i: 1, q: 2, h: 1}. What is the expected number of occurrences of the pattern 'f*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, i: 1, t: 1, v: 3}. What is the expected number of occurrences of the pattern 'lt+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 4, z: 2} to form a word, what is the expected number of matches of the pattern 'fz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, a: 2, h: 1, n: 1}, what is the expected number of times the pattern 'w+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, v: 2, c: 3}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, s: 1, b: 2, w: 2}, what is the expected number of times the pattern 'w*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 4, j: 2} to form a word, what is the expected number of matches of the pattern 'jc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, q: 1, p: 1, y: 3}. What is the expected number of occurrences of the pattern 'qv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, w: 1, o: 2, h: 1}, what is the expected number of times the pattern 'os*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, m: 2, p: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, y: 2, k: 3}, what is the expected number of times the pattern 'y+k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, i: 1, j: 2} to form a word, what is the expected number of matches of the pattern 'g.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, k: 1, d: 2, e: 2} to form a word, what is the expected number of matches of the pattern 'ky*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, m: 3}. What is the expected number of occurrences of the pattern 't+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, v: 1, s: 1, q: 1, c: 2}. What is the expected number of occurrences of the pattern 'v*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, u: 3}, what is the expected number of times the pattern 'ut*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, g: 2, u: 1, q: 1, l: 1}. What is the expected number of occurrences of the pattern 'lu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, e: 1, x: 2, y: 1}, what is the expected number of times the pattern 'ex+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, d: 2, k: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, y: 1, b: 3, d: 1}. What is the expected number of occurrences of the pattern 'n.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, u: 2, t: 2} to form a word, what is the expected number of matches of the pattern 'ut+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 4, v: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, d: 2, b: 1, j: 1}, what is the expected number of times the pattern 'j+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, l: 2, r: 2} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, j: 2, g: 3}, what is the expected number of times the pattern 'g.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, v: 1, b: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, m: 4} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, h: 2, f: 1}. What is the expected number of occurrences of the pattern 'tf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, r: 2, x: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'v*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, o: 2, t: 1}. What is the expected number of occurrences of the pattern 'r+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, n: 1, j: 1, p: 2, w: 1}. What is the expected number of occurrences of the pattern 'w*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, d: 2, e: 2}, what is the expected number of times the pattern 'e.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, h: 3, x: 2} to form a word, what is the expected number of matches of the pattern 'g+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, e: 1, y: 3} to form a word, what is the expected number of matches of the pattern 'e.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, o: 1, e: 1, t: 2, b: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, m: 1, k: 1, v: 1, q: 2} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, g: 1, e: 1, d: 1, x: 2}, what is the expected number of times the pattern 'nx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 4, h: 2}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, e: 2, l: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'ci*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, a: 2, l: 1, i: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, k: 2, j: 1, y: 2}, what is the expected number of times the pattern 'y*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, c: 2, a: 3} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, u: 1, p: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, n: 1, h: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, r: 1, c: 3} to form a word, what is the expected number of matches of the pattern 'cu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, f: 2, m: 3} to form a word, what is the expected number of matches of the pattern 'fg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, u: 5} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, e: 3, c: 1, f: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, h: 1, f: 1, z: 1, r: 1}, what is the expected number of times the pattern 'f+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 4, n: 1, s: 1}, what is the expected number of times the pattern 'es+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, c: 2, u: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'o*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, m: 2, a: 1, i: 2}, what is the expected number of times the pattern 'am+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, u: 1, j: 1, e: 1, h: 2}, what is the expected number of times the pattern 'ze*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, t: 5} to form a word, what is the expected number of matches of the pattern 'o*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, k: 1, a: 2, g: 1, r: 1}. What is the expected number of occurrences of the pattern 'ka*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, s: 1, t: 1, w: 2}, what is the expected number of times the pattern 'ls*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, o: 1, b: 1, l: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'ss*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 4, s: 2} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, j: 1, h: 1, a: 2, r: 1}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, u: 1, c: 2}. What is the expected number of occurrences of the pattern 'u*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, n: 3, g: 1} to form a word, what is the expected number of matches of the pattern 'z*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, x: 1, m: 1, f: 3}. What is the expected number of occurrences of the pattern 'k+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 4, z: 2}. What is the expected number of occurrences of the pattern 'x.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, t: 3} to form a word, what is the expected number of matches of the pattern 'ta+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, q: 1, p: 1, z: 2, f: 1}, what is the expected number of times the pattern 'f+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 5, l: 1}, what is the expected number of times the pattern 'lc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, o: 5} to form a word, what is the expected number of matches of the pattern 'go*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, d: 1, l: 1, i: 1, h: 2}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, e: 2, s: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, t: 2, y: 1, n: 2}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, r: 1, e: 1, g: 1, n: 2}, what is the expected number of times the pattern 'g+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 4, w: 2} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, j: 1, g: 2} to form a word, what is the expected number of matches of the pattern 's.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, m: 2, t: 1, y: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'om+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, y: 1, t: 4} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, b: 1, h: 1, l: 2, y: 1}. What is the expected number of occurrences of the pattern 'zl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, s: 2, m: 2}. What is the expected number of occurrences of the pattern 'm*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, e: 1, c: 2, q: 2} to form a word, what is the expected number of matches of the pattern 'q.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, x: 2, m: 2}. What is the expected number of occurrences of the pattern 'my+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, b: 1, i: 1, m: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'mm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, k: 2, v: 1, o: 1}, what is the expected number of times the pattern 'e.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, t: 3, r: 2}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, s: 1, a: 1, p: 3} to form a word, what is the expected number of matches of the pattern 'p.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, g: 3, r: 2}. What is the expected number of occurrences of the pattern 'g.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, x: 1, c: 2}. What is the expected number of occurrences of the pattern 'xc+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, f: 1, p: 2, x: 2}. What is the expected number of occurrences of the pattern 'fp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, d: 1, j: 1, f: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, y: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'yc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, j: 3, y: 1}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, n: 1, u: 2, y: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'k*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, q: 2, t: 1} to form a word, what is the expected number of matches of the pattern 'o*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, y: 2, i: 2, v: 1}. What is the expected number of occurrences of the pattern 'i+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, s: 1, w: 1, y: 3} to form a word, what is the expected number of matches of the pattern 'q+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, j: 3, v: 2} to form a word, what is the expected number of matches of the pattern 'v.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, a: 4} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'hg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, q: 1, h: 1, c: 2}. What is the expected number of occurrences of the pattern 'hc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, o: 1, v: 1, e: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'eo+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, k: 2, w: 2, x: 1}. What is the expected number of occurrences of the pattern 'kw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, y: 1, a: 1, v: 2, f: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, b: 3}. What is the expected number of occurrences of the pattern 'u.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, o: 1, w: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, x: 1, g: 2, b: 1, r: 1}. What is the expected number of occurrences of the pattern 'l+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, d: 1, s: 1, q: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'q.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, n: 2, k: 1, p: 2}, what is the expected number of times the pattern 'ak*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, q: 3} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, b: 3, w: 2}. What is the expected number of occurrences of the pattern 'y*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, d: 5} to form a word, what is the expected number of matches of the pattern 'ed*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, p: 2, o: 1, x: 1}. What is the expected number of occurrences of the pattern 'j.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, f: 1, c: 2, m: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'c+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, i: 1, y: 1, u: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'is*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, o: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'o+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, l: 2, p: 2}. What is the expected number of occurrences of the pattern 'r*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, p: 2, r: 3}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, x: 1, y: 1, a: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, q: 1, t: 1, g: 1, v: 2}. What is the expected number of occurrences of the pattern 'ig*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, t: 1, a: 2, l: 1, u: 1}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, z: 1, c: 1, s: 1, d: 2}. What is the expected number of occurrences of the pattern 'db+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, n: 4}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, x: 1, k: 1, q: 2, u: 1}. What is the expected number of occurrences of the pattern 'jq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, b: 1, z: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, a: 2, t: 2}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, v: 1, e: 1, l: 1, n: 1}, what is the expected number of times the pattern 'rn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, m: 1, i: 1, g: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'i+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 4, b: 2} to form a word, what is the expected number of matches of the pattern 'pb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, h: 1, s: 1, j: 1, p: 1}, what is the expected number of times the pattern 'jl*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, i: 2, z: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'zj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, x: 1, g: 1, k: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'mk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, q: 1, f: 1, g: 1, u: 2}. What is the expected number of occurrences of the pattern 'dg*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, q: 1, i: 3}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, o: 4, v: 1} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, l: 2, j: 1, r: 2}, what is the expected number of times the pattern 'l*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, p: 1, i: 1, y: 1, w: 2}. What is the expected number of occurrences of the pattern 'wi*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, v: 4}. What is the expected number of occurrences of the pattern 'v*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, w: 1, v: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, g: 3} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, z: 1, j: 1, p: 1, t: 2} to form a word, what is the expected number of matches of the pattern 'zp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, u: 3, p: 2} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 4, k: 2}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, v: 4}, what is the expected number of times the pattern 'y+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, g: 2, a: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'u.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, m: 2, h: 1, y: 1}. What is the expected number of occurrences of the pattern 'y.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, n: 5}. What is the expected number of occurrences of the pattern 'nh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, r: 1, m: 1, l: 1, x: 2}. What is the expected number of occurrences of the pattern 'l.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, k: 2, w: 2, e: 1}. What is the expected number of occurrences of the pattern 'lw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, o: 3}, what is the expected number of times the pattern 'c*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, e: 1, v: 2, y: 2}. What is the expected number of occurrences of the pattern 'qy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, c: 1, m: 2, e: 2}. What is the expected number of occurrences of the pattern 'c*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, i: 1, v: 2}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, d: 1, p: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, j: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'k.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, r: 4}. What is the expected number of occurrences of the pattern 'fr+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, n: 1, u: 2, i: 1}, what is the expected number of times the pattern 'ik+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, u: 3, k: 1}, what is the expected number of times the pattern 'k+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, i: 2, r: 1, m: 1, n: 1}. What is the expected number of occurrences of the pattern 'u+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, c: 4} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, q: 1, z: 3}. What is the expected number of occurrences of the pattern 'zq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, i: 1, a: 1, z: 1, c: 2}, what is the expected number of times the pattern 'a+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, o: 2, l: 1, t: 1}. What is the expected number of occurrences of the pattern 'l.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, z: 3}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, u: 2, a: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'ay*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, h: 3} to form a word, what is the expected number of matches of the pattern 's*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, o: 4}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 3, w: 2, b: 1} to form a word, what is the expected number of matches of the pattern 'w.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, p: 2}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, c: 3}. What is the expected number of occurrences of the pattern 'u+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, r: 3, p: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, y: 1, t: 2}. What is the expected number of occurrences of the pattern 't*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, v: 2, p: 3}, what is the expected number of times the pattern 'wp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, p: 1, z: 2, e: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, w: 2, i: 2}, what is the expected number of times the pattern 'ow*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, n: 3} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, n: 2, w: 3} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, j: 1, p: 2, l: 1}. What is the expected number of occurrences of the pattern 'a*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, z: 3}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, x: 2, g: 1, o: 1, f: 1}. What is the expected number of occurrences of the pattern 'og+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, r: 1, a: 2, b: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'ia+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, r: 1, u: 3, z: 1} to form a word, what is the expected number of matches of the pattern 'z*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, z: 1, q: 1, s: 3}, what is the expected number of times the pattern 'uq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 4, s: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'z*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, r: 2, l: 3}. What is the expected number of occurrences of the pattern 'l+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, y: 3} to form a word, what is the expected number of matches of the pattern 'y.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, k: 1, n: 2, d: 2}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, l: 2, c: 1}. What is the expected number of occurrences of the pattern 'c+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, m: 2, u: 1}, what is the expected number of times the pattern 'u*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, o: 2, u: 1, a: 1, x: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, j: 1, s: 1, v: 1, k: 1}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 5, f: 1}. What is the expected number of occurrences of the pattern 'if*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, d: 2, g: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, o: 1, n: 1, d: 3} to form a word, what is the expected number of matches of the pattern 'o+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, b: 2, j: 1, e: 1}. What is the expected number of occurrences of the pattern 'xb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, y: 2, e: 2}. What is the expected number of occurrences of the pattern 'e+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 4, y: 2} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, g: 1, v: 1, w: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, d: 2, m: 1} to form a word, what is the expected number of matches of the pattern 'd.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, u: 1, w: 1, s: 2, l: 1}, what is the expected number of times the pattern 'y+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, l: 3} to form a word, what is the expected number of matches of the pattern 'li+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, e: 3, m: 1, r: 1}. What is the expected number of occurrences of the pattern 'e+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 4, g: 2}. What is the expected number of occurrences of the pattern 'g+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, r: 2, j: 1, t: 2}, what is the expected number of times the pattern 'y+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, u: 2, s: 1, o: 1, y: 1}. What is the expected number of occurrences of the pattern 'ou+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, k: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'vk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 4, c: 2}. What is the expected number of occurrences of the pattern 'cg+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, v: 2, x: 1}, what is the expected number of times the pattern 'z*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, f: 1, z: 2}. What is the expected number of occurrences of the pattern 'rz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, e: 1, v: 1, g: 1, h: 1}, what is the expected number of times the pattern 'e*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, d: 1, p: 2, i: 1, v: 1}, what is the expected number of times the pattern 'v*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, p: 2, q: 1, t: 2} to form a word, what is the expected number of matches of the pattern 'p*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, p: 1, v: 3}, what is the expected number of times the pattern 'vp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, h: 1, g: 1, w: 1, f: 1}, what is the expected number of times the pattern 'g.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, k: 2, p: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'px+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, r: 3}, what is the expected number of times the pattern 'r+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, x: 2, b: 3}. What is the expected number of occurrences of the pattern 'x*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, l: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'vl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, d: 4}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, g: 1, o: 1, u: 3}, what is the expected number of times the pattern 'ux+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, c: 2, a: 1, v: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, l: 3, j: 2} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, m: 3} to form a word, what is the expected number of matches of the pattern 'm+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, j: 2, r: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, s: 1, j: 2, k: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, x: 1, m: 1, a: 1, k: 1}. What is the expected number of occurrences of the pattern 'i*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, e: 3}, what is the expected number of times the pattern 'me+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, d: 4}, what is the expected number of times the pattern 'u*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, w: 3, s: 2} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, d: 5} to form a word, what is the expected number of matches of the pattern 'dt+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, e: 2, h: 3}. What is the expected number of occurrences of the pattern 'em*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, c: 2, j: 1, o: 1, m: 1}, what is the expected number of times the pattern 'jo+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 4, j: 2}. What is the expected number of occurrences of the pattern 'm+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, s: 4} to form a word, what is the expected number of matches of the pattern 's*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 3, l: 3}. What is the expected number of occurrences of the pattern 'n+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, d: 4} to form a word, what is the expected number of matches of the pattern 'x*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, e: 1, r: 2, v: 1, b: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, g: 1, i: 2, l: 2}, what is the expected number of times the pattern 'vg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, n: 2, l: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'ln*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, p: 2, e: 2, y: 1}, what is the expected number of times the pattern 'ep+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 5, e: 1} to form a word, what is the expected number of matches of the pattern 'k+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, k: 1, v: 1, x: 2, a: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, e: 3}, what is the expected number of times the pattern 'o+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, z: 2, w: 1, t: 1, u: 1}. What is the expected number of occurrences of the pattern 'nw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, p: 1, j: 2, i: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'ip*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 5, q: 1} to form a word, what is the expected number of matches of the pattern 'q+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, r: 1, t: 2, h: 1, d: 1}, what is the expected number of times the pattern 'h+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, g: 1, e: 3} to form a word, what is the expected number of matches of the pattern 'g+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, o: 3}. What is the expected number of occurrences of the pattern 'o+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 4, j: 1, a: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, j: 4} to form a word, what is the expected number of matches of the pattern 'pj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, a: 3, w: 2}, what is the expected number of times the pattern 'wh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, h: 2, s: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, a: 3} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, h: 1, r: 1, x: 1, s: 1}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, u: 1, n: 1, y: 2}. What is the expected number of occurrences of the pattern 'i.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, l: 2, c: 1, t: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'c*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'v.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, n: 1, e: 2}, what is the expected number of times the pattern 'ej*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, i: 2, t: 1, c: 2}. What is the expected number of occurrences of the pattern 't*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, f: 2, s: 1, l: 1, a: 1}. What is the expected number of occurrences of the pattern 's+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 4, f: 2}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, k: 1, i: 4}, what is the expected number of times the pattern 'kl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, t: 3}. What is the expected number of occurrences of the pattern 'tj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, x: 1, v: 2, j: 2}, what is the expected number of times the pattern 'xj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, g: 2, z: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, i: 2, k: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'k+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, r: 4}. What is the expected number of occurrences of the pattern 'r*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, g: 1, b: 1, t: 3}. What is the expected number of occurrences of the pattern 'ng*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, v: 1, y: 2, p: 1}. What is the expected number of occurrences of the pattern 'v*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, s: 2, t: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, v: 3, j: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, f: 1, e: 1, b: 1}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, x: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, g: 1, v: 1, x: 1, s: 2}. What is the expected number of occurrences of the pattern 'a+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, l: 1, b: 1, v: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'l+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, q: 2, c: 1, f: 1, v: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, d: 2}. What is the expected number of occurrences of the pattern 'dt+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, s: 2, d: 1, p: 1}, what is the expected number of times the pattern 'ds*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, q: 2, l: 1, x: 1}, what is the expected number of times the pattern 'q.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, l: 3, c: 1}. What is the expected number of occurrences of the pattern 'lc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, u: 2, o: 1, g: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 4, r: 2}. What is the expected number of occurrences of the pattern 'rs*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, h: 4, t: 1}, what is the expected number of times the pattern 'qt+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 3, h: 3}. What is the expected number of occurrences of the pattern 'h+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, o: 4}, what is the expected number of times the pattern 'w+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, l: 1, i: 2, q: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'ql+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, f: 5}, what is the expected number of times the pattern 'd+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, g: 2, r: 1, i: 2}, what is the expected number of times the pattern 'rv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, b: 1, z: 2, r: 1, e: 1}. What is the expected number of occurrences of the pattern 'u.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, c: 1, x: 1, m: 1, t: 2}, what is the expected number of times the pattern 'tm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, d: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'dp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, i: 3}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, s: 4}, what is the expected number of times the pattern 'rs+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, k: 2, p: 1, h: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'fk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, o: 1, f: 1, t: 2, x: 1}, what is the expected number of times the pattern 'x*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, x: 2, j: 3} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, o: 2, d: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'od*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 3, w: 3}. What is the expected number of occurrences of the pattern 'w.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, n: 4, o: 1}. What is the expected number of occurrences of the pattern 'on+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, b: 2, q: 1, j: 1, d: 1}. What is the expected number of occurrences of the pattern 'dj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, v: 1, e: 4}. What is the expected number of occurrences of the pattern 'v*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 4, c: 2}, what is the expected number of times the pattern 'u+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, a: 3} to form a word, what is the expected number of matches of the pattern 'y+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, v: 1, s: 1, y: 1, p: 1}. What is the expected number of occurrences of the pattern 'vs*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, c: 2, l: 1, v: 1, y: 1}, what is the expected number of times the pattern 'ry+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, u: 1, q: 3}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, o: 1, i: 2, f: 1, v: 1}. What is the expected number of occurrences of the pattern 'oi+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, d: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'zu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, u: 3, i: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, f: 2, w: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, z: 1, w: 2, b: 1}. What is the expected number of occurrences of the pattern 'yb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, x: 1, q: 2, c: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, u: 1, x: 1, l: 1, w: 2}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 4, t: 2} to form a word, what is the expected number of matches of the pattern 't*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, n: 2, d: 1, h: 2}. What is the expected number of occurrences of the pattern 'kn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, l: 1, h: 3}. What is the expected number of occurrences of the pattern 'n+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 4, k: 2}. What is the expected number of occurrences of the pattern 'k+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, w: 1, f: 1, q: 2, y: 1}, what is the expected number of times the pattern 'f.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, e: 2, l: 2}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, p: 1, q: 1, b: 2, e: 1}. What is the expected number of occurrences of the pattern 'db*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, k: 1, a: 1, b: 2}. What is the expected number of occurrences of the pattern 'm+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, d: 2, b: 1, m: 1, t: 1}, what is the expected number of times the pattern 'm*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, d: 1, m: 2}, what is the expected number of times the pattern 'jm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, o: 1, x: 2}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, j: 1, a: 1, u: 1, k: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 4, y: 2}, what is the expected number of times the pattern 'y.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, f: 3} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 5, y: 1} to form a word, what is the expected number of matches of the pattern 'ty+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, j: 2, w: 3} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, y: 3, t: 2}, what is the expected number of times the pattern 't*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, i: 5} to form a word, what is the expected number of matches of the pattern 'qi*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, s: 1, m: 1, u: 1, j: 2} to form a word, what is the expected number of matches of the pattern 'jc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, i: 2, s: 3} to form a word, what is the expected number of matches of the pattern 'ik+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, t: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'j*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, s: 3, c: 1, x: 1}. What is the expected number of occurrences of the pattern 'c+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, w: 1, u: 2, z: 1, j: 1}. What is the expected number of occurrences of the pattern 'w.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, z: 1, g: 1, e: 1, p: 1}. What is the expected number of occurrences of the pattern 'ef*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, e: 1, p: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 4, p: 2} to form a word, what is the expected number of matches of the pattern 'pt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 3, t: 3}, what is the expected number of times the pattern 'y*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, x: 2, u: 1}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, h: 1, g: 1, j: 1, p: 2}, what is the expected number of times the pattern 'gl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, q: 2, c: 3}, what is the expected number of times the pattern 'qu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, i: 2, g: 2}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, l: 2, c: 1, z: 1, j: 1}, what is the expected number of times the pattern 'z+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, k: 2, g: 1, w: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'g.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, k: 1, w: 2, v: 2}, what is the expected number of times the pattern 'w+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, q: 5} to form a word, what is the expected number of matches of the pattern 'q.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, f: 1, n: 1, t: 3}, what is the expected number of times the pattern 'f+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, t: 1, u: 1, x: 1, i: 1}, what is the expected number of times the pattern 'c.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, j: 1, o: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'w+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, x: 2, q: 2, u: 1}. What is the expected number of occurrences of the pattern 'u.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, l: 2, g: 2} to form a word, what is the expected number of matches of the pattern 'gx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, n: 2, j: 1, f: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'a*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, t: 1, g: 2, h: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, y: 2, i: 1, z: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, b: 2, m: 1, h: 2}, what is the expected number of times the pattern 'h+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, f: 3}. What is the expected number of occurrences of the pattern 'fa*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, d: 1, c: 1, q: 2, u: 1}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, r: 1, p: 2, y: 1}. What is the expected number of occurrences of the pattern 'rp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, v: 1, i: 1, c: 2}, what is the expected number of times the pattern 'v.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, m: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'n.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, r: 1, l: 1, a: 2, u: 1}. What is the expected number of occurrences of the pattern 'lu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, i: 1, r: 2, n: 1, g: 1}, what is the expected number of times the pattern 'nr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, y: 2, a: 1}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, t: 1, f: 1, b: 2, j: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 5, h: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, o: 4}, what is the expected number of times the pattern 'ao*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, x: 1, e: 1, r: 1, c: 1} to form a word, what is the expected number of matches of the pattern 're*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, q: 1, p: 1, a: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, n: 1, j: 2, d: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, g: 1, u: 1, w: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'g+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, s: 4} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, y: 1, f: 2, d: 2}, what is the expected number of times the pattern 'f.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, v: 1, r: 1, o: 2}, what is the expected number of times the pattern 'r+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, m: 1, r: 2, j: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, f: 1, r: 2, c: 2}. What is the expected number of occurrences of the pattern 'f+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, u: 1, f: 3}. What is the expected number of occurrences of the pattern 'u.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, t: 1, l: 1, e: 2, m: 1} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, t: 1, k: 1, e: 1, a: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, p: 3} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, c: 4}, what is the expected number of times the pattern 'e+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, h: 2, o: 1, x: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'mx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, w: 2, y: 2, n: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, m: 1, c: 4} to form a word, what is the expected number of matches of the pattern 'mz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, f: 1, r: 2, m: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, j: 4}. What is the expected number of occurrences of the pattern 'j*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, w: 1, e: 1, a: 1, c: 1}, what is the expected number of times the pattern 'c.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, e: 1, v: 1, s: 1, y: 2}, what is the expected number of times the pattern 'yk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, y: 1, r: 1, q: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'rq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, z: 2, p: 2, s: 1}. What is the expected number of occurrences of the pattern 'ps+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, s: 3, y: 1, i: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, g: 1, c: 1, d: 1, h: 2}. What is the expected number of occurrences of the pattern 'h+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, r: 1, y: 1, n: 1, h: 1}, what is the expected number of times the pattern 'y.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, v: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'k*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, v: 1, r: 1, d: 2, g: 1}. What is the expected number of occurrences of the pattern 'dr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, y: 2, x: 2, h: 1}. What is the expected number of occurrences of the pattern 'yh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, m: 1, g: 1, j: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'am*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, h: 3}. What is the expected number of occurrences of the pattern 'a+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, f: 5}. What is the expected number of occurrences of the pattern 'c+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, i: 5}. What is the expected number of occurrences of the pattern 'i+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, z: 1, x: 1, s: 2, c: 1}, what is the expected number of times the pattern 'zz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 4, g: 2}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, s: 1, n: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'n.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, k: 1, y: 1, t: 1, p: 1}, what is the expected number of times the pattern 'y*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, g: 2, r: 1, d: 1, i: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, w: 2, i: 3}, what is the expected number of times the pattern 'o*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, m: 1, v: 1, g: 1, q: 2}, what is the expected number of times the pattern 'k.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, q: 2, o: 1}. What is the expected number of occurrences of the pattern 'qr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, w: 2, x: 3}. What is the expected number of occurrences of the pattern 'j*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, a: 1, y: 3}. What is the expected number of occurrences of the pattern 'y.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, t: 3, u: 1, e: 1} to form a word, what is the expected number of matches of the pattern 't+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, p: 1, h: 1, n: 1}, what is the expected number of times the pattern 'hn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, e: 2, s: 3} to form a word, what is the expected number of matches of the pattern 's*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 4, y: 2} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, n: 3}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, u: 1, z: 1, e: 3}, what is the expected number of times the pattern 'z+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, v: 1, z: 2, k: 1, l: 1}, what is the expected number of times the pattern 'v+k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, p: 1, i: 1, s: 2}. What is the expected number of occurrences of the pattern 'pq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, r: 1, f: 1, v: 2, t: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, k: 2, z: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'zv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'dh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 4, i: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, g: 1, a: 1, r: 1}. What is the expected number of occurrences of the pattern 'xg*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 3, o: 2, u: 1}, what is the expected number of times the pattern 'ou+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, f: 3}, what is the expected number of times the pattern 'f+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, k: 2, f: 1, p: 1, l: 1}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, g: 1, j: 1, w: 1, l: 2}, what is the expected number of times the pattern 'w*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, n: 2, p: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'kn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, x: 1, j: 1, r: 1, o: 1}, what is the expected number of times the pattern 'rx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, q: 2, k: 3}, what is the expected number of times the pattern 'k.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 4, g: 2} to form a word, what is the expected number of matches of the pattern 'o*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, k: 2, z: 1, m: 1, c: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, k: 2, f: 3}, what is the expected number of times the pattern 'w.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, i: 2, s: 2}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, s: 1, x: 1, n: 3}. What is the expected number of occurrences of the pattern 'ws+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, y: 3, d: 2} to form a word, what is the expected number of matches of the pattern 'dy*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, y: 2, n: 1, s: 1}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, e: 2, n: 1, r: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, o: 2, t: 2}. What is the expected number of occurrences of the pattern 'u*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, c: 2, f: 2} to form a word, what is the expected number of matches of the pattern 'jf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, d: 3} to form a word, what is the expected number of matches of the pattern 'dn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, r: 4}, what is the expected number of times the pattern 'r+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, x: 3, a: 1}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, k: 1, v: 1, u: 1, b: 1}. What is the expected number of occurrences of the pattern 'vb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 5, j: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 4, u: 2}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, f: 1, n: 2, u: 2}, what is the expected number of times the pattern 'n.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, x: 3}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, m: 3, a: 1, r: 1}. What is the expected number of occurrences of the pattern 'a+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, z: 1, d: 3, g: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, g: 1, b: 3}. What is the expected number of occurrences of the pattern 'p+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, y: 3, f: 2}, what is the expected number of times the pattern 'yf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, r: 2, b: 1, z: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, k: 2, s: 2}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, c: 1, b: 1, t: 1, e: 2}. What is the expected number of occurrences of the pattern 'ct*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, p: 2, j: 1, l: 1}, what is the expected number of times the pattern 'wj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, e: 4}, what is the expected number of times the pattern 'i*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, x: 4} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, z: 3} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 4, f: 2} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, u: 1, e: 4}. What is the expected number of occurrences of the pattern 'u.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, p: 5} to form a word, what is the expected number of matches of the pattern 'op+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, e: 2, f: 1, a: 1, w: 1}, what is the expected number of times the pattern 'aw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, e: 1, v: 4}, what is the expected number of times the pattern 'oe+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 4, y: 2} to form a word, what is the expected number of matches of the pattern 'y*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, h: 3}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, y: 1, o: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, s: 1, o: 3} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, t: 1, d: 3, i: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, d: 1, t: 2, c: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 4, t: 1, h: 1}. What is the expected number of occurrences of the pattern 'tb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, m: 2}. What is the expected number of occurrences of the pattern 'tm*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, v: 3}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, n: 1, a: 1, b: 1, l: 1}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, v: 3, z: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, a: 1, u: 2, m: 1, z: 1}. What is the expected number of occurrences of the pattern 'z+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, l: 2, i: 1, m: 1, j: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, r: 3}, what is the expected number of times the pattern 'z+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, q: 3, l: 2} to form a word, what is the expected number of matches of the pattern 'l+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, g: 3}. What is the expected number of occurrences of the pattern 'k*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, n: 1, j: 3}, what is the expected number of times the pattern 'n*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, k: 1, f: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, p: 2, m: 2}, what is the expected number of times the pattern 'pf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, i: 4} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, a: 3}, what is the expected number of times the pattern 'a.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, r: 2, l: 2}. What is the expected number of occurrences of the pattern 'v.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, t: 4}, what is the expected number of times the pattern 't*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, s: 3, x: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, m: 3, q: 2} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, i: 3, j: 2}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, v: 1, x: 2}, what is the expected number of times the pattern 'ov+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, o: 2, t: 1}. What is the expected number of occurrences of the pattern 'ob+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 4, s: 2}, what is the expected number of times the pattern 'y.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, c: 1, r: 1, i: 1}, what is the expected number of times the pattern 'z.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, d: 3} to form a word, what is the expected number of matches of the pattern 'od+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, q: 1, k: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'ka+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 4, v: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, q: 4}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 5, k: 1} to form a word, what is the expected number of matches of the pattern 'k+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, j: 1, z: 2, b: 2}, what is the expected number of times the pattern 'w+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, j: 3, q: 2}, what is the expected number of times the pattern 'qj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, d: 2, h: 1, k: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'do+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, o: 3}, what is the expected number of times the pattern 'to*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, v: 3}. What is the expected number of occurrences of the pattern 'wv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, g: 2, t: 3}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, v: 1, g: 1, a: 1, z: 2}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, f: 3}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, r: 1, f: 1, x: 1, s: 1}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, l: 1, t: 1, d: 2}, what is the expected number of times the pattern 'tl*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, r: 1, q: 2, z: 2}. What is the expected number of occurrences of the pattern 'qh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, l: 2, q: 1, p: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'q+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, t: 2, m: 2, d: 1}, what is the expected number of times the pattern 'w.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, o: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'lt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, r: 1, g: 1, b: 2, c: 1}. What is the expected number of occurrences of the pattern 'rm*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 4, t: 2}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 5, n: 1}. What is the expected number of occurrences of the pattern 'jn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, u: 1, n: 1, g: 3} to form a word, what is the expected number of matches of the pattern 'g*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, v: 4}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, w: 2, u: 1}, what is the expected number of times the pattern 'w+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, m: 2, v: 1, n: 2}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 4, l: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'v+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, w: 2, q: 1, b: 1, s: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, o: 1, i: 3}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, z: 1, y: 1, n: 1, i: 2}. What is the expected number of occurrences of the pattern 'i+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 3, u: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, h: 3}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, k: 3} to form a word, what is the expected number of matches of the pattern 'k*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, u: 2, o: 1, d: 2}. What is the expected number of occurrences of the pattern 'oe+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, j: 1, m: 1, a: 2}, what is the expected number of times the pattern 'mc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, h: 4}, what is the expected number of times the pattern 'x.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, g: 2, s: 1, n: 2}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, q: 1, o: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'qo+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, q: 2, t: 2} to form a word, what is the expected number of matches of the pattern 'qr+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, o: 2, q: 1, s: 1, v: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, g: 1, s: 1, m: 2, c: 1} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, p: 2, k: 1, d: 1, l: 1}. What is the expected number of occurrences of the pattern 'pk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, v: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, l: 2, m: 1, e: 1, f: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, s: 2, q: 2} to form a word, what is the expected number of matches of the pattern 'sz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, p: 1, l: 1, i: 2, x: 1}, what is the expected number of times the pattern 'xw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, p: 2, f: 1, g: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'pm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, q: 2, o: 1, d: 1}. What is the expected number of occurrences of the pattern 'i.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, z: 3}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, t: 2, j: 1, p: 1, m: 1}, what is the expected number of times the pattern 'j*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, h: 2, f: 2} to form a word, what is the expected number of matches of the pattern 'pf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, k: 2, e: 2, s: 1}, what is the expected number of times the pattern 'k+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, q: 4} to form a word, what is the expected number of matches of the pattern 'q+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, p: 2, c: 3} to form a word, what is the expected number of matches of the pattern 'c+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, q: 2, d: 1, a: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'da+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, n: 2, d: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, g: 1, o: 2, i: 1}. What is the expected number of occurrences of the pattern 'og*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, s: 5} to form a word, what is the expected number of matches of the pattern 's.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, k: 2, r: 2, q: 1}. What is the expected number of occurrences of the pattern 'kq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, k: 1, p: 1, q: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'p.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, z: 1, w: 1, g: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'vw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, c: 2, t: 3}. What is the expected number of occurrences of the pattern 'c+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, h: 3}, what is the expected number of times the pattern 'm+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, z: 2, i: 1, h: 1}, what is the expected number of times the pattern 'y.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, f: 1, q: 2, o: 1, e: 1}. What is the expected number of occurrences of the pattern 'co*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, p: 3, g: 1}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, i: 3, d: 2}, what is the expected number of times the pattern 'd+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, m: 1, i: 1, d: 1, o: 2}. What is the expected number of occurrences of the pattern 'io+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, m: 1, a: 1, r: 2, x: 1}, what is the expected number of times the pattern 'a+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, v: 2, k: 1}. What is the expected number of occurrences of the pattern 'vt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, s: 3, f: 1} to form a word, what is the expected number of matches of the pattern 'f*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, z: 1, x: 1, u: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'vz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, r: 3, y: 1}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, q: 2, j: 1, b: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'ee+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, n: 3} to form a word, what is the expected number of matches of the pattern 'n+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, o: 1, w: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'n+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, h: 2, o: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'n+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, p: 1, r: 3, n: 1}, what is the expected number of times the pattern 'rq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, z: 2, d: 2}. What is the expected number of occurrences of the pattern 'fz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, g: 1, o: 1, j: 1, k: 2}. What is the expected number of occurrences of the pattern 'gk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, g: 2, l: 2, q: 1}, what is the expected number of times the pattern 'd.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, m: 1, j: 2, c: 2}. What is the expected number of occurrences of the pattern 'j.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, w: 1, s: 2}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 4, l: 2}. What is the expected number of occurrences of the pattern 'vl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, p: 1, c: 3}, what is the expected number of times the pattern 'j+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, l: 3}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, p: 4}, what is the expected number of times the pattern 'p.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, m: 1, t: 2, j: 1, k: 1}, what is the expected number of times the pattern 't*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 4, p: 2}. What is the expected number of occurrences of the pattern 'p*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, m: 4} to form a word, what is the expected number of matches of the pattern 'im*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, u: 1, p: 1, q: 1, i: 1}. What is the expected number of occurrences of the pattern 'iu+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, q: 1, k: 1, v: 1, m: 1}, what is the expected number of times the pattern 'm+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, f: 3} to form a word, what is the expected number of matches of the pattern 'v.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, w: 1, y: 1, a: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'yw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, h: 2, l: 1}, what is the expected number of times the pattern 'lo*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, q: 1, l: 3} to form a word, what is the expected number of matches of the pattern 'ld*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, a: 1, x: 2, w: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 3, f: 3}. What is the expected number of occurrences of the pattern 'fp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, y: 2, a: 1, b: 1, v: 1}. What is the expected number of occurrences of the pattern 'v+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, e: 1, f: 1, b: 1, p: 2}, what is the expected number of times the pattern 'f+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, y: 1, e: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'y.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, w: 1, b: 1, s: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'fs*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, f: 1, l: 2, x: 2}. What is the expected number of occurrences of the pattern 'x+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, q: 4}. What is the expected number of occurrences of the pattern 'q*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, j: 1, o: 2, z: 1, a: 1}. What is the expected number of occurrences of the pattern 'zj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, g: 2, t: 2}, what is the expected number of times the pattern 'gt*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, f: 2, t: 3}. What is the expected number of occurrences of the pattern 'f*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, b: 2, r: 1, k: 2}, what is the expected number of times the pattern 'k+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, u: 1, n: 1, r: 1, b: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, e: 3, g: 1}. What is the expected number of occurrences of the pattern 'ge*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, n: 1, r: 2, b: 1, c: 1}. What is the expected number of occurrences of the pattern 'n+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, z: 2, l: 2} to form a word, what is the expected number of matches of the pattern 'z+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, j: 1, f: 1, v: 3}, what is the expected number of times the pattern 'j*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, t: 2, z: 1, l: 2}, what is the expected number of times the pattern 't*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, k: 4} to form a word, what is the expected number of matches of the pattern 'xk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, r: 3, e: 1}, what is the expected number of times the pattern 're+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 4, c: 1, g: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, z: 2, p: 2, l: 1}. What is the expected number of occurrences of the pattern 'yp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, m: 4}, what is the expected number of times the pattern 'u*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, e: 2, m: 1, t: 1, u: 1}. What is the expected number of occurrences of the pattern 'o*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, z: 1, t: 1, o: 1, a: 1}, what is the expected number of times the pattern 'z*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, k: 2, p: 1, l: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'i+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, j: 1, e: 1, q: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, k: 1, v: 1, y: 1, w: 1}, what is the expected number of times the pattern 'w+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, p: 2, u: 1}, what is the expected number of times the pattern 'pu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, z: 2, v: 3} to form a word, what is the expected number of matches of the pattern 'z*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, y: 1, s: 1, r: 1, j: 2}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, y: 2, n: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, j: 3, h: 1, i: 1}, what is the expected number of times the pattern 'm.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 5, r: 1} to form a word, what is the expected number of matches of the pattern 'r+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, l: 2, n: 1, s: 1}. What is the expected number of occurrences of the pattern 'a*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, f: 4}. What is the expected number of occurrences of the pattern 'vf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, r: 4}, what is the expected number of times the pattern 'i.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 4, f: 1, s: 1}, what is the expected number of times the pattern 'sc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, a: 2, i: 2}. What is the expected number of occurrences of the pattern 'ai+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, s: 1, a: 2, e: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, l: 1, w: 2, i: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'li*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, t: 2, m: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'd.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, i: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'i.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, n: 1, m: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'pn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, i: 1, f: 1, d: 1, x: 2}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 5, p: 1} to form a word, what is the expected number of matches of the pattern 'a+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, k: 1, v: 1, o: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, a: 2, g: 1, n: 2}, what is the expected number of times the pattern 'gn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, t: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'v.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, m: 1, w: 2, s: 1, v: 1}, what is the expected number of times the pattern 'aw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'd.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, f: 3}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, f: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, p: 1, h: 3}, what is the expected number of times the pattern 'p.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, y: 2, v: 2}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, c: 2, h: 3} to form a word, what is the expected number of matches of the pattern 'h.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, t: 1, m: 4}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, t: 4}. What is the expected number of occurrences of the pattern 't.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, p: 2, v: 1, q: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'q.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, w: 3, k: 2} to form a word, what is the expected number of matches of the pattern 'm+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, f: 3} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 4, r: 2}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, y: 2, v: 2}, what is the expected number of times the pattern 'y+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, d: 2, o: 1, t: 1, p: 1} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, y: 2, r: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'y*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, i: 1, k: 1, t: 2, m: 1}, what is the expected number of times the pattern 'm*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, r: 2, q: 2}, what is the expected number of times the pattern 'q*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, h: 4}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, c: 1, m: 1, f: 1, j: 1}, what is the expected number of times the pattern 'mp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, b: 3}, what is the expected number of times the pattern 'cc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, h: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, r: 1, j: 1, h: 1, t: 1}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, u: 2, y: 1, a: 1, k: 1}. What is the expected number of occurrences of the pattern 'yk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, t: 3, n: 1}, what is the expected number of times the pattern 't+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, f: 4}, what is the expected number of times the pattern 'f*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 4, x: 2} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, x: 2, j: 3}. What is the expected number of occurrences of the pattern 'xj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, h: 1, s: 2, c: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, m: 1, v: 1, l: 3}, what is the expected number of times the pattern 'lv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, w: 1, y: 2, t: 2}. What is the expected number of occurrences of the pattern 'tl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, o: 2, c: 2}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, z: 1, q: 1, l: 1, o: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, t: 3} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, e: 4, i: 1} to form a word, what is the expected number of matches of the pattern 'i.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, v: 2, l: 1, m: 2}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, d: 2, q: 1, n: 1, o: 1}, what is the expected number of times the pattern 'no*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, j: 4}, what is the expected number of times the pattern 'o+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, o: 2, e: 2} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, y: 1, v: 1, f: 1, t: 1}, what is the expected number of times the pattern 'f.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, r: 2, x: 2}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, o: 1, v: 2, e: 1, l: 1}, what is the expected number of times the pattern 'o+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, y: 4}, what is the expected number of times the pattern 'z*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, b: 3, x: 1, s: 1}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, l: 1, f: 4} to form a word, what is the expected number of matches of the pattern 'of+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 4, q: 2}. What is the expected number of occurrences of the pattern 'q.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, e: 1, q: 2, f: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'eq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, k: 2, w: 1, b: 1, v: 1}. What is the expected number of occurrences of the pattern 'g+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, g: 3}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, n: 3}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, e: 4}, what is the expected number of times the pattern 'e*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, y: 3}. What is the expected number of occurrences of the pattern 'y+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, i: 3, g: 1, c: 1}. What is the expected number of occurrences of the pattern 'z+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, k: 3} to form a word, what is the expected number of matches of the pattern 'kc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, a: 2, b: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, x: 1, b: 2, n: 1, j: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, t: 1, y: 2, q: 2}. What is the expected number of occurrences of the pattern 'y+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, j: 1, a: 1, d: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'an*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, n: 2, p: 1, d: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, d: 3, z: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, x: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'x.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, k: 3}. What is the expected number of occurrences of the pattern 'o.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, r: 1, q: 2, p: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, k: 3, q: 1, p: 1}, what is the expected number of times the pattern 'p+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, o: 2, s: 2}, what is the expected number of times the pattern 'y+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, b: 3}, what is the expected number of times the pattern 'q*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, w: 2, k: 2, q: 1}. What is the expected number of occurrences of the pattern 'q+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, b: 3}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, k: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'dk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, m: 1, i: 1, n: 2}, what is the expected number of times the pattern 'a.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, o: 3, v: 2}, what is the expected number of times the pattern 'o*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, v: 2, a: 1, k: 1, i: 1}. What is the expected number of occurrences of the pattern 'k.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, w: 1, n: 1, m: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'wm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, k: 1, l: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'kl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, b: 2, n: 1, u: 1}. What is the expected number of occurrences of the pattern 'u*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, f: 1, r: 2, q: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, z: 1, q: 1, m: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, m: 4}. What is the expected number of occurrences of the pattern 'm*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, v: 1, r: 1, k: 2, p: 1}, what is the expected number of times the pattern 'p*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'hv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 4, u: 2} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, r: 1, m: 4}. What is the expected number of occurrences of the pattern 'q*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, j: 2, t: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'v+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, e: 4} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, v: 2, m: 2, l: 1}, what is the expected number of times the pattern 'vl*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, z: 1, b: 1, x: 3}, what is the expected number of times the pattern 'n.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, l: 1, n: 2, i: 1, j: 1}, what is the expected number of times the pattern 'ji+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, v: 1, r: 1, f: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, e: 1, r: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'rv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, j: 2, v: 3}. What is the expected number of occurrences of the pattern 'v.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, b: 1, y: 1, z: 3}. What is the expected number of occurrences of the pattern 'yt+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, r: 2, d: 1, i: 1, v: 1}. What is the expected number of occurrences of the pattern 'q*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, u: 3, t: 1, p: 1}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, b: 1, h: 1, r: 1, m: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, j: 1, n: 2}, what is the expected number of times the pattern 'h+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 4, y: 2}, what is the expected number of times the pattern 'v*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, p: 1, r: 2, j: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, b: 3, q: 2}, what is the expected number of times the pattern 'pq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, x: 2, s: 3} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, o: 1, i: 3}, what is the expected number of times the pattern 'k+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, h: 3, r: 1, d: 1}, what is the expected number of times the pattern 'dr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, g: 4}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, p: 4} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, x: 2, e: 2} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, p: 1, n: 4} to form a word, what is the expected number of matches of the pattern 'pz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, x: 3, w: 1, n: 1}, what is the expected number of times the pattern 'wn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, j: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'jc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, m: 1, f: 1, g: 1, w: 1}. What is the expected number of occurrences of the pattern 'w+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 4, d: 2}, what is the expected number of times the pattern 'w+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, d: 2, t: 1, w: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, r: 3, x: 2}, what is the expected number of times the pattern 'r*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, q: 2, d: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, u: 1, m: 2, j: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'j+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, k: 5}, what is the expected number of times the pattern 'qk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, g: 1, h: 3}. What is the expected number of occurrences of the pattern 'g+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, o: 4}, what is the expected number of times the pattern 'o*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, k: 2, h: 1, l: 2}. What is the expected number of occurrences of the pattern 'k.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, h: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'rc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, q: 2, c: 1, v: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'v*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 4, x: 2}, what is the expected number of times the pattern 'h+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, y: 1, a: 2, t: 1, v: 1}. What is the expected number of occurrences of the pattern 'av*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, t: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'so*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, n: 2, y: 3} to form a word, what is the expected number of matches of the pattern 'yn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, f: 1, d: 1, l: 1, z: 2}. What is the expected number of occurrences of the pattern 'd+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, w: 2, l: 2}, what is the expected number of times the pattern 'l*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, x: 2, a: 2}. What is the expected number of occurrences of the pattern 'ea+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, r: 1, l: 2, y: 2}, what is the expected number of times the pattern 'l.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, l: 3, u: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 4, w: 2} to form a word, what is the expected number of matches of the pattern 'w*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, s: 2, r: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, o: 1, y: 3} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, t: 1, f: 3} to form a word, what is the expected number of matches of the pattern 't.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, n: 2, f: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, j: 1, m: 1, r: 1}. What is the expected number of occurrences of the pattern 'm+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, c: 2, y: 1, d: 2}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, g: 2, l: 1, r: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'l+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, w: 2, r: 1, s: 1, g: 1} to form a word, what is the expected number of matches of the pattern 's+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 5, y: 1}, what is the expected number of times the pattern 'd.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, h: 1, m: 1, o: 1, n: 2}, what is the expected number of times the pattern 'mu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, p: 2, h: 1, s: 1}. What is the expected number of occurrences of the pattern 'h.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, d: 1, x: 1, v: 1, s: 2}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, h: 2, y: 1, z: 1, n: 1}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, l: 2, y: 1, c: 1, m: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, g: 2, e: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'g*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, x: 1, n: 1, q: 2, y: 1}, what is the expected number of times the pattern 'u*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, e: 2, l: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, d: 1, z: 2, b: 1}, what is the expected number of times the pattern 'l*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, s: 1, z: 1, t: 1, c: 2}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, c: 1, v: 3} to form a word, what is the expected number of matches of the pattern 'v.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, t: 1, y: 1, z: 1, o: 2}, what is the expected number of times the pattern 'ou+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, t: 3, a: 1, q: 1}. What is the expected number of occurrences of the pattern 'm+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, f: 1, c: 1, a: 1, b: 1}, what is the expected number of times the pattern 'c*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, b: 4}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, s: 1, w: 1, c: 1, q: 1}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, u: 3, l: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, h: 1, g: 1, e: 2, t: 1}, what is the expected number of times the pattern 'q.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, v: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'iv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, j: 1, u: 3}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, s: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'hs+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, t: 4} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, h: 3}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, e: 1, w: 1, f: 2, m: 1}. What is the expected number of occurrences of the pattern 'cf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 4, p: 2}. What is the expected number of occurrences of the pattern 'a+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 4, l: 1, n: 1}, what is the expected number of times the pattern 'nu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, z: 1, t: 1, r: 2, m: 1}. What is the expected number of occurrences of the pattern 'i.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, q: 1, x: 1, f: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, y: 1, t: 1, e: 1, a: 2}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, l: 3, z: 2}, what is the expected number of times the pattern 'l+k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, y: 1, z: 1, u: 1, v: 1}, what is the expected number of times the pattern 'y.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, s: 4}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, s: 1, x: 1, z: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, l: 1, s: 4}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, x: 1, y: 2, a: 1}, what is the expected number of times the pattern 'v*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, e: 4}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, i: 1, w: 1, s: 1, q: 1}. What is the expected number of occurrences of the pattern 'q.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, e: 1, m: 1}. What is the expected number of occurrences of the pattern 'm+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, p: 1, h: 1, d: 1, r: 2}. What is the expected number of occurrences of the pattern 'p+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, j: 2, f: 2} to form a word, what is the expected number of matches of the pattern 'jf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, b: 2, j: 3}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, m: 2, r: 2}, what is the expected number of times the pattern 'rm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, g: 2, d: 3}. What is the expected number of occurrences of the pattern 'ug*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, q: 2, v: 1, e: 1, y: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, q: 3, r: 1, m: 1}. What is the expected number of occurrences of the pattern 'u+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, s: 3}. What is the expected number of occurrences of the pattern 'ts+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, b: 5}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, v: 1, m: 1, r: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'm*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, n: 2, c: 2, x: 1}. What is the expected number of occurrences of the pattern 'cy*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'x.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 4, v: 2} to form a word, what is the expected number of matches of the pattern 'v*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, o: 1, d: 2, r: 1, j: 1}. What is the expected number of occurrences of the pattern 'od+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, h: 3, w: 2}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, u: 1, l: 3, v: 1} to form a word, what is the expected number of matches of the pattern 'vl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 4, r: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'v+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, u: 1, b: 2, i: 1}, what is the expected number of times the pattern 'd*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, n: 2, s: 2, r: 1}. What is the expected number of occurrences of the pattern 'r+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, e: 2, l: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, r: 1, z: 3}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, z: 1, a: 2, o: 1, h: 1}. What is the expected number of occurrences of the pattern 'h+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, h: 3, d: 1}. What is the expected number of occurrences of the pattern 'd.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, r: 2, p: 1}, what is the expected number of times the pattern 'rb+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, b: 1, k: 1, n: 2}. What is the expected number of occurrences of the pattern 'r+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, s: 3, k: 1}. What is the expected number of occurrences of the pattern 's.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, k: 2, n: 1, i: 1, f: 1}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 4, w: 2} to form a word, what is the expected number of matches of the pattern 'mw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, l: 2, a: 1}, what is the expected number of times the pattern 'ae*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, w: 3}. What is the expected number of occurrences of the pattern 'lw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, k: 1, i: 2, j: 2} to form a word, what is the expected number of matches of the pattern 'ji*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, t: 1, c: 2, h: 1}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, i: 1, y: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, c: 1, r: 1, l: 1, t: 2} to form a word, what is the expected number of matches of the pattern 'tl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, v: 2, o: 2}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, p: 4, l: 1}. What is the expected number of occurrences of the pattern 'l.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, k: 2, v: 1, z: 1, d: 1}. What is the expected number of occurrences of the pattern 'zk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, h: 1, k: 1, l: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'rh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, v: 2, q: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'sv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, s: 1, a: 3, y: 1}, what is the expected number of times the pattern 'a+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, p: 2, z: 1}. What is the expected number of occurrences of the pattern 'z+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, c: 3, e: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, t: 4}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, g: 2, w: 2}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, n: 3, u: 2}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, p: 1, t: 1, k: 1}, what is the expected number of times the pattern 'kp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, s: 1, m: 1, y: 1, a: 2}. What is the expected number of occurrences of the pattern 't+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, n: 1, i: 3, w: 1}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, v: 1, l: 2, p: 1, j: 1}. What is the expected number of occurrences of the pattern 'v.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, z: 1, d: 2, b: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, d: 3}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, m: 3, l: 2}. What is the expected number of occurrences of the pattern 'i+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, y: 1, j: 2, k: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'k.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, r: 3}, what is the expected number of times the pattern 'cr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, q: 3}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, u: 3}, what is the expected number of times the pattern 'u.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, f: 2, m: 1, p: 1, t: 1}. What is the expected number of occurrences of the pattern 'ft+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, w: 3}. What is the expected number of occurrences of the pattern 'j.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 4, a: 2}. What is the expected number of occurrences of the pattern 'ah+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 4, e: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, c: 3, y: 2}. What is the expected number of occurrences of the pattern 'v.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, l: 1, y: 2}, what is the expected number of times the pattern 'l.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, d: 1, e: 1, m: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, z: 1, d: 2}. What is the expected number of occurrences of the pattern 'z*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, s: 2, a: 1, w: 1}. What is the expected number of occurrences of the pattern 'xw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, j: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'v.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, g: 1, y: 1, d: 2}, what is the expected number of times the pattern 'j*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, g: 4} to form a word, what is the expected number of matches of the pattern 'gk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, u: 3, p: 1}, what is the expected number of times the pattern 'pu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, j: 2, e: 2}. What is the expected number of occurrences of the pattern 'je*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, d: 1, o: 1, p: 1, u: 1}, what is the expected number of times the pattern 'pd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, d: 2, k: 1, v: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, f: 1, n: 1, d: 2}, what is the expected number of times the pattern 'dm+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, b: 1, v: 1, e: 1}. What is the expected number of occurrences of the pattern 'ee+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, o: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'o+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, k: 3, z: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'z+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, s: 1, w: 2, e: 2} to form a word, what is the expected number of matches of the pattern 'et+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, m: 2, h: 2}, what is the expected number of times the pattern 'ym*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, n: 1, s: 1, r: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 4, w: 2}, what is the expected number of times the pattern 'dw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, s: 1, c: 3, k: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, x: 1, g: 1, c: 1, q: 1}, what is the expected number of times the pattern 'cg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, f: 2}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, s: 1, c: 2, y: 1}. What is the expected number of occurrences of the pattern 's*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 5, p: 1}. What is the expected number of occurrences of the pattern 'p*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, o: 2, k: 1, n: 1, p: 1}. What is the expected number of occurrences of the pattern 's*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, g: 3} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, l: 1, a: 1, v: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, d: 1, w: 2, y: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, b: 1, m: 1, a: 1, o: 1}, what is the expected number of times the pattern 'z+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, p: 1, w: 3, x: 1}, what is the expected number of times the pattern 's+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, d: 1, i: 1, q: 2, h: 1}, what is the expected number of times the pattern 'i.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, s: 3}. What is the expected number of occurrences of the pattern 's*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 4, t: 2} to form a word, what is the expected number of matches of the pattern 't+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, j: 1, w: 1, l: 2, e: 1}, what is the expected number of times the pattern 'j.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, v: 3}, what is the expected number of times the pattern 'vb+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, z: 2, g: 2}. What is the expected number of occurrences of the pattern 'q.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 4, l: 2}. What is the expected number of occurrences of the pattern 'z*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, e: 1, y: 1, b: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'we*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, a: 1, e: 2, n: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'gn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, h: 2, u: 3}, what is the expected number of times the pattern 'h*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, p: 5}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 4, l: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, p: 1, a: 1, e: 1, t: 1}, what is the expected number of times the pattern 'a*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, b: 1, s: 2, f: 2}, what is the expected number of times the pattern 'fc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, o: 1, z: 1, h: 2, v: 1}. What is the expected number of occurrences of the pattern 'o.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, s: 1, o: 2}, what is the expected number of times the pattern 'ts*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, t: 2, p: 1, r: 1, w: 1}, what is the expected number of times the pattern 'w+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, a: 1, z: 3}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 5, u: 1} to form a word, what is the expected number of matches of the pattern 'f.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, e: 2, r: 2}, what is the expected number of times the pattern 're+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, k: 2, m: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'p.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, m: 1, q: 2, w: 1, y: 1}. What is the expected number of occurrences of the pattern 'q+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, q: 1, a: 1, y: 1, b: 1}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, b: 1, m: 1, x: 1, l: 1}. What is the expected number of occurrences of the pattern 'm*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 4, e: 2}. What is the expected number of occurrences of the pattern 'we+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, a: 1, x: 1, j: 2, t: 1} to form a word, what is the expected number of matches of the pattern 't+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, v: 1, p: 1, d: 2, m: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, w: 1, x: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'wn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, o: 1, d: 2}, what is the expected number of times the pattern 'do*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, l: 2, j: 3}. What is the expected number of occurrences of the pattern 'l*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, p: 3}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, j: 2, w: 2} to form a word, what is the expected number of matches of the pattern 'w*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 3, f: 1, g: 2}, what is the expected number of times the pattern 'g+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 4, m: 2}, what is the expected number of times the pattern 'a+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, g: 2, s: 1, r: 1, t: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, t: 4}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, d: 3, s: 1}. What is the expected number of occurrences of the pattern 'ss*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, k: 1, b: 2, h: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, g: 1, f: 2, e: 1, s: 1}, what is the expected number of times the pattern 'g*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, n: 1, o: 2}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, z: 3, r: 1}. What is the expected number of occurrences of the pattern 'r*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, h: 1, x: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'zh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, b: 3}, what is the expected number of times the pattern 'f.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, s: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'sg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, k: 1, l: 1, y: 1, p: 1}, what is the expected number of times the pattern 'mp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, w: 3} to form a word, what is the expected number of matches of the pattern 'wq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, m: 2, n: 2}, what is the expected number of times the pattern 'me+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, u: 3}, what is the expected number of times the pattern 'u.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, u: 1, s: 2}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 4, c: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'cg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, s: 2, a: 2}, what is the expected number of times the pattern 'ls+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, n: 1, u: 1, y: 1, k: 1}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, f: 2, j: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'sf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, u: 2, i: 1, k: 1, t: 1}, what is the expected number of times the pattern 'i.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, w: 1, h: 2, s: 1, v: 1}. What is the expected number of occurrences of the pattern 'sd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, n: 1, f: 2, t: 1} to form a word, what is the expected number of matches of the pattern 'tn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, p: 3}. What is the expected number of occurrences of the pattern 'p.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, p: 3} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, k: 1, q: 3}. What is the expected number of occurrences of the pattern 'q+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, u: 2, k: 1, l: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, v: 3}, what is the expected number of times the pattern 'g.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, h: 1, v: 1, g: 1, l: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, h: 4}, what is the expected number of times the pattern 'h.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, r: 1, s: 2, w: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, r: 1, w: 3, s: 1}, what is the expected number of times the pattern 't+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 4, c: 1, o: 1}. What is the expected number of occurrences of the pattern 'o.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, f: 2, x: 3} to form a word, what is the expected number of matches of the pattern 'xm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, g: 1, y: 2}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, t: 1, y: 1, h: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'hm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, b: 1, u: 1, p: 1, i: 1}. What is the expected number of occurrences of the pattern 'i*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, a: 2, g: 3}. What is the expected number of occurrences of the pattern 'ag+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, j: 3, m: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, g: 3, c: 2}. What is the expected number of occurrences of the pattern 'u.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, n: 2, x: 2, d: 1}. What is the expected number of occurrences of the pattern 'n*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, w: 2, u: 1, s: 1, y: 1}, what is the expected number of times the pattern 'wu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, y: 3, n: 1, r: 1}. What is the expected number of occurrences of the pattern 'uy*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, d: 1, g: 2, w: 2} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, g: 2, w: 3}, what is the expected number of times the pattern 'u*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, j: 2, h: 1, v: 2}, what is the expected number of times the pattern 'v.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, p: 3} to form a word, what is the expected number of matches of the pattern 'up+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, d: 2, a: 1, k: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'p+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, k: 3, r: 2}. What is the expected number of occurrences of the pattern 'qk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 4, r: 2}, what is the expected number of times the pattern 'r.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, y: 3, i: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, u: 3}. What is the expected number of occurrences of the pattern 'ul*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, i: 3}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, h: 4}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, i: 1, e: 1, z: 1}, what is the expected number of times the pattern 'qz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, o: 1, d: 1, s: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, h: 3, w: 1}, what is the expected number of times the pattern 'cw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, o: 1, q: 1, u: 1, b: 2}. What is the expected number of occurrences of the pattern 'o.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, n: 3} to form a word, what is the expected number of matches of the pattern 'v.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, y: 2, n: 1, x: 1, s: 1}, what is the expected number of times the pattern 'n+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, r: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'l+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, n: 4}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, k: 1, q: 2, v: 2}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, s: 1, z: 1, g: 1, i: 1}, what is the expected number of times the pattern 'hg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, u: 1, x: 1, d: 1, a: 1}. What is the expected number of occurrences of the pattern 'fx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, s: 4}, what is the expected number of times the pattern 'sn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, a: 3, b: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, r: 1, m: 2, t: 1, p: 1}. What is the expected number of occurrences of the pattern 'r.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, n: 2, z: 3}, what is the expected number of times the pattern 'nz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, i: 4} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 4, t: 2} to form a word, what is the expected number of matches of the pattern 't+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, u: 1, y: 1, i: 2}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, p: 2, r: 1}. What is the expected number of occurrences of the pattern 'r.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, p: 1, g: 1, y: 1, e: 2}, what is the expected number of times the pattern 'cy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, g: 1, r: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'hz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, z: 1, m: 1, e: 2, c: 1}, what is the expected number of times the pattern 'e*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, j: 2, a: 2}, what is the expected number of times the pattern 'a.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, v: 2, b: 1, x: 1, m: 1}, what is the expected number of times the pattern 'xc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, i: 2, s: 2} to form a word, what is the expected number of matches of the pattern 's*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, v: 1, q: 3} to form a word, what is the expected number of matches of the pattern 'vh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, b: 4}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, l: 1, a: 2}, what is the expected number of times the pattern 'l+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, y: 4} to form a word, what is the expected number of matches of the pattern 'z.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, q: 1, f: 1, w: 1, c: 2}, what is the expected number of times the pattern 'yc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, s: 1, a: 3}. What is the expected number of occurrences of the pattern 's*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, h: 1, t: 1, p: 3}, what is the expected number of times the pattern 'p+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, o: 1, e: 1, d: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, z: 3, a: 1}. What is the expected number of occurrences of the pattern 'yz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, i: 1, c: 2, e: 2}. What is the expected number of occurrences of the pattern 'i+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, y: 1, u: 2}. What is the expected number of occurrences of the pattern 'x+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, t: 3}. What is the expected number of occurrences of the pattern 'jt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, h: 2, e: 1, a: 1}. What is the expected number of occurrences of the pattern 'ha+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, l: 3, w: 1}. What is the expected number of occurrences of the pattern 'l+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, o: 2, u: 1, m: 1, n: 1}, what is the expected number of times the pattern 'nw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, p: 1, l: 1, q: 3} to form a word, what is the expected number of matches of the pattern 'np*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, w: 1, z: 1, o: 1, y: 1}, what is the expected number of times the pattern 'to*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, i: 1, n: 3} to form a word, what is the expected number of matches of the pattern 'in+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, a: 1, c: 2, x: 2}, what is the expected number of times the pattern 'a*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, b: 2, j: 1, w: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'w.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, t: 1, x: 1, e: 1}. What is the expected number of occurrences of the pattern 'ex+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, p: 3, d: 1}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, b: 2, s: 2} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, w: 1, e: 2, y: 1, s: 1}. What is the expected number of occurrences of the pattern 'e*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, e: 1, a: 3, o: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, c: 1, b: 1, j: 2, u: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, i: 1, w: 1, j: 3}. What is the expected number of occurrences of the pattern 'wl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, v: 1, e: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'n+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, v: 1, h: 3} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 4, k: 2} to form a word, what is the expected number of matches of the pattern 'kl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, u: 1, k: 1, t: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, g: 2, j: 2} to form a word, what is the expected number of matches of the pattern 'jg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, f: 1, p: 1, m: 1}. What is the expected number of occurrences of the pattern 'wm*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, s: 2, x: 1} to form a word, what is the expected number of matches of the pattern 'sn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, s: 2, g: 2} to form a word, what is the expected number of matches of the pattern 'c.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, a: 2, l: 1, g: 1, u: 1}. What is the expected number of occurrences of the pattern 'g.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, e: 4} to form a word, what is the expected number of matches of the pattern 'ez+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, z: 1, h: 1, e: 2, g: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, t: 1, k: 1, s: 1, g: 2}. What is the expected number of occurrences of the pattern 'sd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, f: 2, h: 2, l: 1}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, s: 4}, what is the expected number of times the pattern 's.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, p: 4} to form a word, what is the expected number of matches of the pattern 'pk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, p: 1, k: 1, q: 3}. What is the expected number of occurrences of the pattern 'k.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, y: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'j*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 4, w: 1, a: 1}, what is the expected number of times the pattern 'a+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, v: 1, k: 1, s: 1, r: 1}, what is the expected number of times the pattern 'r+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 4, h: 1, x: 1}, what is the expected number of times the pattern 'n.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, n: 4}, what is the expected number of times the pattern 'nl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, j: 3}. What is the expected number of occurrences of the pattern 'fj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, q: 1, g: 1, l: 2, i: 1}, what is the expected number of times the pattern 'gl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, c: 1, g: 2, z: 1}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, f: 2}. What is the expected number of occurrences of the pattern 'u+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, h: 1, p: 2}. What is the expected number of occurrences of the pattern 'h.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, o: 3, u: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'oi*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, s: 3, t: 1}. What is the expected number of occurrences of the pattern 't.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, j: 1, l: 2, g: 1}. What is the expected number of occurrences of the pattern 'j.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, h: 3}, what is the expected number of times the pattern 'zh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, k: 1, u: 4}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 4, y: 2} to form a word, what is the expected number of matches of the pattern 'y.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, g: 1, k: 1, x: 3}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, d: 3}. What is the expected number of occurrences of the pattern 'd*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, i: 3, m: 1}. What is the expected number of occurrences of the pattern 'x*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, h: 1, q: 3} to form a word, what is the expected number of matches of the pattern 'hq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, r: 2, w: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'gw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, y: 1, i: 1, c: 1}. What is the expected number of occurrences of the pattern 'c*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, m: 4} to form a word, what is the expected number of matches of the pattern 'd+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, u: 1, l: 4}. What is the expected number of occurrences of the pattern 'rl+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, j: 2, e: 1, i: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'ik*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, l: 2, j: 2}, what is the expected number of times the pattern 'x*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, n: 2, x: 3} to form a word, what is the expected number of matches of the pattern 'kn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, r: 1, l: 1, j: 1, t: 1}, what is the expected number of times the pattern 'rp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, y: 1, e: 2, u: 1}, what is the expected number of times the pattern 'ue*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, i: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'l*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, u: 3, m: 1}. What is the expected number of occurrences of the pattern 'mq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, c: 1, w: 1, t: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'v.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, w: 1, c: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'co+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, z: 2, w: 1, u: 1, f: 1}, what is the expected number of times the pattern 'f+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, e: 1, t: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'c+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, o: 2, d: 1, f: 2}, what is the expected number of times the pattern 'df+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, l: 3}, what is the expected number of times the pattern 'f.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, g: 2, t: 2}. What is the expected number of occurrences of the pattern 't+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, z: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, a: 1, i: 1, y: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'oi*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, s: 2, z: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'gz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, e: 3, g: 1} to form a word, what is the expected number of matches of the pattern 'ep+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, o: 3}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, b: 1, h: 2}, what is the expected number of times the pattern 'hh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, z: 2, u: 2}, what is the expected number of times the pattern 'ua+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'k*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, i: 1, u: 2}. What is the expected number of occurrences of the pattern 'ui*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, i: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, l: 1, g: 4} to form a word, what is the expected number of matches of the pattern 'g.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, q: 1, r: 1, y: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'qn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 4, a: 2}, what is the expected number of times the pattern 'ga+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, w: 5}. What is the expected number of occurrences of the pattern 'w+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, g: 2, s: 2}, what is the expected number of times the pattern 'gm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, i: 1, q: 2, b: 1, a: 1}, what is the expected number of times the pattern 'qi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, e: 3, f: 2}, what is the expected number of times the pattern 'p+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, x: 3}. What is the expected number of occurrences of the pattern 'qx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, m: 3, x: 1, o: 1}. What is the expected number of occurrences of the pattern 'm+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, m: 2, d: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'l.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, p: 1, t: 3}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, a: 3, e: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, s: 1, z: 1, v: 1, k: 2}, what is the expected number of times the pattern 's*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, z: 3, k: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 4, e: 2}. What is the expected number of occurrences of the pattern 'ze*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, u: 1, v: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'vq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, m: 1, b: 2, n: 2}, what is the expected number of times the pattern 'm*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, o: 1, w: 2, x: 1, p: 1}, what is the expected number of times the pattern 'p*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, m: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'l.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, d: 4}. What is the expected number of occurrences of the pattern 'a.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, e: 1, b: 2, k: 2}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, s: 1, z: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'o*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, x: 2, k: 1, f: 1, i: 1}, what is the expected number of times the pattern 'x.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, x: 1, b: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'h.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, i: 4} to form a word, what is the expected number of matches of the pattern 'i*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, g: 1, b: 2, i: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'i+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, s: 1, g: 3, k: 1}, what is the expected number of times the pattern 'sr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, j: 1, w: 1, d: 1, v: 1}, what is the expected number of times the pattern 'dw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, g: 2, k: 1, p: 2}, what is the expected number of times the pattern 'g.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, z: 1, d: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'ez+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, p: 1, w: 1, l: 1, j: 1}. What is the expected number of occurrences of the pattern 'lb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, o: 1, e: 1, u: 2, j: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, b: 2, s: 1, d: 2}. What is the expected number of occurrences of the pattern 'kk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, y: 1, t: 2, e: 2}, what is the expected number of times the pattern 'l.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, b: 1, s: 1, a: 1, n: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, e: 2, j: 1, a: 2}. What is the expected number of occurrences of the pattern 'ae+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, q: 1, e: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'e+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, m: 2, z: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'f*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, v: 2, c: 3}, what is the expected number of times the pattern 'v+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, g: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'vw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, l: 1, x: 1, h: 3} to form a word, what is the expected number of matches of the pattern 'f.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, l: 1, y: 4}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, k: 1, t: 2, v: 1, a: 1}. What is the expected number of occurrences of the pattern 'e+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, x: 3}, what is the expected number of times the pattern 'xj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, t: 3, m: 1}, what is the expected number of times the pattern 'c.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, l: 2, u: 1, a: 1, n: 1}. What is the expected number of occurrences of the pattern 'un*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, f: 4}. What is the expected number of occurrences of the pattern 'f+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 4, d: 2}. What is the expected number of occurrences of the pattern 'dw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 4, s: 2} to form a word, what is the expected number of matches of the pattern 's.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, h: 1, s: 2, g: 2} to form a word, what is the expected number of matches of the pattern 'g.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, v: 5} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, v: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'v*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, m: 2, z: 1, b: 1}. What is the expected number of occurrences of the pattern 'f*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, e: 1, a: 1, s: 1, w: 2}, what is the expected number of times the pattern 'as*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, t: 1, q: 1, x: 2, n: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, w: 3} to form a word, what is the expected number of matches of the pattern 'w*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, z: 3, r: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'g*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, j: 1, s: 1, y: 1, u: 2}, what is the expected number of times the pattern 'u+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, n: 3}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, i: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'i+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, u: 1, h: 2, t: 1, q: 1} to form a word, what is the expected number of matches of the pattern 't*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, x: 3}, what is the expected number of times the pattern 'i+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, w: 2, b: 1}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, f: 3} to form a word, what is the expected number of matches of the pattern 'ft+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, z: 1, h: 2, p: 2}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, d: 1, h: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, x: 2, v: 1}. What is the expected number of occurrences of the pattern 'x*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, j: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, j: 2, b: 3}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 4, d: 2}. What is the expected number of occurrences of the pattern 'wd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, t: 4}, what is the expected number of times the pattern 't.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, a: 1, d: 2, x: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, a: 3}, what is the expected number of times the pattern 'ja*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, t: 1, w: 1, v: 2}, what is the expected number of times the pattern 'wv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, q: 1, l: 1, e: 1, y: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, u: 3, j: 2}, what is the expected number of times the pattern 'aj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 4, x: 2} to form a word, what is the expected number of matches of the pattern 'x.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, a: 2, i: 2}, what is the expected number of times the pattern 'ia+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, z: 2, t: 1, r: 1}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 4, k: 2} to form a word, what is the expected number of matches of the pattern 's+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, u: 5} to form a word, what is the expected number of matches of the pattern 'lu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, l: 1, d: 2, p: 1, o: 1}, what is the expected number of times the pattern 'd+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, y: 3}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, j: 1, a: 1, p: 3}. What is the expected number of occurrences of the pattern 'j.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, y: 2, x: 2, e: 1}. What is the expected number of occurrences of the pattern 'x.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, t: 3} to form a word, what is the expected number of matches of the pattern 'ht*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 3, b: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, y: 2, c: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, x: 4}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, o: 3} to form a word, what is the expected number of matches of the pattern 'od+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, l: 2, f: 1}, what is the expected number of times the pattern 'of*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, o: 4}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, f: 2, k: 2}. What is the expected number of occurrences of the pattern 'f+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, x: 2, b: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'pq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, w: 1, b: 2, x: 2}. What is the expected number of occurrences of the pattern 'x+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, c: 3}. What is the expected number of occurrences of the pattern 'w.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, h: 2, y: 1, k: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, n: 2, y: 2}, what is the expected number of times the pattern 'n+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, r: 2, p: 1, v: 1}, what is the expected number of times the pattern 'lv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, n: 3} to form a word, what is the expected number of matches of the pattern 'nv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, h: 2, s: 2, x: 1}, what is the expected number of times the pattern 'x+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, j: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, b: 1, e: 1, f: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'e+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, y: 2, q: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, l: 1, h: 1, j: 3}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, m: 1, k: 1, r: 2, g: 1}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, b: 3}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, h: 3}, what is the expected number of times the pattern 'hc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, l: 2, t: 1, d: 1, u: 1}. What is the expected number of occurrences of the pattern 'l*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, c: 1, j: 2, s: 1}, what is the expected number of times the pattern 'j*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, x: 1, o: 3, p: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, x: 1, s: 2, v: 1, r: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, j: 1, n: 3}, what is the expected number of times the pattern 'dn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, c: 2, r: 1}. What is the expected number of occurrences of the pattern 'c+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, s: 1, y: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 4, y: 2}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, c: 4}, what is the expected number of times the pattern 'c.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, v: 2, g: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'vu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, a: 1, s: 3, r: 1} to form a word, what is the expected number of matches of the pattern 'v*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, m: 1, t: 1, r: 1, s: 1}. What is the expected number of occurrences of the pattern 't*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, f: 1, t: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'kx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, h: 1, y: 2, x: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, y: 2, r: 1, d: 2}. What is the expected number of occurrences of the pattern 'y+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, f: 2, p: 3}, what is the expected number of times the pattern 'f+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, n: 4}. What is the expected number of occurrences of the pattern 'n+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, o: 4} to form a word, what is the expected number of matches of the pattern 'mo+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, a: 1, e: 2, b: 2}, what is the expected number of times the pattern 'i*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 4, f: 2} to form a word, what is the expected number of matches of the pattern 'r+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, f: 3, r: 2} to form a word, what is the expected number of matches of the pattern 'rf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, h: 2, w: 2}, what is the expected number of times the pattern 'u.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, c: 1, x: 1, u: 1, w: 2}. What is the expected number of occurrences of the pattern 'tx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, a: 4, e: 1} to form a word, what is the expected number of matches of the pattern 'ea+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, r: 4}. What is the expected number of occurrences of the pattern 'u.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 4, b: 2}, what is the expected number of times the pattern 'kb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, d: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'v*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'cv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, a: 2, p: 1, g: 2}, what is the expected number of times the pattern 'g*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, l: 2, k: 1, x: 1, c: 1}, what is the expected number of times the pattern 'lq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, s: 1, i: 2, p: 2}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 4, k: 2}. What is the expected number of occurrences of the pattern 'k.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, q: 4}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, f: 2, g: 1}, what is the expected number of times the pattern 'f*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, p: 3}. What is the expected number of occurrences of the pattern 'g.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, a: 2, u: 3}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, d: 1, j: 2, q: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, t: 1, e: 2, k: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'k.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'ht+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 5, g: 1} to form a word, what is the expected number of matches of the pattern 'g.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 4, w: 2}. What is the expected number of occurrences of the pattern 'we*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, a: 2, h: 2}. What is the expected number of occurrences of the pattern 'ha+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, a: 1, k: 2, u: 1}. What is the expected number of occurrences of the pattern 'c.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, u: 1, c: 1, g: 1, b: 1}. What is the expected number of occurrences of the pattern 'cc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, g: 2, b: 1, v: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'hh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, l: 2, o: 1, z: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'on*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, e: 3}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, o: 3, r: 1}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, z: 1, p: 3}. What is the expected number of occurrences of the pattern 'kz*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, g: 2, s: 1, v: 2}, what is the expected number of times the pattern 'v*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, a: 2, n: 1}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, c: 3} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, g: 1, f: 3, y: 1}, what is the expected number of times the pattern 'f*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, o: 3} to form a word, what is the expected number of matches of the pattern 'w+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, b: 1, k: 1, w: 3} to form a word, what is the expected number of matches of the pattern 'h+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, l: 2, f: 1, k: 2}. What is the expected number of occurrences of the pattern 'rl+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, m: 1, w: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'i*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, v: 1, d: 2, m: 1} to form a word, what is the expected number of matches of the pattern 'h.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, m: 2, j: 1, v: 1}, what is the expected number of times the pattern 'm*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, i: 1, m: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'mg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, n: 2, z: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 4, z: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, g: 2, l: 2} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, v: 5}. What is the expected number of occurrences of the pattern 'p.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, a: 1, m: 1, s: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, a: 1, v: 1, y: 1, i: 2}, what is the expected number of times the pattern 'u*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, w: 1, d: 1, j: 1}. What is the expected number of occurrences of the pattern 'd.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, k: 2, z: 2}. What is the expected number of occurrences of the pattern 'k*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 5, i: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 4, f: 2}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, r: 1, k: 1, n: 2, m: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, z: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'oz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, e: 1, r: 1, c: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, t: 3, j: 2}, what is the expected number of times the pattern 'lj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, i: 2, s: 1}. What is the expected number of occurrences of the pattern 's.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, e: 2, a: 1, i: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, s: 2, l: 2}. What is the expected number of occurrences of the pattern 'l*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, x: 5} to form a word, what is the expected number of matches of the pattern 'xu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, o: 4}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, n: 1, v: 1, o: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'n+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, p: 2, q: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'e.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, p: 4}. What is the expected number of occurrences of the pattern 'p+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, d: 2, p: 1}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, s: 1, i: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, d: 1, o: 1, n: 1, t: 1}, what is the expected number of times the pattern 'd*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, c: 4, u: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, t: 1, i: 1, x: 3}, what is the expected number of times the pattern 'tz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, e: 3, z: 1} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, y: 5} to form a word, what is the expected number of matches of the pattern 'ey*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, v: 1, i: 1, t: 2} to form a word, what is the expected number of matches of the pattern 'lv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, l: 1, t: 1, c: 2, o: 1} to form a word, what is the expected number of matches of the pattern 't*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, f: 1, r: 2, x: 1, t: 1}, what is the expected number of times the pattern 'fp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, u: 3, j: 1} to form a word, what is the expected number of matches of the pattern 'u+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, r: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, k: 1, x: 4}, what is the expected number of times the pattern 'kx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, k: 3, y: 1}. What is the expected number of occurrences of the pattern 'k.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, a: 1, j: 2, b: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'a+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, s: 2, v: 2, t: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'v.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 5, d: 1}, what is the expected number of times the pattern 'zd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, d: 1, j: 1, b: 1, c: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, r: 5} to form a word, what is the expected number of matches of the pattern 'r*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, q: 1, c: 1, o: 1, f: 2}. What is the expected number of occurrences of the pattern 'zf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 4, c: 2}, what is the expected number of times the pattern 'w.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 4, j: 2}, what is the expected number of times the pattern 'aj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, d: 1, r: 1, w: 2, h: 1} to form a word, what is the expected number of matches of the pattern 'eh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, d: 4} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, b: 1, x: 2, g: 2} to form a word, what is the expected number of matches of the pattern 'q.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, h: 1, g: 1, r: 2, i: 1}, what is the expected number of times the pattern 'h+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, d: 4}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, h: 4}, what is the expected number of times the pattern 'h.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, o: 2, t: 2}. What is the expected number of occurrences of the pattern 'th+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, q: 3, e: 2}. What is the expected number of occurrences of the pattern 'u*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 3, i: 3}, what is the expected number of times the pattern 'i*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, h: 2, y: 2, v: 1}. What is the expected number of occurrences of the pattern 'y*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, j: 1, v: 1, r: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'vf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 4, i: 2}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, x: 1, l: 1, b: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, o: 4}, what is the expected number of times the pattern 'w.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, b: 1, v: 1, x: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'u*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'i.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, j: 2, d: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'dj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, q: 3}. What is the expected number of occurrences of the pattern 'kq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, w: 2, c: 2, n: 1}, what is the expected number of times the pattern 'nb+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, p: 4}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, o: 2, k: 3} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, n: 2, w: 2, r: 1}, what is the expected number of times the pattern 'wr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, b: 3}. What is the expected number of occurrences of the pattern 'e*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 3, i: 3}, what is the expected number of times the pattern 'y*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, n: 2, f: 1, b: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'f+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, f: 1, d: 2, k: 2}. What is the expected number of occurrences of the pattern 'fd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, q: 2, n: 2}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, r: 1, v: 2, b: 1}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, v: 1, t: 1, x: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'v+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, a: 1, w: 1, x: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, v: 2, n: 2}. What is the expected number of occurrences of the pattern 'vb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, a: 2, n: 1, u: 1, o: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, x: 3}, what is the expected number of times the pattern 'dx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, b: 2, y: 2}, what is the expected number of times the pattern 'y+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, i: 1, w: 1, r: 1, e: 2}. What is the expected number of occurrences of the pattern 're+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, o: 4}, what is the expected number of times the pattern 'wo*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, j: 2, y: 3}. What is the expected number of occurrences of the pattern 'j*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, l: 2, u: 3}, what is the expected number of times the pattern 'h+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, o: 1, r: 2, z: 1, a: 1}, what is the expected number of times the pattern 'o*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, w: 2, y: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, t: 1, a: 2} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, n: 2, o: 1, q: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'o+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 4, h: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'm.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, m: 1, z: 1, i: 3}, what is the expected number of times the pattern 'z*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, k: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'k+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, v: 3}, what is the expected number of times the pattern 'v.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, v: 3}, what is the expected number of times the pattern 'u.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, d: 2, o: 1, x: 2}, what is the expected number of times the pattern 'dx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, t: 1, g: 1, p: 2, e: 1}, what is the expected number of times the pattern 'gp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, q: 2, n: 1, z: 1}. What is the expected number of occurrences of the pattern 'nq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, e: 4} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, v: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, f: 2, u: 3}, what is the expected number of times the pattern 'r*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, q: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, i: 1, d: 4} to form a word, what is the expected number of matches of the pattern 'h.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, g: 3, a: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, r: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, k: 3}, what is the expected number of times the pattern 'k*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, d: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'r*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, m: 1, a: 1, o: 3} to form a word, what is the expected number of matches of the pattern 'a.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, k: 2, x: 2, s: 1}. What is the expected number of occurrences of the pattern 'kx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, v: 1, r: 2, n: 2}. What is the expected number of occurrences of the pattern 'r+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, b: 4}, what is the expected number of times the pattern 'dd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, q: 1, v: 1, y: 1, u: 2}, what is the expected number of times the pattern 'u.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, f: 3, c: 2}, what is the expected number of times the pattern 'fy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, u: 1, w: 1, x: 1, t: 2}, what is the expected number of times the pattern 'xw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, b: 1, r: 2, l: 1}. What is the expected number of occurrences of the pattern 'l.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, a: 1, i: 2, r: 1}, what is the expected number of times the pattern 'ir*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, y: 3, c: 2} to form a word, what is the expected number of matches of the pattern 'uy+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, r: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, a: 2, n: 2, l: 1}. What is the expected number of occurrences of the pattern 'la*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 4, g: 2}, what is the expected number of times the pattern 'c.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, i: 1, t: 1, z: 3}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, c: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'sc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 3, y: 3} to form a word, what is the expected number of matches of the pattern 'ye*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 3, y: 1, j: 1, r: 1}, what is the expected number of times the pattern 'yj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, l: 3, q: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, r: 2, a: 3}, what is the expected number of times the pattern 'a*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 4, h: 2}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, k: 3, p: 1} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, q: 3, x: 2}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, s: 2, c: 1, n: 2}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, p: 5}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, c: 1, g: 2}. What is the expected number of occurrences of the pattern 'kg*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, e: 1, s: 1, g: 2, v: 1}, what is the expected number of times the pattern 'e+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, i: 3} to form a word, what is the expected number of matches of the pattern 'i*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 4, z: 2} to form a word, what is the expected number of matches of the pattern 'z*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, k: 1, d: 1, c: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'ik*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, x: 1, b: 1, q: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'qi*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, h: 2, r: 1, w: 1}, what is the expected number of times the pattern 'r+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 4, r: 2} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, i: 1, u: 3} to form a word, what is the expected number of matches of the pattern 'iu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, i: 1, q: 2} to form a word, what is the expected number of matches of the pattern 'q.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 4, m: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, v: 3, x: 1}, what is the expected number of times the pattern 'p.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, w: 1, g: 2, l: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'wg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, r: 1, g: 2}. What is the expected number of occurrences of the pattern 'g+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, y: 3, q: 1, w: 1}. What is the expected number of occurrences of the pattern 'v+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, e: 3}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'h.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, e: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, d: 1, f: 1, q: 1, m: 2}. What is the expected number of occurrences of the pattern 'mf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, e: 1, t: 1, f: 2, m: 1}. What is the expected number of occurrences of the pattern 't.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, z: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 4, n: 2} to form a word, what is the expected number of matches of the pattern 'r*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, w: 2, c: 2, y: 1}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, r: 2, q: 1, f: 1, c: 1}, what is the expected number of times the pattern 'r+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, d: 1, v: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'hd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, k: 1, m: 2, z: 1, r: 1}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 4, o: 2}. What is the expected number of occurrences of the pattern 'o.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, j: 2, h: 3}. What is the expected number of occurrences of the pattern 'jo*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, l: 1, w: 1, k: 2, p: 1}. What is the expected number of occurrences of the pattern 'p.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, n: 3, k: 1}, what is the expected number of times the pattern 'nm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, w: 1, z: 2, g: 1}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, f: 2, g: 2, w: 1}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, j: 3}, what is the expected number of times the pattern 'jm+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, q: 1, i: 1, x: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'x*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, e: 2, s: 2, t: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, j: 5} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, v: 1, i: 1, n: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'u*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, r: 3, y: 2} to form a word, what is the expected number of matches of the pattern 'y+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, v: 3, j: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, h: 3}, what is the expected number of times the pattern 'hu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, d: 2, m: 1, n: 1, u: 1}, what is the expected number of times the pattern 'pn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, l: 1, r: 2, s: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'l*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, b: 2, x: 1, f: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, w: 4}. What is the expected number of occurrences of the pattern 'cw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, k: 3, t: 1} to form a word, what is the expected number of matches of the pattern 't.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, w: 1, m: 2, r: 2}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, p: 4} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, r: 2, f: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, i: 2, y: 2}. What is the expected number of occurrences of the pattern 'm.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, p: 1, x: 2, h: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, q: 1, b: 1, t: 2} to form a word, what is the expected number of matches of the pattern 'q*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, e: 1, n: 2}, what is the expected number of times the pattern 'n*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, q: 1, n: 1, a: 2}. What is the expected number of occurrences of the pattern 'ny*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, s: 3}. What is the expected number of occurrences of the pattern 'sm*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 4, r: 2}, what is the expected number of times the pattern 't+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, l: 1, u: 1, d: 3} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, x: 3}, what is the expected number of times the pattern 'rx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, a: 2, e: 2}, what is the expected number of times the pattern 'k*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, b: 1, g: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'g.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, m: 1, g: 3, l: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'u+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, m: 2, n: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'mn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, b: 2, u: 2, t: 1} to form a word, what is the expected number of matches of the pattern 't+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, y: 4}, what is the expected number of times the pattern 'y+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, b: 2, t: 2}. What is the expected number of occurrences of the pattern 'r.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, z: 1, n: 3}. What is the expected number of occurrences of the pattern 'gn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, q: 3}, what is the expected number of times the pattern 'zq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 4, r: 2} to form a word, what is the expected number of matches of the pattern 'r+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, n: 3}. What is the expected number of occurrences of the pattern 'yn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, w: 1, t: 2}. What is the expected number of occurrences of the pattern 'x.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, m: 3} to form a word, what is the expected number of matches of the pattern 'm+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, k: 3}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, x: 1, k: 1, r: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, n: 2, j: 1, l: 2}. What is the expected number of occurrences of the pattern 'l+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, d: 3, u: 2}. What is the expected number of occurrences of the pattern 'pd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 4, m: 2}, what is the expected number of times the pattern 'm*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, z: 2, w: 1, a: 1, k: 1}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, v: 1, h: 1, q: 1, j: 2}. What is the expected number of occurrences of the pattern 'zh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, t: 3, f: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, j: 5}. What is the expected number of occurrences of the pattern 'jz*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, l: 2, g: 2}. What is the expected number of occurrences of the pattern 'lx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, f: 2, e: 1, p: 1}. What is the expected number of occurrences of the pattern 'e+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, y: 1, l: 1, g: 2}. What is the expected number of occurrences of the pattern 'f+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, c: 3} to form a word, what is the expected number of matches of the pattern 'c*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, x: 1, h: 2, w: 1}. What is the expected number of occurrences of the pattern 'hl+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, p: 2, m: 3}. What is the expected number of occurrences of the pattern 'm+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, q: 1, r: 1, u: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'q+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, e: 2, s: 1, z: 1, b: 1}, what is the expected number of times the pattern 'se+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, x: 2, r: 1, t: 1, a: 1}. What is the expected number of occurrences of the pattern 'at*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, s: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, i: 2, p: 1}. What is the expected number of occurrences of the pattern 'gp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, z: 1, r: 2, i: 1, y: 1}, what is the expected number of times the pattern 'yr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, o: 4}. What is the expected number of occurrences of the pattern 'or+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 3, d: 3}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, y: 5}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, c: 3, x: 1, d: 1}. What is the expected number of occurrences of the pattern 'ec+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, c: 4}, what is the expected number of times the pattern 'c*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, s: 2, l: 1}. What is the expected number of occurrences of the pattern 's.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, y: 2, l: 3}. What is the expected number of occurrences of the pattern 'y+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, a: 1, r: 1, n: 1}, what is the expected number of times the pattern 'r*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 4, c: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'f.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, r: 1, o: 1, z: 2}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, e: 1, j: 1, o: 2, m: 1} to form a word, what is the expected number of matches of the pattern 'o.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, g: 2, l: 2}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, y: 1, z: 1, w: 1, u: 1}. What is the expected number of occurrences of the pattern 'h.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, z: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, u: 3}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, b: 3}. What is the expected number of occurrences of the pattern 'ee+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, f: 4}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, v: 3, t: 1}. What is the expected number of occurrences of the pattern 'u+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, k: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'k.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, t: 2, e: 1, q: 1, h: 1}. What is the expected number of occurrences of the pattern 'e.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, c: 2, l: 1, r: 1}, what is the expected number of times the pattern 'r*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, g: 2, d: 2}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, x: 2, g: 1}. What is the expected number of occurrences of the pattern 'xm+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, j: 2, u: 3}, what is the expected number of times the pattern 'i+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, f: 3, s: 2} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, r: 1, i: 1, f: 2}, what is the expected number of times the pattern 'p+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, j: 1, s: 3} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, s: 3, v: 1, c: 1}, what is the expected number of times the pattern 'cv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, n: 2, v: 2, f: 1}. What is the expected number of occurrences of the pattern 'n*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, i: 2, b: 1, e: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, z: 1, w: 1, m: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, t: 2, f: 1, b: 2}, what is the expected number of times the pattern 'ft+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 4, w: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, y: 2, k: 1, c: 1, n: 1}, what is the expected number of times the pattern 'y*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, o: 4}. What is the expected number of occurrences of the pattern 'o*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, v: 1, x: 1, t: 1, j: 2}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, e: 2, q: 2, o: 1}. What is the expected number of occurrences of the pattern 'm+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, c: 1, u: 1, o: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'u.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, q: 1, j: 2, s: 1}, what is the expected number of times the pattern 'q.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, r: 1, t: 2, j: 1}. What is the expected number of occurrences of the pattern 'r.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, b: 4} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, l: 2, u: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, n: 3}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, i: 2, h: 1} to form a word, what is the expected number of matches of the pattern 'hu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, n: 1, z: 2, o: 2}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, e: 3}, what is the expected number of times the pattern 'e+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, j: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'j*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, o: 2, h: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'f.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, k: 3} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, v: 3, j: 1} to form a word, what is the expected number of matches of the pattern 'tj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, s: 2, o: 3}, what is the expected number of times the pattern 'sc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, k: 1, r: 2, p: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, v: 3}, what is the expected number of times the pattern 'v+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, h: 1, j: 3, a: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, k: 2, p: 2}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, d: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'z*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, t: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'tm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, i: 3, f: 2}. What is the expected number of occurrences of the pattern 'vf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, h: 1, y: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, v: 2, w: 2} to form a word, what is the expected number of matches of the pattern 'd.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, e: 1, s: 2, o: 2}, what is the expected number of times the pattern 'ce+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, q: 1, y: 3, h: 1} to form a word, what is the expected number of matches of the pattern 'qy+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, i: 3} to form a word, what is the expected number of matches of the pattern 'in+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, k: 2, r: 2}. What is the expected number of occurrences of the pattern 'k*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, t: 2, b: 2}, what is the expected number of times the pattern 't+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, k: 1, i: 2, c: 2}. What is the expected number of occurrences of the pattern 'cy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, f: 4} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, y: 1, f: 1, v: 1, s: 2}. What is the expected number of occurrences of the pattern 'ys*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, c: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'pk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, e: 2, l: 1, y: 2}, what is the expected number of times the pattern 'y.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, j: 2, z: 2}. What is the expected number of occurrences of the pattern 'zj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, w: 1, j: 1, u: 1, g: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 4, c: 2}. What is the expected number of occurrences of the pattern 'c+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, f: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'jf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, m: 2, v: 2}. What is the expected number of occurrences of the pattern 'v*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, d: 1, b: 1, l: 1, i: 1}. What is the expected number of occurrences of the pattern 'it+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, o: 5} to form a word, what is the expected number of matches of the pattern 'o*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 4, y: 2}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 4, m: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'h.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, b: 4} to form a word, what is the expected number of matches of the pattern 'nb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, x: 1, n: 2, e: 1, j: 1}, what is the expected number of times the pattern 'nj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, b: 3, j: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, j: 3} to form a word, what is the expected number of matches of the pattern 'j*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, x: 4} to form a word, what is the expected number of matches of the pattern 'xs*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, j: 1, y: 1, x: 2}, what is the expected number of times the pattern 'x+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, b: 1, s: 2, v: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'm*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, r: 1, z: 1, i: 2, e: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, n: 1, a: 3, q: 1}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, m: 1, t: 3}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, x: 2, o: 1, z: 1, k: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, x: 2, s: 1, g: 1, f: 1}, what is the expected number of times the pattern 'g.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, e: 2, g: 2}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, e: 4} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 4, v: 1, w: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, e: 1, a: 2, f: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, v: 3, c: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'v.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, u: 1, f: 1, c: 2}, what is the expected number of times the pattern 'lf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, q: 3, a: 1}. What is the expected number of occurrences of the pattern 'qz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, x: 1, q: 2, n: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, e: 2, f: 3}, what is the expected number of times the pattern 'g*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 4, b: 2} to form a word, what is the expected number of matches of the pattern 'e.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, p: 1, r: 1, j: 1, n: 2}, what is the expected number of times the pattern 'r*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, r: 4} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, l: 1, d: 1, z: 2, f: 1}, what is the expected number of times the pattern 'l.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, k: 3}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, x: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, a: 4}. What is the expected number of occurrences of the pattern 'a+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, s: 1, z: 1}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, c: 2, j: 2, t: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, y: 1, o: 2, h: 2}. What is the expected number of occurrences of the pattern 'h.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, e: 3} to form a word, what is the expected number of matches of the pattern 'e.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, b: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, k: 1, g: 3}, what is the expected number of times the pattern 's+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, u: 2, t: 3}, what is the expected number of times the pattern 'ta+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, s: 4}. What is the expected number of occurrences of the pattern 'sc+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, n: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, h: 2, e: 1, i: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, b: 2, i: 1, x: 1, j: 1}. What is the expected number of occurrences of the pattern 'is+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, l: 3, j: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, v: 1, z: 1, m: 2}. What is the expected number of occurrences of the pattern 'i.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, n: 3, d: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'k.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, o: 3, d: 1}, what is the expected number of times the pattern 'hd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, x: 3, m: 1, k: 1}, what is the expected number of times the pattern 'kx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, e: 2, a: 3}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, s: 1, d: 1, q: 1, f: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, x: 1, q: 3} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, i: 3, q: 1} to form a word, what is the expected number of matches of the pattern 'ki+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, v: 2, b: 1, p: 1}. What is the expected number of occurrences of the pattern 'v*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, u: 2, l: 1, i: 1, c: 1}, what is the expected number of times the pattern 'u.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, w: 1, h: 2, c: 2}, what is the expected number of times the pattern 'w*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, q: 4} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, w: 3}. What is the expected number of occurrences of the pattern 'wq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, l: 1, k: 1, q: 2, u: 1}. What is the expected number of occurrences of the pattern 'lu+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, h: 2, e: 1, i: 2}. What is the expected number of occurrences of the pattern 'e.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, g: 2, i: 1, z: 1, t: 1}. What is the expected number of occurrences of the pattern 'rz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, j: 1, e: 1, t: 2} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, n: 1, t: 2, e: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, j: 1, g: 1, p: 2}, what is the expected number of times the pattern 'y*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, b: 3, r: 1}. What is the expected number of occurrences of the pattern 'rr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, d: 1, l: 3} to form a word, what is the expected number of matches of the pattern 'x*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, e: 4} to form a word, what is the expected number of matches of the pattern 'i*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, e: 2, o: 1, w: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, x: 1, t: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, p: 4, m: 1}. What is the expected number of occurrences of the pattern 'o.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, j: 1, m: 2, b: 1}. What is the expected number of occurrences of the pattern 'cb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 4, e: 1, l: 1}, what is the expected number of times the pattern 'ee+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, y: 1, s: 1, e: 2}. What is the expected number of occurrences of the pattern 'yq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, i: 3} to form a word, what is the expected number of matches of the pattern 'il*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 5, e: 1} to form a word, what is the expected number of matches of the pattern 'e.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, k: 3, r: 2}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, a: 4, y: 1}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, u: 4}. What is the expected number of occurrences of the pattern 'w*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, y: 1, k: 3} to form a word, what is the expected number of matches of the pattern 'k*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, u: 2, s: 1, q: 1, d: 1}. What is the expected number of occurrences of the pattern 'du+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, q: 1, i: 3}. What is the expected number of occurrences of the pattern 's.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, w: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'p.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, i: 3}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, v: 1, k: 2, u: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'n+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 4, s: 2}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, o: 2, t: 1}. What is the expected number of occurrences of the pattern 't*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, l: 2, d: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, p: 1, d: 2}. What is the expected number of occurrences of the pattern 'vd+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, v: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'us+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, y: 1, a: 2, q: 2} to form a word, what is the expected number of matches of the pattern 'yt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, p: 1, a: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, d: 3}, what is the expected number of times the pattern 'd.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, l: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'l*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 4, y: 2}, what is the expected number of times the pattern 'sy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, j: 2, h: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'y.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, t: 1, n: 2, p: 2}. What is the expected number of occurrences of the pattern 'n+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, h: 1, j: 2, u: 1, p: 1}. What is the expected number of occurrences of the pattern 'a+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, k: 1, n: 2, c: 1} to form a word, what is the expected number of matches of the pattern 'l+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, v: 1, s: 1, p: 1, i: 1}. What is the expected number of occurrences of the pattern 's.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 4, z: 2} to form a word, what is the expected number of matches of the pattern 'oz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, g: 2, q: 3}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, h: 1, w: 1, v: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'wv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, f: 2, l: 1, v: 2}, what is the expected number of times the pattern 'vf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, b: 4} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, p: 4}. What is the expected number of occurrences of the pattern 'e+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 4, o: 2}, what is the expected number of times the pattern 'so+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, o: 1, a: 1, k: 1, u: 1}, what is the expected number of times the pattern 'u*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, b: 1, r: 2, n: 1}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, g: 1, s: 2, r: 1}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, k: 2, b: 2}, what is the expected number of times the pattern 'w*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, h: 4} to form a word, what is the expected number of matches of the pattern 'h*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, j: 1, v: 1, t: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'm+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, k: 4}, what is the expected number of times the pattern 'k*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, f: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, i: 2, z: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 4, s: 2}. What is the expected number of occurrences of the pattern 'm+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, d: 2, h: 3}. What is the expected number of occurrences of the pattern 'd*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, v: 2, q: 2, u: 1}. What is the expected number of occurrences of the pattern 'v*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, n: 1, i: 1, f: 1, w: 1}. What is the expected number of occurrences of the pattern 'w.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, r: 1, g: 1, d: 1, m: 1}. What is the expected number of occurrences of the pattern 's*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, g: 2, l: 3}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, x: 1, k: 2, f: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, c: 4}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, p: 2, h: 1, j: 2}. What is the expected number of occurrences of the pattern 'p*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 3, q: 3}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 4, c: 2}. What is the expected number of occurrences of the pattern 'p*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 4, w: 2}, what is the expected number of times the pattern 'w.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, k: 3, r: 2}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, f: 2, m: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, b: 1, g: 1, u: 1, w: 2}. What is the expected number of occurrences of the pattern 'w.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, j: 1, q: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'jx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, g: 1, b: 1, f: 3}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, f: 5} to form a word, what is the expected number of matches of the pattern 'k.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, l: 1, j: 1, i: 2, a: 1}. What is the expected number of occurrences of the pattern 'j.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, m: 3}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 4, x: 2} to form a word, what is the expected number of matches of the pattern 'xx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, a: 3}, what is the expected number of times the pattern 'oa*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, g: 2, w: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'aw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, n: 1, e: 1, k: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'yx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, y: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'h.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, l: 3} to form a word, what is the expected number of matches of the pattern 'o+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, d: 4}. What is the expected number of occurrences of the pattern 'd.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, t: 3}, what is the expected number of times the pattern 'u+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, b: 1, o: 2, i: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, u: 1, w: 1, f: 2, g: 1}, what is the expected number of times the pattern 'kw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, s: 2, r: 1, y: 1, f: 1}. What is the expected number of occurrences of the pattern 'q.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, u: 3, y: 1}, what is the expected number of times the pattern 'yu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, f: 2, y: 1, t: 2} to form a word, what is the expected number of matches of the pattern 'x+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, q: 2, e: 3}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, u: 1, g: 2, d: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, n: 1, k: 1, i: 2, w: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, y: 1, v: 2, a: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, y: 3, x: 2}. What is the expected number of occurrences of the pattern 'y.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, l: 3}. What is the expected number of occurrences of the pattern 'il+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, g: 2, u: 3}, what is the expected number of times the pattern 'ui+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, j: 2, h: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, b: 1, m: 2, s: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, a: 1, b: 3, z: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, s: 3}. What is the expected number of occurrences of the pattern 's*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, b: 5} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, e: 1, a: 3}, what is the expected number of times the pattern 'a.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, h: 2, l: 1, c: 1}, what is the expected number of times the pattern 'x*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, o: 2, y: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, y: 3, w: 1}. What is the expected number of occurrences of the pattern 'vw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, p: 1, s: 2, h: 1}. What is the expected number of occurrences of the pattern 'qs+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, u: 2, t: 1, c: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, i: 1, g: 2, v: 2}, what is the expected number of times the pattern 'cg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 4, d: 2} to form a word, what is the expected number of matches of the pattern 'dc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, w: 4, m: 1} to form a word, what is the expected number of matches of the pattern 'k*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, m: 1, o: 3, l: 1}, what is the expected number of times the pattern 'l.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, f: 4} to form a word, what is the expected number of matches of the pattern 'v.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, e: 2, h: 2}, what is the expected number of times the pattern 'n+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, e: 1, y: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, u: 1, p: 2, e: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, a: 1, k: 1, j: 1, m: 2}. What is the expected number of occurrences of the pattern 'aj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, h: 1, t: 1, a: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'pt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, o: 3}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, z: 2, t: 3} to form a word, what is the expected number of matches of the pattern 'zn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, g: 4}, what is the expected number of times the pattern 'g+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 4, r: 2}. What is the expected number of occurrences of the pattern 'r+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, o: 1, b: 1, c: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, s: 1, z: 1, y: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'sc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, n: 4}. What is the expected number of occurrences of the pattern 'a*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, f: 1, x: 1, r: 3} to form a word, what is the expected number of matches of the pattern 'qf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, h: 2, n: 2, s: 1}, what is the expected number of times the pattern 'hn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'w*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, n: 4, f: 1} to form a word, what is the expected number of matches of the pattern 'f+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 5, a: 1}, what is the expected number of times the pattern 'y*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, o: 1, q: 1, b: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, k: 3, w: 1}, what is the expected number of times the pattern 'vw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, j: 2, x: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'o.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, n: 1, s: 2}. What is the expected number of occurrences of the pattern 's*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, l: 2, j: 2}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, f: 2, y: 1, i: 2}. What is the expected number of occurrences of the pattern 'y.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, h: 1, a: 4}. What is the expected number of occurrences of the pattern 'h*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, f: 2, h: 1, q: 1}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, t: 2, r: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, r: 1, l: 3, p: 1}. What is the expected number of occurrences of the pattern 'rp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, d: 3, h: 2}, what is the expected number of times the pattern 'a+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 4, z: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, n: 1, w: 1, a: 1, g: 1}. What is the expected number of occurrences of the pattern 'gn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, s: 3, c: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, n: 1, t: 2, f: 2}. What is the expected number of occurrences of the pattern 'f+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, m: 1, n: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'g*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, o: 3} to form a word, what is the expected number of matches of the pattern 'ko+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, j: 1, o: 2, p: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, z: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'z*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, i: 3} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, w: 1, s: 1, m: 2, x: 1}. What is the expected number of occurrences of the pattern 'ws+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, f: 4}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, t: 1, e: 1, f: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'g.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, n: 1, i: 3, c: 1}, what is the expected number of times the pattern 'i+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, n: 1, j: 1, g: 1, v: 2}. What is the expected number of occurrences of the pattern 'jn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, v: 1, f: 1, m: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'h*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, e: 1, f: 4}. What is the expected number of occurrences of the pattern 'y+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, l: 3, u: 1}. What is the expected number of occurrences of the pattern 'p.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, c: 2, v: 2, y: 1}. What is the expected number of occurrences of the pattern 'v.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, y: 2, q: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, x: 1, o: 1, s: 1, b: 2}. What is the expected number of occurrences of the pattern 'o+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, w: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'h*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, t: 2, e: 1, d: 1, l: 1}. What is the expected number of occurrences of the pattern 'e*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, f: 4} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, l: 1, t: 1, m: 1, d: 1}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, t: 1, f: 2}. What is the expected number of occurrences of the pattern 'o*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, k: 2, o: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'k*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, u: 1, i: 1, f: 1}. What is the expected number of occurrences of the pattern 'iu+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, v: 2, i: 1, w: 1}. What is the expected number of occurrences of the pattern 'jv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, f: 3, w: 1}. What is the expected number of occurrences of the pattern 'f*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, c: 5}, what is the expected number of times the pattern 'r.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, x: 1, p: 1, d: 3} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, w: 2, r: 2}. What is the expected number of occurrences of the pattern 'wg+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, s: 3}. What is the expected number of occurrences of the pattern 'sm+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, f: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'mf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, r: 1, p: 1, c: 1}. What is the expected number of occurrences of the pattern 'k.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, u: 4} to form a word, what is the expected number of matches of the pattern 'uq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, l: 2, x: 3} to form a word, what is the expected number of matches of the pattern 'l+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, s: 4}. What is the expected number of occurrences of the pattern 'ns*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, l: 1, f: 2, r: 1}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 4, i: 2} to form a word, what is the expected number of matches of the pattern 'd.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, m: 1, n: 1, a: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'ma*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, d: 1, t: 3, n: 1} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, d: 2, z: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'z.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, u: 1, q: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'p+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 5, k: 1}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, u: 2, m: 2, c: 1}, what is the expected number of times the pattern 'm+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, p: 3, t: 2}. What is the expected number of occurrences of the pattern 'ps*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, o: 1, g: 1, h: 1, b: 1}, what is the expected number of times the pattern 'hg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, w: 3}. What is the expected number of occurrences of the pattern 'w.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, z: 1, l: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, h: 4}. What is the expected number of occurrences of the pattern 'h.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, m: 1, o: 2, e: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, y: 1, a: 1, p: 2, l: 1}, what is the expected number of times the pattern 'p+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, x: 2, l: 3} to form a word, what is the expected number of matches of the pattern 'nl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, f: 1, e: 1, i: 2}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, c: 3, f: 1, m: 1}, what is the expected number of times the pattern 'fc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, h: 3}. What is the expected number of occurrences of the pattern 'l+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, m: 1, o: 1, n: 1}, what is the expected number of times the pattern 'om*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, i: 3, b: 2} to form a word, what is the expected number of matches of the pattern 'i+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, l: 3, i: 2} to form a word, what is the expected number of matches of the pattern 'l+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, f: 1, a: 2, r: 1, i: 1}, what is the expected number of times the pattern 'i*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 5, g: 1}. What is the expected number of occurrences of the pattern 'gw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, m: 3, f: 2}, what is the expected number of times the pattern 'f.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, r: 2, y: 1, g: 1, c: 1}, what is the expected number of times the pattern 'gy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, p: 3, g: 2} to form a word, what is the expected number of matches of the pattern 'gp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, s: 2, n: 1, e: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, m: 4}, what is the expected number of times the pattern 'n.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, a: 2, d: 1, t: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'rt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, c: 1, d: 1, q: 1, n: 2}. What is the expected number of occurrences of the pattern 'c*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, c: 2, u: 2}, what is the expected number of times the pattern 'n*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 4, n: 1, a: 1}. What is the expected number of occurrences of the pattern 'a+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, o: 1, s: 1, g: 1, q: 1}, what is the expected number of times the pattern 'o+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, s: 4} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, b: 2, k: 1, q: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'qa+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, v: 3, s: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'vm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, x: 1, f: 2, u: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'f+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, g: 1, b: 1, m: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, w: 3, b: 1} to form a word, what is the expected number of matches of the pattern 'ww*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, i: 4, z: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, n: 2, y: 3} to form a word, what is the expected number of matches of the pattern 'l+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, p: 1, k: 2, z: 1, x: 1}, what is the expected number of times the pattern 'x*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 5, i: 1} to form a word, what is the expected number of matches of the pattern 'im+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, d: 1, x: 1, e: 1, g: 2}. What is the expected number of occurrences of the pattern 'm*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 3, r: 1, t: 1, g: 1} to form a word, what is the expected number of matches of the pattern 't.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, m: 2, b: 1, s: 1, j: 1}. What is the expected number of occurrences of the pattern 'j.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, a: 1, w: 1, b: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'wp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 4, w: 2}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, w: 2, k: 1}. What is the expected number of occurrences of the pattern 'w+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, c: 1, i: 1, y: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'i+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, v: 3}, what is the expected number of times the pattern 'iv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 4, o: 2}, what is the expected number of times the pattern 'oj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, c: 3}, what is the expected number of times the pattern 'xc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, y: 1, a: 1, v: 1, m: 1}. What is the expected number of occurrences of the pattern 'aw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 4, x: 1, c: 1}. What is the expected number of occurrences of the pattern 'x+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, y: 1, q: 1, p: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'p+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, o: 2, n: 1, f: 1, b: 1}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, v: 2, d: 1, e: 1, h: 1}, what is the expected number of times the pattern 'd.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, s: 2, v: 2}. What is the expected number of occurrences of the pattern 's+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, q: 2, j: 2}. What is the expected number of occurrences of the pattern 'q*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, m: 1, n: 1, r: 3} to form a word, what is the expected number of matches of the pattern 'm.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 4, f: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, e: 1, s: 1, n: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'nf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, b: 3, d: 1}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, r: 1, x: 1, i: 1, z: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, e: 2, z: 1, b: 1, s: 1} to form a word, what is the expected number of matches of the pattern 's.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, h: 1, j: 2, p: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'u*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, s: 2, g: 3}. What is the expected number of occurrences of the pattern 'm*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, q: 3, o: 1} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, h: 1, n: 2}, what is the expected number of times the pattern 'v+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, z: 2, v: 2, b: 1}, what is the expected number of times the pattern 'vq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, y: 1, s: 2, m: 2}, what is the expected number of times the pattern 'ys+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, e: 1, h: 1, n: 1, l: 2}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, x: 1, c: 2, m: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'x+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, u: 3, g: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'u*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, k: 2, u: 2, a: 1}, what is the expected number of times the pattern 'e+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, e: 2, w: 1, k: 1}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, w: 1, j: 1, e: 1, m: 1}. What is the expected number of occurrences of the pattern 'j+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, h: 1, t: 1, o: 2, a: 1}, what is the expected number of times the pattern 'h.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 4, h: 2}. What is the expected number of occurrences of the pattern 'h+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, i: 1, x: 3, j: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, t: 3}. What is the expected number of occurrences of the pattern 't*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, j: 2, b: 1, f: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, p: 3, m: 1}. What is the expected number of occurrences of the pattern 'm.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, q: 1, c: 1, l: 1}, what is the expected number of times the pattern 'c*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, r: 1, j: 3}. What is the expected number of occurrences of the pattern 'r*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, z: 1, u: 1, n: 2, a: 1}, what is the expected number of times the pattern 'z+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, o: 1, m: 1, h: 1, i: 1}. What is the expected number of occurrences of the pattern 'h*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, x: 1, q: 2, n: 2}. What is the expected number of occurrences of the pattern 'nx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 3, c: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'r+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, j: 3, l: 2} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, z: 2, g: 1, b: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, q: 1, n: 2}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, y: 1, l: 2, r: 1, g: 1}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, i: 1, w: 1, f: 3}, what is the expected number of times the pattern 'f.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, l: 2, b: 1, p: 2}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, p: 1, b: 2, j: 1, k: 1}, what is the expected number of times the pattern 'jk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, j: 1, q: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'ju+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, y: 2, z: 2, r: 1}. What is the expected number of occurrences of the pattern 'y.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, a: 1, j: 1, c: 1, w: 2}. What is the expected number of occurrences of the pattern 'ja*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, o: 2, y: 1, h: 1}, what is the expected number of times the pattern 'ob*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, g: 1, e: 1, i: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 4, k: 2} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, l: 2, t: 2, s: 1}, what is the expected number of times the pattern 's*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, e: 3, q: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, a: 3, m: 1}, what is the expected number of times the pattern 'ma*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, e: 1, l: 1, p: 2}. What is the expected number of occurrences of the pattern 'p+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, t: 3}. What is the expected number of occurrences of the pattern 'te*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, g: 3, j: 1}. What is the expected number of occurrences of the pattern 'j.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, m: 2, h: 2, r: 1}. What is the expected number of occurrences of the pattern 'm.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, z: 3, k: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'e.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, s: 4}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 4, v: 1, n: 1}. What is the expected number of occurrences of the pattern 'nv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, a: 4} to form a word, what is the expected number of matches of the pattern 'a*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 5, y: 1}, what is the expected number of times the pattern 'xy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, o: 2, i: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 4, z: 2} to form a word, what is the expected number of matches of the pattern 'z+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, l: 3, f: 2}, what is the expected number of times the pattern 'lc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, p: 1, o: 2, i: 1, a: 1}, what is the expected number of times the pattern 'a.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, a: 1, p: 2, c: 1}, what is the expected number of times the pattern 'c.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, g: 1, n: 2, d: 1}, what is the expected number of times the pattern 'n*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, d: 1, s: 3}, what is the expected number of times the pattern 'gd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, a: 3} to form a word, what is the expected number of matches of the pattern 'ka*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, f: 1, g: 1, h: 3}. What is the expected number of occurrences of the pattern 'hf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 5, l: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, b: 1, a: 2, v: 1, x: 1}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, u: 2, b: 1}. What is the expected number of occurrences of the pattern 'u+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, r: 1, p: 2, t: 2}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, q: 1, c: 1, o: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'tg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, k: 1, n: 1, t: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'ql+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, h: 1, x: 1, o: 1, n: 2}, what is the expected number of times the pattern 'o*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, b: 5}, what is the expected number of times the pattern 'o.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, h: 3, r: 2}. What is the expected number of occurrences of the pattern 'g+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, d: 4}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, f: 1, w: 2}. What is the expected number of occurrences of the pattern 'f.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, g: 3} to form a word, what is the expected number of matches of the pattern 'g+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, d: 3, c: 1} to form a word, what is the expected number of matches of the pattern 'd.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, r: 3, a: 1}. What is the expected number of occurrences of the pattern 'ra*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, x: 3, g: 1}. What is the expected number of occurrences of the pattern 'g*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, a: 3}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, w: 1, f: 1, c: 2, s: 1}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, m: 1, q: 1, h: 2}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, w: 1, o: 1, q: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'wk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, a: 1, v: 1, o: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'zo+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 3, m: 2, f: 1}, what is the expected number of times the pattern 'ms*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, d: 2, y: 1, g: 1, z: 1}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, x: 2, r: 1, i: 1}. What is the expected number of occurrences of the pattern 'm+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, a: 4, m: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, l: 3, u: 2}. What is the expected number of occurrences of the pattern 'zu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, x: 1, w: 1, h: 2, v: 1}. What is the expected number of occurrences of the pattern 'wh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, t: 2, i: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, o: 1, m: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'lo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, k: 1, g: 1, t: 1, h: 2}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, k: 1, m: 1, l: 3}. What is the expected number of occurrences of the pattern 'k.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, k: 2, q: 2}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, n: 1, f: 1, z: 2, r: 1}. What is the expected number of occurrences of the pattern 'r+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, w: 3, c: 2}. What is the expected number of occurrences of the pattern 'c.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, v: 1, n: 3, y: 1} to form a word, what is the expected number of matches of the pattern 'n+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, f: 4}. What is the expected number of occurrences of the pattern 'ef+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, w: 2, v: 1, q: 1, b: 1}. What is the expected number of occurrences of the pattern 'v*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, d: 2, w: 1, l: 1, n: 1}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, r: 2, y: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, c: 2, b: 1, u: 1, d: 1}, what is the expected number of times the pattern 'd*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, b: 3, r: 1}, what is the expected number of times the pattern 'v+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, x: 3, m: 1, k: 1}. What is the expected number of occurrences of the pattern 'x+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, c: 1, k: 2, l: 2} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, q: 1, m: 2, d: 2}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, m: 4, t: 1}. What is the expected number of occurrences of the pattern 'd*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 4, i: 2}. What is the expected number of occurrences of the pattern 'ik+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, y: 3, c: 1, a: 1}. What is the expected number of occurrences of the pattern 'c*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, q: 1, e: 1, z: 2, t: 1}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, z: 1, j: 1, d: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'jp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, p: 4}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, r: 3, o: 2} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, g: 1, p: 1, z: 1}, what is the expected number of times the pattern 'z*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, z: 3, v: 1, n: 1}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, f: 1, o: 1, j: 1, q: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, u: 2, a: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, l: 2, a: 1, b: 1, u: 1}, what is the expected number of times the pattern 'l+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 4, b: 1, k: 1}, what is the expected number of times the pattern 'i.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, b: 1, l: 3}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, h: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'h+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, b: 1, y: 2, p: 1, r: 1}. What is the expected number of occurrences of the pattern 'pr+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, g: 1, k: 3, h: 1}, what is the expected number of times the pattern 'hx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, b: 2, r: 2} to form a word, what is the expected number of matches of the pattern 'rr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, v: 1, d: 2, c: 2} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, f: 1, k: 1, g: 2, p: 1}. What is the expected number of occurrences of the pattern 'f*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, e: 3} to form a word, what is the expected number of matches of the pattern 'e*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, e: 1, k: 3}. What is the expected number of occurrences of the pattern 'ke*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, n: 2, o: 3} to form a word, what is the expected number of matches of the pattern 'ln*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, h: 1, y: 1, b: 2}. What is the expected number of occurrences of the pattern 'h*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, u: 4} to form a word, what is the expected number of matches of the pattern 'y*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, k: 1, v: 1, q: 2, c: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, d: 1, f: 1, h: 1}. What is the expected number of occurrences of the pattern 'h.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, o: 3}. What is the expected number of occurrences of the pattern 'oj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, u: 3, p: 2} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 4, d: 2}, what is the expected number of times the pattern 'd*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, o: 2, n: 3}. What is the expected number of occurrences of the pattern 'o*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 5, c: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, x: 1, z: 2, o: 1, f: 1}. What is the expected number of occurrences of the pattern 'o*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, n: 4}, what is the expected number of times the pattern 's.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, v: 1, o: 1, i: 3}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 4, b: 2} to form a word, what is the expected number of matches of the pattern 'qb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, w: 2, l: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, b: 2, r: 2, i: 1}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, e: 1, i: 3}. What is the expected number of occurrences of the pattern 't+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, p: 1, n: 1, a: 3} to form a word, what is the expected number of matches of the pattern 'ma*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, t: 1, d: 1, y: 2, c: 1}, what is the expected number of times the pattern 'i.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, v: 1, t: 3}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, n: 1, l: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, o: 2, q: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'on+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, c: 2}. What is the expected number of occurrences of the pattern 'u*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, p: 1, g: 2, o: 1, m: 1} to form a word, what is the expected number of matches of the pattern 't.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, b: 1, x: 1, k: 2, n: 1}, what is the expected number of times the pattern 'n*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 4, o: 2}, what is the expected number of times the pattern 'o*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, h: 1, u: 1, j: 3} to form a word, what is the expected number of matches of the pattern 'hj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, r: 2, w: 1, y: 1, b: 1}, what is the expected number of times the pattern 'r.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, i: 3}. What is the expected number of occurrences of the pattern 'ei+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 4, s: 2}, what is the expected number of times the pattern 'as*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, y: 1, q: 1, p: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'q+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, m: 1, u: 2, z: 1, g: 1}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, p: 2, k: 2}. What is the expected number of occurrences of the pattern 'k+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, z: 1, v: 4}. What is the expected number of occurrences of the pattern 'v*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, x: 3, y: 1}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, x: 2, q: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, d: 2, l: 2}, what is the expected number of times the pattern 'y*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, e: 2, p: 1, y: 2}, what is the expected number of times the pattern 'e+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, c: 1, d: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, b: 1, z: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, x: 1, d: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'f+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, e: 2, w: 2}. What is the expected number of occurrences of the pattern 'wi+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, r: 1, w: 2, k: 2}. What is the expected number of occurrences of the pattern 'kw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, a: 1, c: 1, y: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'y*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 4, n: 2} to form a word, what is the expected number of matches of the pattern 'nf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 3, m: 3} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 4, w: 1, j: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 4, b: 2} to form a word, what is the expected number of matches of the pattern 'u+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, s: 2, d: 1, w: 1, a: 1}, what is the expected number of times the pattern 'a*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, l: 1, u: 1, j: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'w+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, i: 4} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, b: 1, w: 1, l: 2, v: 1}, what is the expected number of times the pattern 'w*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, w: 3}. What is the expected number of occurrences of the pattern 'w*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'lb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, n: 1, k: 1, l: 2, b: 1} to form a word, what is the expected number of matches of the pattern 'nn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, h: 1, g: 2, r: 1, p: 1}. What is the expected number of occurrences of the pattern 'h.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, f: 1, v: 1, o: 3}, what is the expected number of times the pattern 'f+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, k: 1, q: 1, p: 1, i: 2}, what is the expected number of times the pattern 'i.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, f: 1, q: 3}, what is the expected number of times the pattern 'pq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, x: 1, k: 1, r: 1, s: 2} to form a word, what is the expected number of matches of the pattern 's*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, j: 1, w: 2, t: 2}, what is the expected number of times the pattern 'wt*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, t: 1, y: 2}. What is the expected number of occurrences of the pattern 'ti+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, z: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, v: 3}. What is the expected number of occurrences of the pattern 'v*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, b: 3, p: 1, h: 1}. What is the expected number of occurrences of the pattern 'lh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, l: 1, g: 1, d: 2}, what is the expected number of times the pattern 'dg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, k: 4} to form a word, what is the expected number of matches of the pattern 'k*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 4, a: 2}. What is the expected number of occurrences of the pattern 'h.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, a: 3, d: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, i: 1, l: 3}, what is the expected number of times the pattern 'lg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, j: 3, b: 1}. What is the expected number of occurrences of the pattern 'js+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 3, j: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'j.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 4, c: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, f: 4} to form a word, what is the expected number of matches of the pattern 'h+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 4, c: 2}. What is the expected number of occurrences of the pattern 'cv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, t: 1, v: 1, r: 1, e: 1}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, n: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'xn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 3, m: 3} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, i: 1, q: 2, k: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, f: 1, q: 2, j: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'l*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, u: 1, p: 2, c: 1, v: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, v: 1, z: 2, j: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, q: 3} to form a word, what is the expected number of matches of the pattern 'q+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, s: 3}, what is the expected number of times the pattern 's.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, a: 1, i: 2}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, q: 2, s: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, v: 4}, what is the expected number of times the pattern 'zv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, m: 1, c: 1, t: 2}, what is the expected number of times the pattern 'y*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, i: 3, k: 1}, what is the expected number of times the pattern 'si*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, f: 4, g: 1}. What is the expected number of occurrences of the pattern 'f+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, w: 1, p: 1, z: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, v: 3, p: 1}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, s: 2, o: 1, w: 1, x: 1}. What is the expected number of occurrences of the pattern 'os+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 4, j: 2}. What is the expected number of occurrences of the pattern 'hj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, p: 4}. What is the expected number of occurrences of the pattern 'w.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, n: 1, f: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'f.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, x: 3, y: 1}, what is the expected number of times the pattern 't*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, h: 2, w: 1, r: 1, c: 1}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, h: 1, w: 2, l: 1, q: 1}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, t: 1, h: 1, r: 1, v: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, k: 1, w: 2, r: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'k.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, l: 4, f: 1}, what is the expected number of times the pattern 'g.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, z: 2, f: 3} to form a word, what is the expected number of matches of the pattern 'f.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, w: 1, e: 2, r: 2}. What is the expected number of occurrences of the pattern 'jw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, c: 1, p: 3, x: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, v: 1, q: 3, h: 1}. What is the expected number of occurrences of the pattern 'vh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, g: 3}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, r: 2, i: 1, q: 1}. What is the expected number of occurrences of the pattern 'ri+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, f: 1, o: 1, z: 2, x: 1} to form a word, what is the expected number of matches of the pattern 'z.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, t: 2, z: 3}, what is the expected number of times the pattern 'z*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, j: 2, b: 1, z: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, p: 1, i: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, n: 2, f: 2}, what is the expected number of times the pattern 'fe*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, w: 4}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, n: 2, f: 2}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, j: 2}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, q: 1, c: 1, d: 1, i: 1}. What is the expected number of occurrences of the pattern 'cn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, n: 2, f: 2, m: 1}. What is the expected number of occurrences of the pattern 'f*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, q: 1, s: 4}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, x: 2, r: 1, e: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'w.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, h: 5}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 4, y: 2} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, j: 2, y: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 4, f: 2}, what is the expected number of times the pattern 'f.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, e: 3, h: 1} to form a word, what is the expected number of matches of the pattern 'm*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, r: 1, s: 3}, what is the expected number of times the pattern 'sw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, i: 2, u: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, l: 1, e: 3} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, w: 1, v: 2, l: 1}. What is the expected number of occurrences of the pattern 'a.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, y: 5}, what is the expected number of times the pattern 'y.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, l: 1, k: 3} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, m: 1, f: 1, j: 3} to form a word, what is the expected number of matches of the pattern 'a.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, z: 1, n: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, w: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, s: 1, t: 2}, what is the expected number of times the pattern 'sr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'vp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, h: 3, x: 2} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, f: 3}, what is the expected number of times the pattern 'f.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, i: 2}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, o: 2, c: 1, d: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 4, w: 2} to form a word, what is the expected number of matches of the pattern 's*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, k: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, g: 2, i: 2}, what is the expected number of times the pattern 'i*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, s: 3} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, k: 1, t: 2, m: 1, g: 1}. What is the expected number of occurrences of the pattern 'ge*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, v: 1, n: 3, h: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, g: 1, n: 1, d: 2, r: 1}, what is the expected number of times the pattern 'nd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 4, k: 2} to form a word, what is the expected number of matches of the pattern 'k*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, w: 1, i: 1, b: 1, c: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, g: 3, n: 1}. What is the expected number of occurrences of the pattern 'ne+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, r: 2, w: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'rq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, q: 1, z: 2, w: 1, j: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, n: 2, r: 3}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, i: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'r.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, q: 2, j: 2}, what is the expected number of times the pattern 'g+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, u: 1, b: 1, q: 1, v: 2}. What is the expected number of occurrences of the pattern 'q.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 4, u: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, l: 2, q: 1, u: 2}. What is the expected number of occurrences of the pattern 'q+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, d: 1, p: 1, h: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'h.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, f: 4} to form a word, what is the expected number of matches of the pattern 'fd+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, z: 2, j: 2}. What is the expected number of occurrences of the pattern 'jz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, l: 3}, what is the expected number of times the pattern 'i.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, k: 2, t: 1, d: 1, j: 1}. What is the expected number of occurrences of the pattern 'd*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, w: 1, d: 1, z: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'w.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, d: 1, f: 2}, what is the expected number of times the pattern 'fd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, o: 2, x: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'wx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, j: 2, d: 1, m: 1, e: 1}, what is the expected number of times the pattern 'j+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, w: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'h.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, q: 4, p: 1} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, k: 3, e: 1}. What is the expected number of occurrences of the pattern 'e.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, x: 1, q: 3}. What is the expected number of occurrences of the pattern 'qq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, u: 1, l: 2, a: 1}. What is the expected number of occurrences of the pattern 'y+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 4, w: 1, a: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, m: 2, v: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, q: 1, g: 1, e: 1, n: 2}, what is the expected number of times the pattern 'g.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, y: 4}, what is the expected number of times the pattern 'u.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 3, y: 1, a: 1, d: 1}. What is the expected number of occurrences of the pattern 'p*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, h: 5}. What is the expected number of occurrences of the pattern 'h+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, r: 3}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, g: 2, b: 2}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, o: 2, u: 2, l: 1}, what is the expected number of times the pattern 'l*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, z: 1, j: 1, a: 2}, what is the expected number of times the pattern 'z+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, v: 2, h: 2}. What is the expected number of occurrences of the pattern 'hv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, u: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'up+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, c: 2, m: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'rm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, z: 1, d: 1, f: 1, b: 1}, what is the expected number of times the pattern 'd+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, x: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'xi*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, j: 3, y: 2}, what is the expected number of times the pattern 'pj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, q: 1, i: 2, h: 1, a: 1}, what is the expected number of times the pattern 'hi+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, d: 2, e: 3}. What is the expected number of occurrences of the pattern 't.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, i: 4}, what is the expected number of times the pattern 'li+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, k: 4}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, x: 2, c: 1, s: 2} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, m: 1, a: 1, c: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 4, r: 2}, what is the expected number of times the pattern 'vr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, l: 1, k: 1, x: 2}, what is the expected number of times the pattern 'x+k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, f: 2, n: 2}. What is the expected number of occurrences of the pattern 'fn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, c: 2, l: 2}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, l: 1, b: 1, n: 2}. What is the expected number of occurrences of the pattern 'n+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, c: 4}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, s: 1, m: 2, l: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'i.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, q: 2, m: 2, s: 1}, what is the expected number of times the pattern 'my+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, i: 1, r: 2, u: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, q: 3, h: 2}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, o: 2, z: 3}. What is the expected number of occurrences of the pattern 'o*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, x: 2, f: 1, i: 1, e: 1}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 4, o: 2} to form a word, what is the expected number of matches of the pattern 'o+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 4, s: 1, n: 1}. What is the expected number of occurrences of the pattern 'g*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, q: 2, g: 2} to form a word, what is the expected number of matches of the pattern 'gf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, c: 1, x: 2, p: 2}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, c: 2, l: 2} to form a word, what is the expected number of matches of the pattern 'l.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, l: 1, d: 1, g: 3} to form a word, what is the expected number of matches of the pattern 'l*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, t: 1, e: 2, f: 1}, what is the expected number of times the pattern 'fe*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, l: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'n+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, s: 1, k: 1, y: 1, v: 2}. What is the expected number of occurrences of the pattern 'vk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, o: 1, c: 3, u: 1}. What is the expected number of occurrences of the pattern 'p*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, k: 1, o: 1, z: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, z: 3, s: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, k: 1, q: 1, f: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'q*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, m: 5}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, w: 1, u: 1, v: 1, k: 2}. What is the expected number of occurrences of the pattern 'kv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, d: 4}, what is the expected number of times the pattern 'd*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, d: 2, v: 1, m: 1, u: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 4, x: 2}, what is the expected number of times the pattern 'ox*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, d: 1, k: 1, j: 1, s: 2}. What is the expected number of occurrences of the pattern 's*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, b: 2, g: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, e: 3}, what is the expected number of times the pattern 'e.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, a: 1, p: 3}, what is the expected number of times the pattern 'pa+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, u: 2, g: 2, s: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, n: 1, z: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, i: 2, a: 1, o: 1, c: 1}. What is the expected number of occurrences of the pattern 'o*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, d: 1, n: 3} to form a word, what is the expected number of matches of the pattern 'f*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, k: 2, s: 2, a: 1}, what is the expected number of times the pattern 'a+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, m: 4}. What is the expected number of occurrences of the pattern 'u.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, d: 1, b: 2, e: 1, q: 1}. What is the expected number of occurrences of the pattern 'n.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, l: 1, i: 1, t: 2, b: 1} to form a word, what is the expected number of matches of the pattern 'ti+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 4, m: 2} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, u: 2, r: 1, y: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'r.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 4, l: 2}, what is the expected number of times the pattern 'l+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, a: 1, o: 1, w: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, h: 3, m: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, i: 1, n: 1, s: 2}. What is the expected number of occurrences of the pattern 'i+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, l: 2, b: 1, k: 1, s: 1}. What is the expected number of occurrences of the pattern 'lb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, h: 3, v: 2}, what is the expected number of times the pattern 'v.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, h: 1, w: 1, o: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, p: 2, j: 1, r: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, d: 2, e: 1, b: 2}. What is the expected number of occurrences of the pattern 'c.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, f: 2, n: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'nf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 4, e: 2} to form a word, what is the expected number of matches of the pattern 'w.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, v: 1, b: 2, m: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, y: 3, f: 2} to form a word, what is the expected number of matches of the pattern 'c+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, h: 1, c: 1, v: 1, s: 2}, what is the expected number of times the pattern 'hj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, k: 2, y: 2}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 3, o: 3} to form a word, what is the expected number of matches of the pattern 'e*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, q: 1, e: 1, c: 3} to form a word, what is the expected number of matches of the pattern 'e.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, d: 2, f: 1, c: 1, v: 1}, what is the expected number of times the pattern 'a*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, x: 1, a: 2}. What is the expected number of occurrences of the pattern 'xa*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, w: 2, l: 3}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 4, k: 2}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 4, t: 2}, what is the expected number of times the pattern 't.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 4, f: 1, c: 1}, what is the expected number of times the pattern 'ff*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, i: 4}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'm.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, s: 4}. What is the expected number of occurrences of the pattern 'sp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, z: 1, j: 1, e: 1, q: 2}. What is the expected number of occurrences of the pattern 'z*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, o: 2, k: 2, e: 1}. What is the expected number of occurrences of the pattern 'v+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, d: 4}, what is the expected number of times the pattern 'd*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, c: 3, o: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 4, w: 2}, what is the expected number of times the pattern 'aw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, p: 1, z: 1, c: 1, j: 2} to form a word, what is the expected number of matches of the pattern 'p*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, s: 5} to form a word, what is the expected number of matches of the pattern 'sw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, n: 1, h: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, q: 3, d: 2} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, y: 2}. What is the expected number of occurrences of the pattern 'y+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, a: 1, u: 3, d: 1} to form a word, what is the expected number of matches of the pattern 'ya+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, b: 1, a: 1, r: 2}. What is the expected number of occurrences of the pattern 'a*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, r: 1, a: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, y: 4} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, i: 1, r: 3}. What is the expected number of occurrences of the pattern 'ri+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, b: 2, h: 3}, what is the expected number of times the pattern 'h.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, f: 2, y: 2}, what is the expected number of times the pattern 'fy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, l: 3}, what is the expected number of times the pattern 'ul*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, m: 3} to form a word, what is the expected number of matches of the pattern 'd*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, a: 1, l: 1, v: 1, j: 1}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 4, m: 2}. What is the expected number of occurrences of the pattern 'mz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 4, i: 2} to form a word, what is the expected number of matches of the pattern 'is*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, l: 1, y: 2, d: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, d: 3}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, f: 2, t: 3}. What is the expected number of occurrences of the pattern 'tf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, t: 2, g: 3}, what is the expected number of times the pattern 'gz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, z: 3, o: 1, r: 1}. What is the expected number of occurrences of the pattern 'q+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, a: 3, r: 1}. What is the expected number of occurrences of the pattern 'ra*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, f: 2, x: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'xn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 4, v: 2} to form a word, what is the expected number of matches of the pattern 'v.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, d: 1, m: 3}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, s: 2, f: 2, j: 1}, what is the expected number of times the pattern 'z.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, b: 2, i: 1, a: 1}. What is the expected number of occurrences of the pattern 'q.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, s: 2, o: 1, i: 1}, what is the expected number of times the pattern 's*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, h: 1, u: 2, w: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'm+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, d: 3, b: 1} to form a word, what is the expected number of matches of the pattern 'dv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, o: 4, s: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, n: 2, u: 2, r: 1}, what is the expected number of times the pattern 'mr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, z: 2, k: 1, h: 2}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, x: 1, b: 1, j: 1, k: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, m: 2, t: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, v: 2, x: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, m: 1, v: 1, z: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'm+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, b: 2, s: 2, d: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, y: 1, q: 2, g: 1, i: 1}, what is the expected number of times the pattern 'y+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, x: 2, i: 3}. What is the expected number of occurrences of the pattern 'ci+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, e: 3, z: 2} to form a word, what is the expected number of matches of the pattern 'e+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, s: 2, x: 1, w: 1}. What is the expected number of occurrences of the pattern 'xs+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, q: 1, d: 1, s: 2}, what is the expected number of times the pattern 'qd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, k: 1, z: 3} to form a word, what is the expected number of matches of the pattern 'kz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, e: 1, m: 2, g: 1, z: 1}, what is the expected number of times the pattern 'zc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, l: 4, u: 1}, what is the expected number of times the pattern 'u.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, v: 1, q: 1, i: 2}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, m: 1, z: 1, q: 2}, what is the expected number of times the pattern 'm+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, i: 1, b: 2}. What is the expected number of occurrences of the pattern 'c*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, h: 2, a: 2, l: 1}, what is the expected number of times the pattern 'hj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, t: 1, j: 1, g: 3}. What is the expected number of occurrences of the pattern 't.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 5, a: 1}, what is the expected number of times the pattern 'ag+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, a: 3}. What is the expected number of occurrences of the pattern 'v*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, e: 1, k: 1, f: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'le*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, n: 1, j: 2, o: 1}. What is the expected number of occurrences of the pattern 'q*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, k: 1, b: 1, u: 1, l: 1}, what is the expected number of times the pattern 'uk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 4, g: 2} to form a word, what is the expected number of matches of the pattern 'g+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, l: 4} to form a word, what is the expected number of matches of the pattern 'l*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, e: 2, u: 2, g: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 4, j: 2}, what is the expected number of times the pattern 'j*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, j: 1, l: 1, k: 1, i: 1}, what is the expected number of times the pattern 'kl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, f: 3}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, d: 1, b: 2, n: 1}, what is the expected number of times the pattern 's.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, m: 3, v: 1}. What is the expected number of occurrences of the pattern 'v*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, y: 3}, what is the expected number of times the pattern 'i+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, y: 3}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, m: 1, t: 2, h: 1, y: 1}. What is the expected number of occurrences of the pattern 'y+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, e: 3, b: 2} to form a word, what is the expected number of matches of the pattern 'e*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, q: 1, e: 3}. What is the expected number of occurrences of the pattern 'e+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 4, e: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 4, w: 2}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, q: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, o: 2, q: 3}. What is the expected number of occurrences of the pattern 'o+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 4, t: 2} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, y: 5}. What is the expected number of occurrences of the pattern 'xy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, w: 1, p: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'd.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, b: 2, w: 1, a: 2}, what is the expected number of times the pattern 'a*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, r: 3, o: 1, c: 1}, what is the expected number of times the pattern 'c.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, d: 1, r: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'wr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, z: 2, r: 2, m: 1}, what is the expected number of times the pattern 'r*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, c: 1, z: 1, i: 1, d: 1}. What is the expected number of occurrences of the pattern 'k+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, i: 2, f: 2, b: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 4, i: 2}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, z: 3, y: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, m: 4}. What is the expected number of occurrences of the pattern 'z+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, x: 1, y: 1, k: 1, j: 2}. What is the expected number of occurrences of the pattern 'y.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, h: 2, b: 1} to form a word, what is the expected number of matches of the pattern 'ho*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, d: 1, m: 2, r: 1}. What is the expected number of occurrences of the pattern 'n.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, t: 1, n: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'on*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, o: 1, p: 2, k: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'kp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, o: 4}. What is the expected number of occurrences of the pattern 'jo*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, k: 2, y: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'xy+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, x: 2, u: 1}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, y: 2, z: 1, h: 2}. What is the expected number of occurrences of the pattern 'h*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, k: 4}, what is the expected number of times the pattern 'k.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, c: 4}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, h: 4} to form a word, what is the expected number of matches of the pattern 'ph+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, n: 3, z: 2} to form a word, what is the expected number of matches of the pattern 'nz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, f: 2, h: 1, e: 1, v: 1}, what is the expected number of times the pattern 'f+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, e: 4} to form a word, what is the expected number of matches of the pattern 're*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, u: 3, g: 2} to form a word, what is the expected number of matches of the pattern 'u+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 4, t: 2} to form a word, what is the expected number of matches of the pattern 'ut*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, t: 2, r: 1, a: 2}. What is the expected number of occurrences of the pattern 'rq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, e: 2, s: 2} to form a word, what is the expected number of matches of the pattern 'e*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, i: 3, k: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'ji+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, e: 2, l: 1, j: 1, v: 1}. What is the expected number of occurrences of the pattern 'q*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, f: 4}. What is the expected number of occurrences of the pattern 'y*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, u: 1, t: 4}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, l: 1, g: 1, x: 1, h: 1}, what is the expected number of times the pattern 'x*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, i: 2, e: 1, s: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'ki+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, j: 1, v: 1, r: 3}. What is the expected number of occurrences of the pattern 'u*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, c: 3, s: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, d: 1, n: 2, f: 1, b: 1}, what is the expected number of times the pattern 'ff*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, h: 1, j: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, n: 2, s: 3} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, o: 4}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, h: 2, n: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, u: 1, e: 2, b: 1, g: 1}, what is the expected number of times the pattern 'g.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, q: 3}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, q: 1, c: 1, n: 1, v: 1}. What is the expected number of occurrences of the pattern 'q.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, s: 3, l: 1, w: 1}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 4, v: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'v*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, v: 2, l: 1, m: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, h: 1, w: 1, q: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'q+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, e: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'uc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, e: 2, p: 1, b: 1}. What is the expected number of occurrences of the pattern 'pe+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, h: 1, t: 2}, what is the expected number of times the pattern 'ht+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, q: 1, c: 2}. What is the expected number of occurrences of the pattern 'q*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, s: 1, w: 1, f: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'n*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, k: 1, l: 2, g: 1}. What is the expected number of occurrences of the pattern 'g*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'l*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, u: 2, t: 2}. What is the expected number of occurrences of the pattern 't*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, h: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'zh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, m: 2, y: 1, s: 1}. What is the expected number of occurrences of the pattern 'm.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, e: 5} to form a word, what is the expected number of matches of the pattern 'k*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, s: 3, l: 2} to form a word, what is the expected number of matches of the pattern 'd+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 4, i: 2}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, i: 2, h: 3}. What is the expected number of occurrences of the pattern 'i+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, y: 3} to form a word, what is the expected number of matches of the pattern 'y.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, v: 2, t: 1, l: 1}. What is the expected number of occurrences of the pattern 'jt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, p: 4}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, v: 1, c: 1, x: 3} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, e: 1, d: 1, g: 2, f: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, y: 2, t: 2, s: 1}, what is the expected number of times the pattern 'as*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, a: 1, q: 1, l: 1}. What is the expected number of occurrences of the pattern 'l.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 3, x: 3}. What is the expected number of occurrences of the pattern 'p*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, o: 1, u: 1, c: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'c*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, w: 2, o: 2, i: 1}, what is the expected number of times the pattern 'co+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, g: 2, e: 2, u: 1}. What is the expected number of occurrences of the pattern 'gy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, k: 3}, what is the expected number of times the pattern 'z*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, i: 1, d: 1, w: 2}, what is the expected number of times the pattern 'i*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, x: 1, b: 3, o: 1}. What is the expected number of occurrences of the pattern 'g+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 4, a: 2} to form a word, what is the expected number of matches of the pattern 'ma+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, r: 2, t: 1, j: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'r.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, a: 2, x: 3} to form a word, what is the expected number of matches of the pattern 'xa+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, o: 1, a: 1, m: 3} to form a word, what is the expected number of matches of the pattern 'r+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, a: 1, r: 2, n: 1, y: 1}. What is the expected number of occurrences of the pattern 'n*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 5, g: 1}, what is the expected number of times the pattern 'dg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, c: 1, k: 1, n: 2, u: 1}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, j: 1, h: 1, c: 2, k: 1}. What is the expected number of occurrences of the pattern 'c.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, u: 4, h: 1} to form a word, what is the expected number of matches of the pattern 'w*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, w: 1, y: 2, n: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'n+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, s: 1, u: 1, m: 1, k: 1}. What is the expected number of occurrences of the pattern 'ks+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, b: 2, o: 1, n: 1}, what is the expected number of times the pattern 'o*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, u: 2, m: 1, r: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, u: 3, t: 1, m: 1}, what is the expected number of times the pattern 'u*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, c: 2, o: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 4, x: 2}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, b: 1, c: 1, i: 1, u: 2}, what is the expected number of times the pattern 'j*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, b: 4}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, i: 1, z: 1, w: 2, j: 1}, what is the expected number of times the pattern 'wz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, x: 1, z: 1, d: 1}, what is the expected number of times the pattern 'z*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, y: 1, t: 2, m: 1, x: 1}, what is the expected number of times the pattern 'y*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 4, c: 2} to form a word, what is the expected number of matches of the pattern 'jc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, f: 2, j: 2}. What is the expected number of occurrences of the pattern 'jg*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, c: 2, g: 2}. What is the expected number of occurrences of the pattern 'yc+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 4, m: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, d: 1, s: 1, u: 2, a: 1}, what is the expected number of times the pattern 'ds*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, w: 4}. What is the expected number of occurrences of the pattern 'f.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, n: 3}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, j: 1, e: 1, c: 3} to form a word, what is the expected number of matches of the pattern 'e+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, r: 1, w: 1, g: 2, p: 1}, what is the expected number of times the pattern 'e+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, o: 1, z: 2, i: 1, x: 1}, what is the expected number of times the pattern 'i*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, d: 4} to form a word, what is the expected number of matches of the pattern 'u.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, q: 3}. What is the expected number of occurrences of the pattern 'd+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, a: 1, e: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, n: 1, c: 1, v: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, o: 1, u: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'p.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, y: 1, c: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, d: 2, v: 1, s: 1, l: 1}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, s: 1, c: 1, v: 2, w: 1}. What is the expected number of occurrences of the pattern 's+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, o: 1, y: 1, b: 3}. What is the expected number of occurrences of the pattern 'o*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 5, d: 1}, what is the expected number of times the pattern 'z*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 4, v: 2} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, f: 2, d: 3}. What is the expected number of occurrences of the pattern 'f+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, x: 1, l: 3, d: 1} to form a word, what is the expected number of matches of the pattern 'l+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, h: 3, c: 2} to form a word, what is the expected number of matches of the pattern 'h*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, d: 2, o: 2}. What is the expected number of occurrences of the pattern 'o.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, t: 2, n: 1, i: 2}. What is the expected number of occurrences of the pattern 'ic+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, o: 1, u: 3}. What is the expected number of occurrences of the pattern 'ou*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 4, s: 2} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, m: 3, v: 1, w: 1}. What is the expected number of occurrences of the pattern 'vj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, u: 2, y: 1, t: 1, e: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, r: 1, e: 1, s: 1, v: 1}, what is the expected number of times the pattern 'qv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, w: 2, l: 3}, what is the expected number of times the pattern 'l+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, r: 4}. What is the expected number of occurrences of the pattern 'wr+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, u: 3, w: 2} to form a word, what is the expected number of matches of the pattern 'u.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, s: 1, z: 2, c: 1, k: 1}. What is the expected number of occurrences of the pattern 's*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, b: 2, u: 2, c: 1}. What is the expected number of occurrences of the pattern 'uu+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, c: 3, l: 1}. What is the expected number of occurrences of the pattern 'c+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, q: 2, h: 1, o: 2}. What is the expected number of occurrences of the pattern 'a+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, s: 2, i: 1, k: 1}. What is the expected number of occurrences of the pattern 'y+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, v: 1, i: 1, s: 2}. What is the expected number of occurrences of the pattern 's+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, e: 5} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, e: 1, i: 1, n: 2, m: 1}. What is the expected number of occurrences of the pattern 'ne+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, a: 4} to form a word, what is the expected number of matches of the pattern 'k.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, x: 3, m: 1}, what is the expected number of times the pattern 'jm+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, p: 4} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, k: 4}, what is the expected number of times the pattern 'ka*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, s: 3, r: 1}, what is the expected number of times the pattern 'sr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, x: 1, u: 1, q: 1, g: 2}, what is the expected number of times the pattern 'xd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, j: 1, g: 2, z: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'jz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, x: 1, s: 2, z: 1, e: 1}, what is the expected number of times the pattern 's*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, f: 1, q: 3}, what is the expected number of times the pattern 'h*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, o: 1, z: 1, w: 3} to form a word, what is the expected number of matches of the pattern 'cz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, t: 5} to form a word, what is the expected number of matches of the pattern 'wt+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, g: 2, j: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'jg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, g: 3}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, f: 1, u: 1, r: 1, o: 1}. What is the expected number of occurrences of the pattern 'rf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, p: 1, u: 1, a: 1, v: 2}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, x: 3, w: 1}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, s: 1, c: 2, y: 1}, what is the expected number of times the pattern 's.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, h: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'ha+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, v: 1, c: 1, f: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'i.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, b: 3}. What is the expected number of occurrences of the pattern 'jj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, a: 1, m: 1, f: 3}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 4, h: 2}. What is the expected number of occurrences of the pattern 'sh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, f: 1, o: 3}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, c: 1, b: 2}, what is the expected number of times the pattern 'f.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, n: 1, s: 1, j: 1, y: 1}, what is the expected number of times the pattern 'xn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, v: 2, d: 1, k: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'pk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, q: 1, x: 3}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, d: 1, p: 1, v: 2}, what is the expected number of times the pattern 'vd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, n: 1, g: 3} to form a word, what is the expected number of matches of the pattern 'ng*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, f: 4}, what is the expected number of times the pattern 'nf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, a: 3}. What is the expected number of occurrences of the pattern 'f+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, i: 2, e: 1}, what is the expected number of times the pattern 'h.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, a: 1, m: 1, o: 2}, what is the expected number of times the pattern 'i*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, k: 1, i: 1, v: 1, x: 1}. What is the expected number of occurrences of the pattern 'x.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, v: 4}. What is the expected number of occurrences of the pattern 'c+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, d: 1, q: 1, y: 1, f: 1}, what is the expected number of times the pattern 'f*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, k: 3, m: 1} to form a word, what is the expected number of matches of the pattern 'k*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, w: 2, s: 3} to form a word, what is the expected number of matches of the pattern 'sw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, h: 1, y: 2, p: 1}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, y: 3, p: 1}, what is the expected number of times the pattern 'pb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, e: 1, l: 1, r: 2} to form a word, what is the expected number of matches of the pattern 's+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, r: 3, g: 1}. What is the expected number of occurrences of the pattern 'ra+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, o: 2, c: 2} to form a word, what is the expected number of matches of the pattern 'co*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, k: 1, c: 2, t: 1, b: 1}, what is the expected number of times the pattern 'vt+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, d: 1, t: 1, l: 1, x: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, l: 2, s: 1, k: 1, y: 1}, what is the expected number of times the pattern 's.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, o: 1, z: 1, e: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, c: 1, r: 1, q: 1, p: 2}. What is the expected number of occurrences of the pattern 'r*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, e: 2, u: 1, t: 2}, what is the expected number of times the pattern 't+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, b: 1, x: 1, f: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, a: 3, y: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, m: 1, n: 1, e: 2, c: 1}, what is the expected number of times the pattern 'c.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, i: 1, a: 2, b: 1, z: 1}, what is the expected number of times the pattern 'z+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, t: 1, g: 2, w: 1}. What is the expected number of occurrences of the pattern 'td+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, h: 3}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, o: 2, g: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'g.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, i: 3} to form a word, what is the expected number of matches of the pattern 'ai*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, z: 1, o: 1, i: 2, h: 1}, what is the expected number of times the pattern 'o.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, v: 1, b: 2, l: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'l+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, l: 2, z: 3}, what is the expected number of times the pattern 'lb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, n: 2, h: 1}, what is the expected number of times the pattern 'nh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, q: 2, p: 2}, what is the expected number of times the pattern 'p+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, e: 3}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 4, k: 2} to form a word, what is the expected number of matches of the pattern 'pk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, b: 1, h: 1, g: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 5, i: 1}. What is the expected number of occurrences of the pattern 'i*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, h: 1, k: 3}. What is the expected number of occurrences of the pattern 'k+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, y: 3} to form a word, what is the expected number of matches of the pattern 'y.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, p: 2, g: 2}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, t: 1, c: 1, j: 2, f: 1}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, a: 1, d: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, n: 1, r: 2}, what is the expected number of times the pattern 'v*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, c: 3}. What is the expected number of occurrences of the pattern 'cz*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, t: 1, s: 2, o: 1, b: 1}, what is the expected number of times the pattern 'ot+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 3, h: 2, g: 1}, what is the expected number of times the pattern 'sg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, m: 1, a: 2}, what is the expected number of times the pattern 'i+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, j: 4} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, f: 1, e: 2, i: 1, w: 1}, what is the expected number of times the pattern 'wf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, n: 1, p: 3}. What is the expected number of occurrences of the pattern 'ap*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, k: 1, l: 4}, what is the expected number of times the pattern 'fl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, q: 1, v: 1, h: 1, w: 1}. What is the expected number of occurrences of the pattern 'wv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, q: 2, u: 3} to form a word, what is the expected number of matches of the pattern 'q*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, m: 2, j: 1, y: 1, q: 1}. What is the expected number of occurrences of the pattern 'qf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, o: 1, a: 3}, what is the expected number of times the pattern 'oa*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, d: 2, y: 2}, what is the expected number of times the pattern 'cy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, s: 5} to form a word, what is the expected number of matches of the pattern 's+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, s: 1, r: 1, o: 1, x: 1}. What is the expected number of occurrences of the pattern 's*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, x: 3}, what is the expected number of times the pattern 'cx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, n: 1, m: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'na+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, m: 1, p: 1, a: 2, d: 1}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, y: 2, x: 2}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, m: 1, d: 2, u: 1}. What is the expected number of occurrences of the pattern 'mn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, a: 1, z: 1, u: 2, v: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, d: 1, e: 3, m: 1} to form a word, what is the expected number of matches of the pattern 'e.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, s: 1, b: 3}. What is the expected number of occurrences of the pattern 'ys+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, g: 1, m: 4}, what is the expected number of times the pattern 'lm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, m: 1, f: 2, l: 1, s: 1}, what is the expected number of times the pattern 's.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 4, n: 2}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, y: 2, h: 1, j: 1, x: 1}. What is the expected number of occurrences of the pattern 'hl+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, j: 1, o: 2, z: 1}. What is the expected number of occurrences of the pattern 'j.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, h: 2, q: 2} to form a word, what is the expected number of matches of the pattern 'hs*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, r: 1, x: 1, s: 3}. What is the expected number of occurrences of the pattern 's*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, d: 1, w: 3}. What is the expected number of occurrences of the pattern 'w*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, f: 4}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, a: 4} to form a word, what is the expected number of matches of the pattern 'j+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, f: 3}. What is the expected number of occurrences of the pattern 'f*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, e: 1, j: 3}. What is the expected number of occurrences of the pattern 'je+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, k: 3, l: 2}, what is the expected number of times the pattern 'k.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, d: 2, l: 3} to form a word, what is the expected number of matches of the pattern 'd.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, p: 2, a: 1, y: 2}, what is the expected number of times the pattern 'y.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, k: 1, y: 1, o: 2, d: 1}, what is the expected number of times the pattern 'do*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 4, w: 2} to form a word, what is the expected number of matches of the pattern 'w.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 4, v: 2}, what is the expected number of times the pattern 've*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, p: 1, h: 1, u: 1, w: 2}, what is the expected number of times the pattern 'w*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, w: 1, r: 1, j: 1, s: 2}, what is the expected number of times the pattern 'j*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 4, t: 2} to form a word, what is the expected number of matches of the pattern 't+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, g: 2, t: 2, o: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 4, a: 2}, what is the expected number of times the pattern 'z.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, a: 1, b: 1, l: 2}. What is the expected number of occurrences of the pattern 'y+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, x: 1, d: 1, o: 2}, what is the expected number of times the pattern 'd+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, k: 2, i: 2, z: 1}. What is the expected number of occurrences of the pattern 'ak+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 5, q: 1}. What is the expected number of occurrences of the pattern 'q+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 4, b: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, n: 2, a: 2, z: 1}. What is the expected number of occurrences of the pattern 'h+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, o: 2, u: 1, p: 1, t: 1}, what is the expected number of times the pattern 'up+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, l: 5}. What is the expected number of occurrences of the pattern 'cl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, c: 2, k: 1, r: 1}. What is the expected number of occurrences of the pattern 'r+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, s: 3}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 4, s: 2} to form a word, what is the expected number of matches of the pattern 'f.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, q: 1, s: 2, i: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'gi*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'wr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, i: 3, v: 2}, what is the expected number of times the pattern 'v.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, u: 2, e: 2} to form a word, what is the expected number of matches of the pattern 'eu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 3, q: 3}. What is the expected number of occurrences of the pattern 'qn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, z: 1, m: 1, b: 1}. What is the expected number of occurrences of the pattern 'q+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, l: 2, z: 2, b: 1} to form a word, what is the expected number of matches of the pattern 'zz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, j: 2, s: 1, h: 2} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, b: 1, r: 2, z: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'h+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, j: 1, a: 1, g: 1, t: 1}, what is the expected number of times the pattern 't.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, v: 1, j: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'fz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, m: 1, d: 1, a: 1, y: 2}. What is the expected number of occurrences of the pattern 'm*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, w: 3}. What is the expected number of occurrences of the pattern 'w.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, k: 1, h: 1, j: 2, m: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, c: 1, u: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'nu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 3, t: 3}. What is the expected number of occurrences of the pattern 'n+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, y: 2, j: 1, a: 1}. What is the expected number of occurrences of the pattern 'j.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, i: 1, p: 1, q: 3}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, a: 3}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, u: 3}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, n: 1, s: 1, f: 1, v: 1}. What is the expected number of occurrences of the pattern 'vn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, g: 4, r: 1}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 3, i: 1, u: 2}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, f: 1, h: 1, q: 1, j: 2} to form a word, what is the expected number of matches of the pattern 'p.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, n: 2, c: 1, x: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, d: 1, e: 1, k: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, l: 1, g: 2}. What is the expected number of occurrences of the pattern 'mg+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, m: 3}. What is the expected number of occurrences of the pattern 'mm*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, u: 3, f: 2}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, w: 2, m: 3}. What is the expected number of occurrences of the pattern 'yw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, c: 3}, what is the expected number of times the pattern 'c.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 3, e: 3}, what is the expected number of times the pattern 'se*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, k: 2, v: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'v*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, h: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, d: 1, a: 3}. What is the expected number of occurrences of the pattern 'l*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, w: 1, v: 1, i: 1, k: 2}, what is the expected number of times the pattern 'wi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, t: 1, d: 1, e: 2, r: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, h: 1, l: 3}. What is the expected number of occurrences of the pattern 'l+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 4, v: 2}. What is the expected number of occurrences of the pattern 'v.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, q: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'vx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, c: 1, b: 2, k: 1, l: 1}, what is the expected number of times the pattern 'j*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, l: 3}. What is the expected number of occurrences of the pattern 'ql+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, h: 2, l: 2}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, c: 2, t: 3}, what is the expected number of times the pattern 't.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, e: 4}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, i: 1, s: 1, w: 3} to form a word, what is the expected number of matches of the pattern 'si*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, n: 1, r: 1, l: 1, z: 1}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, f: 2, p: 3}, what is the expected number of times the pattern 'yp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, o: 1, y: 1, m: 2}. What is the expected number of occurrences of the pattern 'yo*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, m: 1, i: 1, q: 1, z: 2}, what is the expected number of times the pattern 'oq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, s: 4, j: 1} to form a word, what is the expected number of matches of the pattern 'is+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, n: 3, k: 1} to form a word, what is the expected number of matches of the pattern 'nk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, c: 3}, what is the expected number of times the pattern 'qc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, y: 1, x: 1, d: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, g: 1, n: 2, m: 1}. What is the expected number of occurrences of the pattern 'u+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, q: 1, h: 1, l: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'l*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, t: 3, v: 2}, what is the expected number of times the pattern 'jv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, q: 1, c: 1, i: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'ie+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, k: 5}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 4, l: 2}. What is the expected number of occurrences of the pattern 'l.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, r: 3, q: 1, p: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, w: 2, u: 2, f: 1}, what is the expected number of times the pattern 'pf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, c: 3}. What is the expected number of occurrences of the pattern 'k.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, a: 2, e: 1, g: 1, m: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, u: 3}. What is the expected number of occurrences of the pattern 'ku+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 4, w: 2} to form a word, what is the expected number of matches of the pattern 'h*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, u: 2, r: 1, e: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, j: 1, q: 1, t: 1, c: 1}, what is the expected number of times the pattern 'cq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, i: 3}. What is the expected number of occurrences of the pattern 'if+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, t: 2, k: 2, z: 1}, what is the expected number of times the pattern 'k.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, w: 1, u: 2}, what is the expected number of times the pattern 'nw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, w: 1, b: 1, x: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'ww+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, y: 1, l: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'y+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 4, k: 2} to form a word, what is the expected number of matches of the pattern 'k*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, u: 1, z: 1, r: 2, g: 1}. What is the expected number of occurrences of the pattern 'v+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, k: 2, s: 1, c: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, b: 3, c: 2} to form a word, what is the expected number of matches of the pattern 'g+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, b: 1, l: 2, a: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'i*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, u: 2, n: 2}. What is the expected number of occurrences of the pattern 'n*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 4, r: 2}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 5, z: 1} to form a word, what is the expected number of matches of the pattern 'z*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, i: 2, h: 1, m: 2}. What is the expected number of occurrences of the pattern 'xi+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, b: 4, g: 1} to form a word, what is the expected number of matches of the pattern 'gg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, j: 1, x: 1, a: 1, i: 2}, what is the expected number of times the pattern 'jn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, f: 2, d: 1, y: 1, b: 1}, what is the expected number of times the pattern 'df*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, c: 4}. What is the expected number of occurrences of the pattern 'p+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, y: 1, f: 2, s: 1, c: 1}. What is the expected number of occurrences of the pattern 'c.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, i: 3} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, y: 2, h: 2, r: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, j: 1, i: 1, g: 3}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, q: 1, u: 1, b: 2, o: 1}. What is the expected number of occurrences of the pattern 'u.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, b: 2, x: 1, t: 1}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, w: 1, z: 1, g: 1, f: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, x: 2, f: 3} to form a word, what is the expected number of matches of the pattern 'mx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, b: 3, c: 2} to form a word, what is the expected number of matches of the pattern 'c+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, r: 1, d: 1, j: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 4, v: 2}. What is the expected number of occurrences of the pattern 'v*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, p: 2, k: 3} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, s: 1, k: 2, y: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'k+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, q: 1, p: 1, n: 3}. What is the expected number of occurrences of the pattern 'nq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, i: 1, e: 2, p: 1, f: 1}. What is the expected number of occurrences of the pattern 'f*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, s: 2, i: 1, u: 2}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, d: 2, q: 2, c: 1}, what is the expected number of times the pattern 'x*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, l: 1, s: 1, h: 1}, what is the expected number of times the pattern 'hs*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, a: 4}. What is the expected number of occurrences of the pattern 'as*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, s: 1, z: 2, l: 1, e: 1}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 4, f: 2}, what is the expected number of times the pattern 'f*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, l: 1, i: 1, b: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, s: 1, h: 2, d: 1}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, z: 1, m: 1, j: 1, y: 2}, what is the expected number of times the pattern 'y*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 4, k: 2}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, g: 1, z: 2, t: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, q: 2, y: 1}, what is the expected number of times the pattern 'y.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 4, q: 2}. What is the expected number of occurrences of the pattern 'q+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, h: 4} to form a word, what is the expected number of matches of the pattern 'h*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, r: 1, f: 3, s: 1}, what is the expected number of times the pattern 'rs+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, k: 1, b: 1, d: 1, x: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'k+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, n: 3}, what is the expected number of times the pattern 'o*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, u: 3, a: 1} to form a word, what is the expected number of matches of the pattern 'ao*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, m: 1, h: 2, v: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'mz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, i: 2, p: 3} to form a word, what is the expected number of matches of the pattern 'p*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 5, l: 1} to form a word, what is the expected number of matches of the pattern 'i.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, r: 1, o: 2, f: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'or+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, g: 1, y: 1, p: 2}. What is the expected number of occurrences of the pattern 'yp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, z: 2, k: 3} to form a word, what is the expected number of matches of the pattern 'zu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, c: 2, i: 1, b: 1, k: 1}. What is the expected number of occurrences of the pattern 'c.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, p: 1, c: 4}, what is the expected number of times the pattern 'cp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, z: 3}, what is the expected number of times the pattern 'vz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, e: 1, p: 1, m: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'uz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, k: 1, n: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, a: 1, s: 1, l: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'o.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, q: 3}. What is the expected number of occurrences of the pattern 'e*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, v: 2, b: 1, k: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'dm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, m: 1, c: 1, q: 2, n: 1}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, x: 3, q: 2}, what is the expected number of times the pattern 'q*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 4, l: 2} to form a word, what is the expected number of matches of the pattern 'v+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, l: 1, p: 2, k: 1}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, n: 3}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, r: 4} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, i: 5}. What is the expected number of occurrences of the pattern 'i+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, v: 1, t: 2} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, s: 1, z: 2, f: 2}, what is the expected number of times the pattern 'fe*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, j: 1, s: 2}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, g: 1, l: 3}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, q: 1, d: 1, f: 1, l: 1}, what is the expected number of times the pattern 'f.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, e: 2, j: 1, c: 1}. What is the expected number of occurrences of the pattern 'j+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, a: 1, f: 2, y: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, m: 2, s: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'k*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, c: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, s: 3}, what is the expected number of times the pattern 's*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, i: 2, z: 3} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, q: 1, b: 2, f: 1}. What is the expected number of occurrences of the pattern 'q+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, w: 1, e: 1, s: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, b: 2, g: 1}, what is the expected number of times the pattern 'g*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 4, y: 2}. What is the expected number of occurrences of the pattern 'l.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, g: 4}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, j: 2, n: 1, v: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'n.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, b: 1, n: 1, p: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'w*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, y: 1, d: 3} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, u: 2, c: 1, l: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'u.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, o: 1, u: 2, z: 1}, what is the expected number of times the pattern 'oz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, e: 1, w: 3, q: 1}, what is the expected number of times the pattern 'q.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, p: 1, q: 2, l: 1, r: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, x: 3, c: 1, p: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, y: 2, b: 1, s: 2}. What is the expected number of occurrences of the pattern 's.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, a: 1, p: 1, j: 2, o: 1}, what is the expected number of times the pattern 'p.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, r: 1, a: 1, h: 2}. What is the expected number of occurrences of the pattern 'gr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, k: 3, j: 2}. What is the expected number of occurrences of the pattern 'j.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, k: 3, j: 1}, what is the expected number of times the pattern 'j.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, s: 1, t: 1, l: 2}. What is the expected number of occurrences of the pattern 's*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, l: 3, h: 1}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, x: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'zq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 4, g: 2}. What is the expected number of occurrences of the pattern 'g.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, g: 1, e: 2, p: 1, o: 1}. What is the expected number of occurrences of the pattern 'oj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, t: 1, i: 1, v: 1, d: 2}, what is the expected number of times the pattern 'dv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, i: 2, w: 1, o: 1} to form a word, what is the expected number of matches of the pattern 's.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, d: 1, h: 1, f: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'd*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, r: 1, b: 2, l: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'l*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 5, w: 1} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, l: 2, f: 2}. What is the expected number of occurrences of the pattern 'n.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, r: 1, j: 3}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, t: 4} to form a word, what is the expected number of matches of the pattern 't+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, h: 2, c: 1, s: 2}, what is the expected number of times the pattern 's.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, x: 2, z: 2, k: 1}, what is the expected number of times the pattern 'k.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, e: 5}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, g: 1, u: 1, o: 2, b: 1}, what is the expected number of times the pattern 'g+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, r: 1, i: 1, s: 1, e: 1}. What is the expected number of occurrences of the pattern 'is*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, l: 3, x: 1}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, d: 4}. What is the expected number of occurrences of the pattern 't.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, r: 1, p: 1, s: 1, l: 2}, what is the expected number of times the pattern 'r.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 4, j: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, g: 2, l: 2}, what is the expected number of times the pattern 'ly*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, l: 2, b: 3}, what is the expected number of times the pattern 'l+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 4, v: 2}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, j: 3, s: 2}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, g: 1, o: 2, e: 2}. What is the expected number of occurrences of the pattern 'o.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, q: 1, w: 1, g: 1, m: 1}. What is the expected number of occurrences of the pattern 'c+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, c: 1, k: 1, g: 3}. What is the expected number of occurrences of the pattern 'c+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, t: 3, j: 2}. What is the expected number of occurrences of the pattern 't+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, p: 1, b: 2, h: 1}, what is the expected number of times the pattern 'a+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, l: 1, n: 2, h: 1, s: 1}, what is the expected number of times the pattern 'h*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, l: 2, y: 1, i: 2}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, d: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'k*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 5, l: 1} to form a word, what is the expected number of matches of the pattern 'l*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, g: 1, t: 1, w: 1, x: 1}, what is the expected number of times the pattern 'xt*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, r: 4}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, l: 1, j: 1, b: 2}, what is the expected number of times the pattern 'l*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, z: 3} to form a word, what is the expected number of matches of the pattern 'z+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, n: 1, l: 1, p: 2, k: 1}. What is the expected number of occurrences of the pattern 'p+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, t: 1, c: 1, p: 1, q: 1}. What is the expected number of occurrences of the pattern 'm*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 4, h: 2}, what is the expected number of times the pattern 'he+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, u: 1, m: 4}, what is the expected number of times the pattern 'm+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, p: 1, i: 2, m: 1, d: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, d: 1, l: 1, f: 1, k: 1}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, g: 1, e: 4} to form a word, what is the expected number of matches of the pattern 'g*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, u: 1, e: 1, t: 1, q: 2}, what is the expected number of times the pattern 'un*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, a: 3}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, c: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'a+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, s: 1, o: 1, i: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'a.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, u: 2, w: 1, n: 1, q: 1}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, h: 1, d: 1, r: 2, m: 1}, what is the expected number of times the pattern 'dh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, c: 1, y: 1, w: 2, r: 1}, what is the expected number of times the pattern 'r*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, g: 3, p: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'a+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, w: 4} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, n: 1, w: 2, u: 2}. What is the expected number of occurrences of the pattern 'n.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, e: 2, h: 2}, what is the expected number of times the pattern 'gh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, o: 3, b: 2} to form a word, what is the expected number of matches of the pattern 'o*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, v: 2, d: 3}. What is the expected number of occurrences of the pattern 'rd+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, o: 2, t: 2} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, m: 1, l: 2, t: 2}, what is the expected number of times the pattern 'ml*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, a: 2, t: 2, x: 1} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, r: 1, i: 1, f: 1, c: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, j: 1, w: 1, h: 2, u: 1}. What is the expected number of occurrences of the pattern 'h+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, h: 3}, what is the expected number of times the pattern 'hh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, u: 1, k: 1, c: 1}. What is the expected number of occurrences of the pattern 'ec*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 3, c: 3}. What is the expected number of occurrences of the pattern 'nc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, t: 2, v: 2}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, l: 2, k: 2, h: 1}, what is the expected number of times the pattern 'lu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, n: 2, y: 2, x: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, e: 2, g: 1, l: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'sg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, d: 4, o: 1}. What is the expected number of occurrences of the pattern 'di+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, n: 2, f: 2, x: 1}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, a: 1, v: 1, h: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'hd+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, b: 1, k: 1, y: 3} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, o: 1, r: 1, b: 1}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, p: 3} to form a word, what is the expected number of matches of the pattern 'y*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, w: 3, o: 1, k: 1}. What is the expected number of occurrences of the pattern 'o+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, s: 1, c: 1, g: 2}. What is the expected number of occurrences of the pattern 'g.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, x: 4}, what is the expected number of times the pattern 'xi+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, f: 2, w: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'p*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, f: 2, z: 2, u: 1}, what is the expected number of times the pattern 'zi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, f: 1, z: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'fz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, z: 4} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, v: 1, h: 2, u: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, m: 2, x: 2}, what is the expected number of times the pattern 'nm+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 4, s: 2}, what is the expected number of times the pattern 'f.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, w: 4}, what is the expected number of times the pattern 'wx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, c: 2, y: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, j: 4} to form a word, what is the expected number of matches of the pattern 't+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, c: 1, m: 1, u: 2}. What is the expected number of occurrences of the pattern 'c*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, g: 3} to form a word, what is the expected number of matches of the pattern 'y*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, r: 1, d: 2, i: 1, y: 1}, what is the expected number of times the pattern 'a+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, i: 1, z: 2, n: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'j.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, y: 2, b: 2}. What is the expected number of occurrences of the pattern 'm.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, u: 1, w: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, z: 1, f: 2, y: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'y*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, c: 2, i: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, m: 1, c: 1, d: 2, j: 1}. What is the expected number of occurrences of the pattern 'c.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, w: 3}. What is the expected number of occurrences of the pattern 'rw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, v: 2, s: 2} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, b: 4} to form a word, what is the expected number of matches of the pattern 'xb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 3, i: 2, o: 1}, what is the expected number of times the pattern 'i.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, f: 2, d: 1, z: 2}. What is the expected number of occurrences of the pattern 'z*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, x: 1, p: 1, c: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, i: 1, o: 1, a: 2}. What is the expected number of occurrences of the pattern 'oi*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 3, w: 3} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, n: 3}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, f: 2, b: 1, z: 2}. What is the expected number of occurrences of the pattern 'z.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, i: 1, w: 1, d: 1, s: 2}, what is the expected number of times the pattern 'wi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, b: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, r: 3, i: 1, h: 1}. What is the expected number of occurrences of the pattern 'h.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, o: 1, v: 1, q: 2, x: 1}, what is the expected number of times the pattern 'x+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, g: 2, y: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, y: 1, q: 2, k: 1, a: 1}. What is the expected number of occurrences of the pattern 'au*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, i: 1, b: 1, h: 1, t: 2}. What is the expected number of occurrences of the pattern 'th+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, w: 3, d: 2} to form a word, what is the expected number of matches of the pattern 'z+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, r: 3}, what is the expected number of times the pattern 'gr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, m: 1, s: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'xs+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, g: 4}, what is the expected number of times the pattern 'gh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, l: 4}. What is the expected number of occurrences of the pattern 'ly*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, o: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'o.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, b: 3, u: 2} to form a word, what is the expected number of matches of the pattern 'u+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, u: 4, d: 1}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, h: 1, k: 1, q: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'q*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, f: 1, h: 1, w: 1, q: 2}, what is the expected number of times the pattern 'qq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, a: 2, o: 2}. What is the expected number of occurrences of the pattern 'ho*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, i: 3, p: 1} to form a word, what is the expected number of matches of the pattern 'il+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, r: 1, o: 1, g: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'g+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, i: 2, w: 1, y: 2}. What is the expected number of occurrences of the pattern 'y.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, h: 1, c: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'r+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, t: 2, k: 2} to form a word, what is the expected number of matches of the pattern 't+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, w: 2, x: 1, m: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'z*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, f: 3}. What is the expected number of occurrences of the pattern 'f.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, c: 1, y: 3, w: 1}, what is the expected number of times the pattern 'ic+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, p: 1, d: 2, m: 1, g: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, e: 2, a: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'i*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, d: 1, a: 3, c: 1}. What is the expected number of occurrences of the pattern 'a+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, x: 1, r: 1, h: 2, o: 1}, what is the expected number of times the pattern 'o.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, e: 2, y: 2}, what is the expected number of times the pattern 'y+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 4, x: 2}, what is the expected number of times the pattern 'tx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, s: 1, w: 1, n: 1}, what is the expected number of times the pattern 'n*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, s: 1, d: 1, v: 1, p: 1}, what is the expected number of times the pattern 'dv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, x: 2, i: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'ni+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, v: 2, x: 1} to form a word, what is the expected number of matches of the pattern 'x.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, q: 1, t: 1, h: 2}. What is the expected number of occurrences of the pattern 'h*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, s: 3} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, b: 1, x: 2, h: 1, c: 1}, what is the expected number of times the pattern 'hh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, q: 2, x: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, l: 3, o: 1}. What is the expected number of occurrences of the pattern 'ob+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 4, q: 1, r: 1}. What is the expected number of occurrences of the pattern 'a*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, v: 5}, what is the expected number of times the pattern 'g.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, h: 1, b: 3, q: 1}. What is the expected number of occurrences of the pattern 'q+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, m: 4}, what is the expected number of times the pattern 'm.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, a: 3, t: 1}, what is the expected number of times the pattern 'ts+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, y: 4, r: 1}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, q: 1, x: 3} to form a word, what is the expected number of matches of the pattern 'x+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, x: 3, z: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'xk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, d: 2, x: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, q: 1, n: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'nq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, f: 1, g: 1, h: 3}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, s: 1, o: 3, u: 1}. What is the expected number of occurrences of the pattern 'sv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, b: 3, f: 1} to form a word, what is the expected number of matches of the pattern 'c.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, h: 2, y: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'y.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, o: 1, y: 2, r: 1, s: 1}. What is the expected number of occurrences of the pattern 'cs+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, s: 1, e: 1, t: 1, v: 2}, what is the expected number of times the pattern 'e+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, a: 2, v: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, g: 4} to form a word, what is the expected number of matches of the pattern 'gw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, y: 1, l: 1, q: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'y.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, x: 2, e: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'x.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, n: 3, z: 2}. What is the expected number of occurrences of the pattern 'z+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, g: 2, t: 1, c: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'c*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 3, i: 3} to form a word, what is the expected number of matches of the pattern 'e*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, a: 2, u: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, n: 2, w: 1, h: 1}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 3, a: 3}, what is the expected number of times the pattern 'a*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, k: 4}, what is the expected number of times the pattern 'd*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, l: 1, p: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'n.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, r: 1, k: 1, w: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'o.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, f: 1, w: 2, u: 1, h: 1}, what is the expected number of times the pattern 'wu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, f: 1, g: 1, u: 2, l: 1}. What is the expected number of occurrences of the pattern 'u*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, r: 2, y: 3} to form a word, what is the expected number of matches of the pattern 'yr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 4, l: 2}. What is the expected number of occurrences of the pattern 's*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, n: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, n: 4, a: 1}. What is the expected number of occurrences of the pattern 'ny+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, n: 4} to form a word, what is the expected number of matches of the pattern 'y*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, j: 2, q: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'vj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, y: 2, u: 1, v: 1, f: 1}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, v: 2, f: 1, a: 2}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, a: 3, r: 1}, what is the expected number of times the pattern 'g+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, i: 3, m: 2}, what is the expected number of times the pattern 'e*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, t: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, q: 1, z: 3, l: 1}, what is the expected number of times the pattern 'sz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, n: 3} to form a word, what is the expected number of matches of the pattern 'ns*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, s: 3, n: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, r: 1, a: 2, e: 2}. What is the expected number of occurrences of the pattern 'le+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, v: 3}. What is the expected number of occurrences of the pattern 'v+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, u: 1, g: 3, h: 1}. What is the expected number of occurrences of the pattern 'hg*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 4, g: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 4, v: 2}. What is the expected number of occurrences of the pattern 'dv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, x: 2, q: 2, s: 1}. What is the expected number of occurrences of the pattern 'q*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, i: 2, f: 1, p: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, j: 3} to form a word, what is the expected number of matches of the pattern 'zj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, d: 1, w: 4}. What is the expected number of occurrences of the pattern 'w+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, e: 1, g: 2, t: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'i+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, s: 3}, what is the expected number of times the pattern 's*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, s: 4}, what is the expected number of times the pattern 'is*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, v: 2, c: 1, f: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'if*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, l: 1, j: 1, i: 1, q: 2}, what is the expected number of times the pattern 'q*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, s: 2, n: 2}, what is the expected number of times the pattern 's*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, i: 2, q: 3}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 5, u: 1}, what is the expected number of times the pattern 'n+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, p: 1, x: 1, j: 2}. What is the expected number of occurrences of the pattern 'w*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, y: 1, b: 1, t: 1, q: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, i: 3, l: 1} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, z: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'xz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, f: 3, v: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, p: 1, t: 1, o: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'ot+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, r: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, a: 1, y: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'y*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, q: 4}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, z: 1, m: 3}, what is the expected number of times the pattern 'zm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, g: 1, b: 1, o: 3}, what is the expected number of times the pattern 'd+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, x: 4}. What is the expected number of occurrences of the pattern 'h*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 4, c: 2}, what is the expected number of times the pattern 'c+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, k: 2, v: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'x.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, i: 2, g: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'a*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, u: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'uh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, p: 2, x: 1, g: 1, f: 1}, what is the expected number of times the pattern 'xg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, b: 1, x: 2}, what is the expected number of times the pattern 'ox*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'm+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, i: 3}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, m: 1, o: 1, d: 1, z: 2}, what is the expected number of times the pattern 'm+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, m: 2, k: 1, g: 1}, what is the expected number of times the pattern 'gv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, q: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, r: 1, c: 1, d: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, f: 1, w: 2, j: 1}, what is the expected number of times the pattern 'w.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, d: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'ud*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, s: 2, k: 1, c: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'k+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, q: 2, m: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'sm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, l: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'lr+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, q: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'q*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, t: 2, p: 3}. What is the expected number of occurrences of the pattern 'tu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, y: 1, p: 2, a: 1, s: 1}, what is the expected number of times the pattern 's*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, l: 1, y: 1, b: 1, k: 1}. What is the expected number of occurrences of the pattern 'yl+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, n: 4}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, o: 3, t: 1}. What is the expected number of occurrences of the pattern 'l*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, f: 4, s: 1}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, d: 1, p: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'id*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, i: 2, a: 3} to form a word, what is the expected number of matches of the pattern 'a+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, t: 2, h: 2}, what is the expected number of times the pattern 'hu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, k: 5} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, m: 4} to form a word, what is the expected number of matches of the pattern 't*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, g: 2, n: 3} to form a word, what is the expected number of matches of the pattern 'np+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, a: 1, z: 3} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, m: 1, f: 1, n: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'mn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, o: 1, t: 1, q: 2, v: 1}. What is the expected number of occurrences of the pattern 'oq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, w: 3, g: 1, o: 1} to form a word, what is the expected number of matches of the pattern 's+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, r: 1, e: 1, q: 2, c: 1}. What is the expected number of occurrences of the pattern 'q.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, g: 4}. What is the expected number of occurrences of the pattern 'g+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, r: 2, d: 1}. What is the expected number of occurrences of the pattern 'od*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, y: 2, n: 1, s: 1, r: 1}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, r: 2, y: 2, k: 1}. What is the expected number of occurrences of the pattern 'r*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, v: 4, p: 1}. What is the expected number of occurrences of the pattern 'vj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, z: 1, x: 1, n: 3}. What is the expected number of occurrences of the pattern 'n+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 3, t: 2, f: 1}, what is the expected number of times the pattern 't*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, l: 1, u: 2, t: 1, d: 1} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, y: 1, x: 3, f: 1} to form a word, what is the expected number of matches of the pattern 'l+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 3, t: 1, o: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, x: 1, e: 1, f: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'fx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, n: 1, k: 1, r: 1}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, x: 4, o: 1}, what is the expected number of times the pattern 'ox+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, f: 2, p: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'ip*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, i: 3, m: 1} to form a word, what is the expected number of matches of the pattern 'm*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, x: 1, l: 1, s: 2}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, p: 1, z: 2}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'r*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, y: 2, f: 1}, what is the expected number of times the pattern 'f*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, f: 1, a: 1, l: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'f.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 4, a: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, h: 3, b: 1}. What is the expected number of occurrences of the pattern 'hh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, d: 5}. What is the expected number of occurrences of the pattern 'd.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, i: 1, q: 3}. What is the expected number of occurrences of the pattern 'ix+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, n: 1, j: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'ga+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, m: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'mu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, x: 2, k: 3}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, k: 1, q: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'gk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, z: 2, j: 2} to form a word, what is the expected number of matches of the pattern 'z*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, o: 4}. What is the expected number of occurrences of the pattern 'o.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, x: 3, j: 2} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, h: 1, c: 1, f: 1, p: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, d: 1, p: 2, t: 1, q: 1}, what is the expected number of times the pattern 'p*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 4, d: 2}, what is the expected number of times the pattern 'df*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 3, a: 3}, what is the expected number of times the pattern 'y*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, m: 3}. What is the expected number of occurrences of the pattern 'm+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, v: 2, g: 3}, what is the expected number of times the pattern 'g*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, w: 1, o: 2}. What is the expected number of occurrences of the pattern 'ko*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, a: 1, k: 1, o: 2, s: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, a: 3}. What is the expected number of occurrences of the pattern 'a+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 4, n: 1, u: 1}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, k: 1, c: 1, m: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, q: 1, x: 3, p: 1} to form a word, what is the expected number of matches of the pattern 'qw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, u: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'u.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, m: 1, d: 1, n: 3}, what is the expected number of times the pattern 'j*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, c: 1, k: 2}. What is the expected number of occurrences of the pattern 'c+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, t: 2, o: 1, u: 1, r: 1}, what is the expected number of times the pattern 'u+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, m: 5} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, w: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'ff*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, r: 2, f: 1, k: 2}, what is the expected number of times the pattern 'fb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, q: 1, y: 2, p: 1}. What is the expected number of occurrences of the pattern 'qy*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, h: 4} to form a word, what is the expected number of matches of the pattern 'x.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, a: 1, b: 3} to form a word, what is the expected number of matches of the pattern 'u*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, n: 1, a: 1, o: 3}, what is the expected number of times the pattern 'o*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 3, s: 3}, what is the expected number of times the pattern 'sy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, m: 1, t: 2, i: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'i+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, s: 4, u: 1}. What is the expected number of occurrences of the pattern 'us+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, x: 1, t: 1, q: 1, m: 2}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, a: 2, v: 2}. What is the expected number of occurrences of the pattern 'v*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, j: 4}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, f: 1, t: 1, o: 2}, what is the expected number of times the pattern 'of+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, y: 2, q: 1, i: 1, c: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 4, c: 2} to form a word, what is the expected number of matches of the pattern 'c*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 4, e: 2}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 4, s: 2} to form a word, what is the expected number of matches of the pattern 'x*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, d: 2, j: 2}. What is the expected number of occurrences of the pattern 'j+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 4, g: 2} to form a word, what is the expected number of matches of the pattern 'g+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, f: 1, x: 1, g: 1, j: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 4, d: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 4, m: 2}, what is the expected number of times the pattern 'mt*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, r: 2, c: 1} to form a word, what is the expected number of matches of the pattern 'c+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, r: 2, k: 1, c: 2}. What is the expected number of occurrences of the pattern 'kr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, g: 1, d: 1, f: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, v: 1, n: 2, o: 1, t: 1}, what is the expected number of times the pattern 'vo*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, j: 4}, what is the expected number of times the pattern 'j.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, i: 1, s: 3, h: 1} to form a word, what is the expected number of matches of the pattern 's*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, u: 2, a: 1, l: 1}, what is the expected number of times the pattern 'g.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, u: 4} to form a word, what is the expected number of matches of the pattern 'f.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, g: 1, z: 1, x: 2, h: 1}. What is the expected number of occurrences of the pattern 'g.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, p: 3}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 4, o: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'h+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, c: 1, r: 1, a: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'c*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, o: 1, u: 1, j: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'ot+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, v: 1, o: 1, h: 2, q: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, s: 2, z: 1, v: 1, m: 1}. What is the expected number of occurrences of the pattern 'sv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 4, w: 2}. What is the expected number of occurrences of the pattern 'w.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, k: 2}. What is the expected number of occurrences of the pattern 'k.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, x: 1, w: 3}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, m: 1, e: 3}. What is the expected number of occurrences of the pattern 'u+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, a: 3, n: 1}, what is the expected number of times the pattern 'ya+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, t: 1, g: 3}. What is the expected number of occurrences of the pattern 't*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 4, b: 2}. What is the expected number of occurrences of the pattern 'o+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, v: 2, c: 2}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, w: 1, b: 1, k: 1, d: 2}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 5, b: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 5, g: 1} to form a word, what is the expected number of matches of the pattern 'g+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 5, g: 1} to form a word, what is the expected number of matches of the pattern 'g*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 3, s: 3} to form a word, what is the expected number of matches of the pattern 's.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, l: 2, z: 1, w: 1, y: 1}, what is the expected number of times the pattern 'q.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, e: 1, n: 2, w: 2}. What is the expected number of occurrences of the pattern 'je*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, z: 1, l: 1, p: 2, u: 1}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, t: 1, v: 1, o: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'tv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, r: 1, l: 2, s: 1, t: 1}, what is the expected number of times the pattern 's*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, a: 2, n: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, x: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, m: 2, s: 1, f: 1, q: 1}. What is the expected number of occurrences of the pattern 's*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 4, r: 2}, what is the expected number of times the pattern 'ur+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, e: 3, h: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, v: 1, x: 1, t: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, b: 1, c: 1, s: 3} to form a word, what is the expected number of matches of the pattern 'c+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 4, t: 2}, what is the expected number of times the pattern 'tm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, y: 3} to form a word, what is the expected number of matches of the pattern 'y+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, c: 1, i: 1, v: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, u: 1, v: 2, s: 2}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, v: 2, p: 1, h: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'p+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, a: 1, e: 1, z: 2}. What is the expected number of occurrences of the pattern 'i+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, n: 2, i: 1, j: 2}. What is the expected number of occurrences of the pattern 'j.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, j: 1, q: 1, d: 1, w: 2}. What is the expected number of occurrences of the pattern 's.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, v: 1, f: 1, i: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, v: 2, t: 2, c: 1}, what is the expected number of times the pattern 'v.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, d: 2, l: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'sv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, v: 1, n: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, c: 3, i: 1, u: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, u: 2, h: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'hb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, j: 1, r: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, b: 1, c: 3}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 4, u: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, o: 1, u: 3, y: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, j: 2, l: 2}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, f: 3, n: 1}. What is the expected number of occurrences of the pattern 'n+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, t: 1, r: 1, l: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'ht+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, h: 1, a: 2, u: 1, m: 1}. What is the expected number of occurrences of the pattern 'qm+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, c: 1, f: 3}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, z: 3}, what is the expected number of times the pattern 'zx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, y: 1, b: 1, k: 3}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, u: 1, o: 3} to form a word, what is the expected number of matches of the pattern 'us*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, n: 2, t: 2} to form a word, what is the expected number of matches of the pattern 't*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, m: 2, h: 1, f: 1, d: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, z: 2, g: 1, x: 1, a: 1}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, u: 1, r: 3, h: 1}. What is the expected number of occurrences of the pattern 'hw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, f: 4}. What is the expected number of occurrences of the pattern 'f*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'm*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, e: 1, t: 2, j: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, u: 4}. What is the expected number of occurrences of the pattern 'au*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, t: 2, p: 2}. What is the expected number of occurrences of the pattern 'p+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 4, t: 2}, what is the expected number of times the pattern 'q+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, y: 1, c: 1, r: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'yc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, m: 1, d: 1, c: 1, g: 2}, what is the expected number of times the pattern 'g.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, e: 1, j: 1, h: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'ju+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, a: 1, k: 1, u: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, n: 3}, what is the expected number of times the pattern 'j*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, g: 4, v: 1} to form a word, what is the expected number of matches of the pattern 'p.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, y: 1, b: 1, m: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'm+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, m: 3}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, n: 1, y: 4}. What is the expected number of occurrences of the pattern 'y+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 4, f: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, y: 1, s: 3}, what is the expected number of times the pattern 's.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, t: 1, e: 3} to form a word, what is the expected number of matches of the pattern 'tl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, q: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, n: 2, d: 1, f: 1}. What is the expected number of occurrences of the pattern 'af*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, q: 1, u: 3, k: 1} to form a word, what is the expected number of matches of the pattern 'qu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, o: 4} to form a word, what is the expected number of matches of the pattern 'oa+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, d: 1, m: 3, j: 1}. What is the expected number of occurrences of the pattern 'd.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, o: 1, w: 1, e: 2, b: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, i: 3, j: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'g.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 4, y: 2}. What is the expected number of occurrences of the pattern 'xy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, h: 4}, what is the expected number of times the pattern 'ht+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 4, f: 2}, what is the expected number of times the pattern 'gf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, y: 2, j: 3} to form a word, what is the expected number of matches of the pattern 'ij*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, t: 2, b: 2}, what is the expected number of times the pattern 'y*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, f: 4}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, w: 2, s: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'ew*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, m: 2, x: 1, i: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, w: 1, i: 2, p: 2}. What is the expected number of occurrences of the pattern 'ip+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 5, y: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 4, d: 2}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, f: 3, i: 1, l: 1}. What is the expected number of occurrences of the pattern 'i.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, b: 4}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, n: 1, g: 1, x: 1, b: 1}. What is the expected number of occurrences of the pattern 'xb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, c: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'z*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, l: 1, c: 1, k: 3} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, g: 1, v: 1, p: 2, y: 1}. What is the expected number of occurrences of the pattern 'g*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, t: 1, x: 1, n: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'k*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, w: 1, k: 1, l: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'cw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, h: 2, u: 2}. What is the expected number of occurrences of the pattern 'dh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, q: 2, p: 1, f: 1, o: 1}. What is the expected number of occurrences of the pattern 'q+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, j: 2, c: 1, u: 1}, what is the expected number of times the pattern 'jc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, n: 1, x: 1, v: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, a: 1, s: 1, n: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'nv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, y: 2, f: 2, h: 1}. What is the expected number of occurrences of the pattern 'yh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, g: 2, y: 1, p: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'wy*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, p: 1, c: 1, e: 2, n: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 4, c: 2}, what is the expected number of times the pattern 'jc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, s: 1, n: 1, w: 2, l: 1}, what is the expected number of times the pattern 'lw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, j: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'jw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, d: 5}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, q: 4}. What is the expected number of occurrences of the pattern 'ql+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, g: 2, p: 2}, what is the expected number of times the pattern 'g.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, z: 4}. What is the expected number of occurrences of the pattern 'v.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, f: 1, s: 1, v: 3}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, h: 2, a: 1, t: 1}. What is the expected number of occurrences of the pattern 'ht+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, i: 3, j: 2}, what is the expected number of times the pattern 'i+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 4, g: 2}. What is the expected number of occurrences of the pattern 'l+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, b: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'y+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, c: 3, h: 2} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, c: 4} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, t: 3}, what is the expected number of times the pattern 'et+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, j: 5} to form a word, what is the expected number of matches of the pattern 'j.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, n: 2, r: 1, i: 2}, what is the expected number of times the pattern 'i*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, g: 1, e: 2}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, k: 2, l: 3}, what is the expected number of times the pattern 'l*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, n: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, d: 1, z: 1, r: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, d: 3, e: 1}, what is the expected number of times the pattern 'zd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, f: 2, u: 1, a: 2}, what is the expected number of times the pattern 'a.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, z: 3} to form a word, what is the expected number of matches of the pattern 'h.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, r: 5}, what is the expected number of times the pattern 'r.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, j: 1, k: 2, o: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, h: 1, y: 1, j: 1, r: 1}, what is the expected number of times the pattern 'r.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, x: 1, r: 3, i: 1}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 4, k: 2}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, l: 2, w: 3} to form a word, what is the expected number of matches of the pattern 'wf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, z: 3, s: 1} to form a word, what is the expected number of matches of the pattern 'sz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, r: 1, y: 1, f: 1, c: 1}, what is the expected number of times the pattern 'c*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, k: 4}, what is the expected number of times the pattern 'k+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, b: 1, e: 1, m: 2, k: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, j: 1, t: 2, h: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, k: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'j*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, k: 1, q: 1, a: 1, f: 2}, what is the expected number of times the pattern 'a.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, q: 1, o: 3}, what is the expected number of times the pattern 'qo*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, f: 2, s: 1, i: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, l: 1, v: 1, j: 1, h: 1}. What is the expected number of occurrences of the pattern 'vl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 3, s: 3}, what is the expected number of times the pattern 'ys+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, p: 3, h: 1, y: 1}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, v: 1, a: 1, z: 1}, what is the expected number of times the pattern 'a+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, f: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'fs*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, x: 1, i: 1, v: 1, t: 2}, what is the expected number of times the pattern 'ts+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 5, u: 1} to form a word, what is the expected number of matches of the pattern 'uf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, g: 3}. What is the expected number of occurrences of the pattern 'gd+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, f: 1, w: 2, x: 1, z: 1}. What is the expected number of occurrences of the pattern 'xf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, m: 5} to form a word, what is the expected number of matches of the pattern 'm.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, d: 1, a: 2, h: 2}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, t: 1, p: 1, c: 2}. What is the expected number of occurrences of the pattern 'c+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, o: 2, y: 2, d: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, e: 1, w: 1, n: 2, r: 1}. What is the expected number of occurrences of the pattern 'c+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, n: 1, m: 3}, what is the expected number of times the pattern 'ny*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 4, o: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, j: 1, e: 1, c: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'y+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 4, e: 2}, what is the expected number of times the pattern 'e+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, p: 5}, what is the expected number of times the pattern 'xp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, s: 3, p: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'gs+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 3, x: 2, g: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, j: 1, g: 1, a: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'ap*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, v: 2, k: 2}. What is the expected number of occurrences of the pattern 'kv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, f: 1, u: 1, t: 2, g: 1}, what is the expected number of times the pattern 'g*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, h: 1, j: 2, r: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'n.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, o: 2, s: 1, t: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, d: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, k: 1, a: 2, m: 1, u: 1}. What is the expected number of occurrences of the pattern 'u+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, o: 1, e: 1, g: 2, z: 1}, what is the expected number of times the pattern 'h.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, y: 1, i: 1, v: 1, h: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, x: 2, j: 1, a: 1}. What is the expected number of occurrences of the pattern 'ax+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, q: 1, k: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'ge*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, w: 4, n: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, m: 2, t: 1, r: 2}, what is the expected number of times the pattern 'mg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'qv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, h: 2, c: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'd.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, l: 3, s: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'y+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, t: 1, m: 1, l: 1}, what is the expected number of times the pattern 'lt*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, x: 3, k: 2} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, u: 1, o: 3} to form a word, what is the expected number of matches of the pattern 'o*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, o: 1, s: 2, c: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, h: 1, b: 2}, what is the expected number of times the pattern 'm*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, q: 1, l: 1, g: 2}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, n: 3}, what is the expected number of times the pattern 'qn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, j: 1, p: 3} to form a word, what is the expected number of matches of the pattern 'p+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, l: 2, g: 1, i: 2}. What is the expected number of occurrences of the pattern 'il*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, g: 2, d: 2}, what is the expected number of times the pattern 'd+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 5, i: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, q: 1, m: 2}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 4, l: 2} to form a word, what is the expected number of matches of the pattern 'zl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, w: 3, b: 1}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, b: 3, m: 2}, what is the expected number of times the pattern 'e.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, y: 1, q: 1, j: 2} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, l: 1, p: 1, z: 2, t: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, q: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'q.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, r: 1, l: 1, z: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'l+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, b: 1, f: 1, p: 1, x: 1}, what is the expected number of times the pattern 'p.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, t: 1, c: 1, o: 2, u: 1}, what is the expected number of times the pattern 'g.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, y: 2, t: 1, e: 1, g: 1}, what is the expected number of times the pattern 's+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, h: 2, z: 3}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, y: 1, v: 2, p: 2}, what is the expected number of times the pattern 'vd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, r: 3, z: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'ad*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, m: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'o.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, o: 2, w: 1, q: 1, g: 1}, what is the expected number of times the pattern 'zg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, e: 1, z: 1, p: 1}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, d: 2, q: 3}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, g: 1, s: 1, v: 1, n: 1}, what is the expected number of times the pattern 'j.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, o: 1, c: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'o.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, u: 1, c: 1, e: 1, j: 1}, what is the expected number of times the pattern 'e+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, r: 2, v: 1, x: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'tr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, m: 2, n: 3}. What is the expected number of occurrences of the pattern 'zn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 4, i: 2}, what is the expected number of times the pattern 'p+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'ha+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, b: 1, j: 2, z: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'z*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, b: 1, p: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'l+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, n: 1, q: 2, v: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'q.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, c: 3, f: 1}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, z: 1, r: 2, h: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'c*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, z: 1, y: 1, n: 1, v: 1}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, b: 1, g: 1, l: 3}, what is the expected number of times the pattern 'gb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, k: 1, i: 1, p: 1, a: 1}, what is the expected number of times the pattern 'i*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, j: 1, u: 2, r: 1}, what is the expected number of times the pattern 'ji+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, h: 1, v: 2, q: 1, t: 1}. What is the expected number of occurrences of the pattern 'q.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, x: 1, j: 1, m: 1}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, s: 4}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, y: 2, x: 2}, what is the expected number of times the pattern 'u*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, n: 4}, what is the expected number of times the pattern 'n.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 4, o: 1, j: 1}. What is the expected number of occurrences of the pattern 'e*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, w: 1, v: 2, z: 1, k: 1}. What is the expected number of occurrences of the pattern 'cv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, s: 1, u: 1, n: 3} to form a word, what is the expected number of matches of the pattern 'n.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, o: 1, k: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'c+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, p: 1, m: 2, h: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'lj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, f: 3}, what is the expected number of times the pattern 'h.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, a: 2, p: 1, x: 1}. What is the expected number of occurrences of the pattern 'a.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, k: 1, w: 1, i: 1, r: 2}. What is the expected number of occurrences of the pattern 'rk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, v: 2, q: 1, a: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, m: 3, p: 1}, what is the expected number of times the pattern 'um*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, q: 2, v: 1, j: 1}. What is the expected number of occurrences of the pattern 'qk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, z: 2, b: 1}, what is the expected number of times the pattern 'nn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, d: 3}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, t: 2, f: 3}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, n: 2, x: 2}. What is the expected number of occurrences of the pattern 'k.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, m: 1, k: 1, n: 1, j: 2}, what is the expected number of times the pattern 'mb+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, n: 2, x: 2}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 4, i: 2}. What is the expected number of occurrences of the pattern 'o+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, w: 1, u: 2, j: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'e+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 4, s: 2} to form a word, what is the expected number of matches of the pattern 'si+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, g: 1, i: 2, a: 1}. What is the expected number of occurrences of the pattern 'i.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, p: 3, n: 2}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, s: 1, v: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'j*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, i: 2, w: 2}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, k: 1, a: 1, f: 3} to form a word, what is the expected number of matches of the pattern 'k.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, f: 2, l: 1, c: 1, o: 1}. What is the expected number of occurrences of the pattern 'i.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, v: 1, d: 2, g: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, n: 1, z: 1, y: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'nx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, b: 2, e: 1, q: 2}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, a: 3, d: 1, r: 1}. What is the expected number of occurrences of the pattern 'ra+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, k: 1, a: 1, s: 1, g: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, a: 1, e: 1, k: 1, d: 1}. What is the expected number of occurrences of the pattern 'w+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, p: 2, v: 1, a: 1, n: 1}, what is the expected number of times the pattern 's+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, l: 1, t: 3, c: 1}. What is the expected number of occurrences of the pattern 'c+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, g: 2, e: 2, x: 1}. What is the expected number of occurrences of the pattern 'xg+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, h: 1, o: 2}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, e: 1, z: 1, w: 1, q: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, l: 1, e: 2, r: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, t: 1, a: 3}, what is the expected number of times the pattern 'at*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 4, x: 2} to form a word, what is the expected number of matches of the pattern 'xa+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, y: 3, p: 1, w: 1}, what is the expected number of times the pattern 'p+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, p: 1, n: 1, e: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'hp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 5, h: 1} to form a word, what is the expected number of matches of the pattern 'ht+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, z: 2, m: 1, s: 1}, what is the expected number of times the pattern 'z+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, k: 1, h: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'h.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, m: 4, k: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, z: 1, p: 1, q: 1, i: 2}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, i: 1, v: 2}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, a: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, f: 3}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, r: 3, t: 2}, what is the expected number of times the pattern 'tr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, h: 2, e: 1, b: 1, s: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, v: 4}, what is the expected number of times the pattern 'r+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, d: 2, f: 2, h: 1}, what is the expected number of times the pattern 'h.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, x: 1, d: 2, b: 2} to form a word, what is the expected number of matches of the pattern 't*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, k: 1, t: 2, p: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'k.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, j: 1, w: 1, m: 2, q: 1}, what is the expected number of times the pattern 'm*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, d: 1, n: 2, b: 1, y: 1}. What is the expected number of occurrences of the pattern 'n.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, e: 1, a: 2, h: 1, y: 1}. What is the expected number of occurrences of the pattern 'e+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, k: 1, g: 1, b: 1, v: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, z: 4}. What is the expected number of occurrences of the pattern 'z.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, z: 3, v: 2}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, c: 5} to form a word, what is the expected number of matches of the pattern 'nc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, k: 3, w: 2}. What is the expected number of occurrences of the pattern 'wt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 5, t: 1}, what is the expected number of times the pattern 'tn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, l: 4} to form a word, what is the expected number of matches of the pattern 'p*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, n: 1, g: 2, q: 2}. What is the expected number of occurrences of the pattern 'g*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, g: 1, l: 2, f: 2}. What is the expected number of occurrences of the pattern 'a.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, k: 3}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 4, y: 2} to form a word, what is the expected number of matches of the pattern 'wy+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, o: 1, c: 1, t: 3} to form a word, what is the expected number of matches of the pattern 'cg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, r: 2, x: 1, q: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, o: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'ko*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 4, j: 2} to form a word, what is the expected number of matches of the pattern 'j.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, v: 4}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, e: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'e+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'vm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, y: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'y*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, w: 1, f: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'j+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, x: 2, p: 1, c: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, u: 1, o: 1, f: 2, v: 1}, what is the expected number of times the pattern 'vh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, e: 1, q: 2, l: 2}. What is the expected number of occurrences of the pattern 'e*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, w: 1, n: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'nl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, p: 2, g: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'x.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, y: 2, l: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, s: 2, a: 2}, what is the expected number of times the pattern 'af+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, b: 2, c: 1, k: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, t: 3}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, g: 1, s: 4}, what is the expected number of times the pattern 'g.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, x: 2, j: 1, y: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'jx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, n: 1, x: 1, g: 1, v: 1}, what is the expected number of times the pattern 'xw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, w: 1, o: 3, q: 1}. What is the expected number of occurrences of the pattern 's*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, c: 4}. What is the expected number of occurrences of the pattern 'u.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, v: 2, w: 1, s: 1}, what is the expected number of times the pattern 'vc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, y: 3, r: 1}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, u: 3, p: 2}, what is the expected number of times the pattern 'u*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, u: 3, i: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, q: 1, u: 1, j: 1}, what is the expected number of times the pattern 'u*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, t: 2, q: 2}, what is the expected number of times the pattern 'u+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, p: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'l+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, y: 1, v: 1, h: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'f.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, j: 1, p: 2, g: 1, s: 1}. What is the expected number of occurrences of the pattern 'jp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 3, i: 3}, what is the expected number of times the pattern 'iy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, s: 2, l: 2, q: 1}. What is the expected number of occurrences of the pattern 'uq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, o: 1, i: 1, y: 2, v: 1}. What is the expected number of occurrences of the pattern 'oy*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, c: 1, m: 1, t: 2} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, w: 2, m: 2}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, r: 4}, what is the expected number of times the pattern 'nr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, y: 1, k: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'y*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 5, o: 1}, what is the expected number of times the pattern 'x.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, k: 2, i: 1}. What is the expected number of occurrences of the pattern 'k.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, a: 3} to form a word, what is the expected number of matches of the pattern 'ya+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, x: 3, m: 2}. What is the expected number of occurrences of the pattern 'm*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, i: 4, a: 1}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, y: 2, b: 1, k: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'r*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 4, u: 2} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, d: 2, j: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, q: 1, p: 2}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, n: 1, p: 1, l: 1, i: 1}, what is the expected number of times the pattern 'nl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, i: 2, l: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, r: 3, g: 2} to form a word, what is the expected number of matches of the pattern 'r.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, g: 3, q: 2}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, b: 2, f: 3}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 4, g: 2} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, i: 2, a: 1, t: 2} to form a word, what is the expected number of matches of the pattern 'v.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 4, p: 2}. What is the expected number of occurrences of the pattern 'q*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, d: 3}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, h: 1, d: 1, z: 2, b: 1}, what is the expected number of times the pattern 'h*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 5, i: 1}. What is the expected number of occurrences of the pattern 'n*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 4, b: 2}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, z: 2, b: 2}. What is the expected number of occurrences of the pattern 'zz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, v: 1, s: 1, e: 1, m: 1}, what is the expected number of times the pattern 've+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, w: 1, g: 2, y: 1, j: 1}. What is the expected number of occurrences of the pattern 'w.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 4, j: 2} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, b: 1, n: 2, e: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, m: 3}. What is the expected number of occurrences of the pattern 'm+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, c: 2, o: 1, g: 2}, what is the expected number of times the pattern 'c*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, g: 3}, what is the expected number of times the pattern 'e*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, d: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, t: 2, a: 2}, what is the expected number of times the pattern 'a.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, t: 1, k: 2, x: 2}. What is the expected number of occurrences of the pattern 'x*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, h: 1, n: 1, r: 1, s: 1} to form a word, what is the expected number of matches of the pattern 't*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, h: 1, u: 1, n: 1, v: 1}. What is the expected number of occurrences of the pattern 'hu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, u: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'qu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, u: 1, a: 1, r: 1, w: 2}, what is the expected number of times the pattern 'a.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, z: 1, i: 3, v: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 4, o: 2}, what is the expected number of times the pattern 'o+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, r: 4} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, w: 3}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, x: 1, j: 2}, what is the expected number of times the pattern 'k.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, h: 1, i: 1, e: 3}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, v: 2, m: 1, l: 1, k: 1}. What is the expected number of occurrences of the pattern 'zv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, h: 2, r: 3}, what is the expected number of times the pattern 'hr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, f: 1, i: 2, q: 2}. What is the expected number of occurrences of the pattern 'i.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, c: 3, f: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, g: 1, u: 2}. What is the expected number of occurrences of the pattern 'g*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, r: 4} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, y: 1, b: 1, u: 3}, what is the expected number of times the pattern 'fu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, v: 1, x: 1, q: 2}. What is the expected number of occurrences of the pattern 'k.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, d: 1, g: 1, c: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, m: 1, h: 1, r: 2}, what is the expected number of times the pattern 'hm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, z: 1, y: 1, p: 1, x: 1}. What is the expected number of occurrences of the pattern 'x.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, i: 4, y: 1} to form a word, what is the expected number of matches of the pattern 'i*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, i: 2, y: 2}, what is the expected number of times the pattern 'i+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, m: 2, g: 3}, what is the expected number of times the pattern 'm.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, v: 1, j: 2, z: 2}, what is the expected number of times the pattern 'v+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, p: 1, f: 1, s: 2, x: 1}. What is the expected number of occurrences of the pattern 'qp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, h: 3}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 5, c: 1}, what is the expected number of times the pattern 'u+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, a: 3} to form a word, what is the expected number of matches of the pattern 'l+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, w: 3, i: 1, o: 1}. What is the expected number of occurrences of the pattern 'iv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, p: 4}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, a: 1, z: 1, b: 1, u: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'l+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, s: 1, y: 1, t: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, z: 3, x: 1}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, k: 1, z: 1, s: 2, y: 1}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, h: 3}. What is the expected number of occurrences of the pattern 'he*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 4, w: 2}, what is the expected number of times the pattern 'yw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, h: 1, l: 1, w: 2, j: 1}, what is the expected number of times the pattern 'l.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, h: 1, r: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'e.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, r: 3, d: 1}, what is the expected number of times the pattern 'r*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 4, u: 2} to form a word, what is the expected number of matches of the pattern 'u+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, o: 1, q: 2} to form a word, what is the expected number of matches of the pattern 'no*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, y: 1, t: 1, o: 2, l: 1}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, c: 2, h: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'uh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, v: 2, h: 3}. What is the expected number of occurrences of the pattern 'hv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, f: 1, q: 1, a: 1, n: 2}, what is the expected number of times the pattern 'a+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, m: 1, j: 2, o: 1}. What is the expected number of occurrences of the pattern 'vj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, p: 2, j: 1, t: 2}, what is the expected number of times the pattern 't+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, z: 4} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, k: 2, h: 1, e: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'h+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, d: 3}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, g: 1, x: 1, p: 1, z: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, g: 1, p: 3} to form a word, what is the expected number of matches of the pattern 'g+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, x: 3}. What is the expected number of occurrences of the pattern 'e*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, g: 2, t: 1}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, i: 2, e: 1, z: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'i+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, v: 3, z: 1, u: 1}, what is the expected number of times the pattern 'mv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, s: 1, j: 1, t: 1, p: 1}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, z: 1, f: 2, b: 1, k: 1}, what is the expected number of times the pattern 'f*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, l: 1, w: 1, u: 3} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, n: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, d: 2, b: 1, a: 1}, what is the expected number of times the pattern 'db*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, g: 3, e: 2}. What is the expected number of occurrences of the pattern 'e*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, d: 1, i: 3, n: 1}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, o: 3}, what is the expected number of times the pattern 'f.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, u: 3, a: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, m: 1, j: 1, i: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'h*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, y: 1, u: 1, d: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'u+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, x: 3}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, s: 2, e: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'e+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, t: 1, y: 2, j: 2}, what is the expected number of times the pattern 't*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, j: 4} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, h: 2, u: 1, b: 1}, what is the expected number of times the pattern 'ub*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, y: 2, e: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, z: 3, u: 2}, what is the expected number of times the pattern 'lu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, s: 2, x: 2}, what is the expected number of times the pattern 's+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, o: 3, i: 2} to form a word, what is the expected number of matches of the pattern 'o+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 4, f: 2} to form a word, what is the expected number of matches of the pattern 'hf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, t: 2, s: 2, i: 1}, what is the expected number of times the pattern 's*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, d: 1, j: 1, s: 1, i: 2}. What is the expected number of occurrences of the pattern 'd+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, p: 2, q: 2}. What is the expected number of occurrences of the pattern 'pj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, b: 2, r: 1, i: 1}. What is the expected number of occurrences of the pattern 'ir*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, u: 4, w: 1}, what is the expected number of times the pattern 'uw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, e: 1, o: 2, r: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, l: 4}. What is the expected number of occurrences of the pattern 'hl+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, u: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, s: 2, w: 1, e: 1}, what is the expected number of times the pattern 's+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, f: 1, h: 1, b: 1, r: 1}, what is the expected number of times the pattern 'gf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, g: 2, x: 1, v: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'mg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, p: 2, m: 2}. What is the expected number of occurrences of the pattern 'pm*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, p: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, m: 1, d: 2, z: 1, t: 1}. What is the expected number of occurrences of the pattern 'tf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 4, s: 1, c: 1}. What is the expected number of occurrences of the pattern 's.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, j: 2, i: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, k: 1, n: 1, h: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'ee+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 4, b: 2}, what is the expected number of times the pattern 'vb+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 3, d: 2, w: 1}, what is the expected number of times the pattern 'd*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, r: 2, g: 2, k: 1}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, c: 3}. What is the expected number of occurrences of the pattern 'ch+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, u: 1, e: 1, x: 2, a: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, f: 2, s: 3}, what is the expected number of times the pattern 'zs+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, y: 3}. What is the expected number of occurrences of the pattern 'y.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, x: 2, n: 1, a: 1, k: 1}. What is the expected number of occurrences of the pattern 'k*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, u: 1, l: 3, o: 1}. What is the expected number of occurrences of the pattern 'u+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, m: 1, i: 2, s: 1, e: 1}, what is the expected number of times the pattern 'e.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, o: 3}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, m: 1, g: 2}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, p: 3, k: 2}, what is the expected number of times the pattern 'k*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, s: 3, o: 1}. What is the expected number of occurrences of the pattern 'o*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, u: 1, b: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'o.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, c: 1, u: 1, m: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, h: 2, p: 2}. What is the expected number of occurrences of the pattern 'p.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, h: 1, j: 1, a: 1, i: 1}. What is the expected number of occurrences of the pattern 'hl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, f: 2, v: 2}, what is the expected number of times the pattern 'v*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, r: 1, j: 3}, what is the expected number of times the pattern 'a*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 4, r: 2}, what is the expected number of times the pattern 'l.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, p: 2, y: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'p.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, y: 2, q: 1, b: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'dy+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, a: 3}, what is the expected number of times the pattern 'c*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, q: 1, u: 3}. What is the expected number of occurrences of the pattern 'us+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, q: 1, b: 1, i: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'jb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, r: 1, g: 2}, what is the expected number of times the pattern 'g.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, z: 2, o: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'o.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, s: 4}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, x: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'x*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, k: 3, p: 1}. What is the expected number of occurrences of the pattern 'pk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, k: 2, f: 1, u: 1}, what is the expected number of times the pattern 'k+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, v: 1, b: 2}, what is the expected number of times the pattern 'vb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, f: 1, v: 3, l: 1}. What is the expected number of occurrences of the pattern 'lv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 4, y: 2}. What is the expected number of occurrences of the pattern 'v*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, t: 1, y: 1, s: 2}. What is the expected number of occurrences of the pattern 'j.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, v: 1, g: 1, y: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'vl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, l: 3, b: 1, m: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, p: 3} to form a word, what is the expected number of matches of the pattern 'pq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, g: 4} to form a word, what is the expected number of matches of the pattern 'gm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, f: 4}, what is the expected number of times the pattern 'fw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, h: 1, p: 2}. What is the expected number of occurrences of the pattern 'p*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, p: 1, u: 1, c: 2, y: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, u: 1, h: 3, j: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, k: 1, p: 1, x: 1, t: 2} to form a word, what is the expected number of matches of the pattern 't.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, l: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'l*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, h: 3, g: 1}. What is the expected number of occurrences of the pattern 't+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, d: 1, q: 1, m: 2, a: 1} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, r: 1, y: 1, b: 2, e: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, k: 2, p: 3}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, h: 4}. What is the expected number of occurrences of the pattern 'h*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, u: 1, e: 1, t: 1, w: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, z: 2, l: 1, v: 1}. What is the expected number of occurrences of the pattern 'z+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, q: 1, g: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'q*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 4, u: 1, a: 1}. What is the expected number of occurrences of the pattern 'n+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, e: 3, h: 1, r: 1}, what is the expected number of times the pattern 'ez+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 4, k: 2}. What is the expected number of occurrences of the pattern 'kq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 3, q: 3}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 4, v: 2}. What is the expected number of occurrences of the pattern 'pv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, c: 1, z: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, e: 1, x: 2, c: 1, b: 1}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, r: 1, i: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, h: 2, l: 1}, what is the expected number of times the pattern 'h+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, w: 1, h: 2, k: 2}. What is the expected number of occurrences of the pattern 'h*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, c: 3}. What is the expected number of occurrences of the pattern 'vc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, d: 1, j: 1, k: 3}, what is the expected number of times the pattern 'j.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, u: 3, m: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 5, j: 1} to form a word, what is the expected number of matches of the pattern 'j*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, r: 3}, what is the expected number of times the pattern 'rm+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, i: 2, r: 1, z: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'i.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 4, a: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, z: 1, m: 1, c: 2}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, w: 2, b: 1, t: 2}. What is the expected number of occurrences of the pattern 'f.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, g: 1, d: 1, t: 2}. What is the expected number of occurrences of the pattern 'kd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, m: 2, s: 1, p: 1, g: 1}. What is the expected number of occurrences of the pattern 's+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, b: 2, d: 1}, what is the expected number of times the pattern 'i+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 5, u: 1}. What is the expected number of occurrences of the pattern 'p.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, y: 3, m: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'jm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, u: 4}. What is the expected number of occurrences of the pattern 'ur+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, m: 4} to form a word, what is the expected number of matches of the pattern 'em+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 4, f: 2}. What is the expected number of occurrences of the pattern 'fe*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, f: 3, m: 1} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, k: 1, u: 1, e: 1, w: 2}. What is the expected number of occurrences of the pattern 'uk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, f: 1, u: 3} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 5, i: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, s: 3, p: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 4, k: 2}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, o: 3}, what is the expected number of times the pattern 'no*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, u: 2, x: 2}. What is the expected number of occurrences of the pattern 'u*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 3, t: 3} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, f: 3, v: 1}, what is the expected number of times the pattern 'gv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, d: 2, y: 1, g: 2}, what is the expected number of times the pattern 'y+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, u: 2, k: 3} to form a word, what is the expected number of matches of the pattern 'pk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 4, m: 2}, what is the expected number of times the pattern 'm.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, y: 2, i: 1}, what is the expected number of times the pattern 'vy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, x: 2, k: 1, d: 1, p: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, g: 1, c: 1, q: 1, r: 2}, what is the expected number of times the pattern 'q+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, v: 2, w: 1, c: 2}, what is the expected number of times the pattern 'w+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, f: 1, x: 1, i: 1, b: 1}. What is the expected number of occurrences of the pattern 'xf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, w: 1, f: 2, n: 1}. What is the expected number of occurrences of the pattern 'ln*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, m: 4}, what is the expected number of times the pattern 'z+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, f: 3}, what is the expected number of times the pattern 'f.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 3, g: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'g+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, e: 3}, what is the expected number of times the pattern 'r*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, q: 3}, what is the expected number of times the pattern 'qm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, q: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, o: 1, x: 3}, what is the expected number of times the pattern 'o+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, u: 1, y: 1, s: 3} to form a word, what is the expected number of matches of the pattern 'uy*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, l: 1, e: 1, v: 1, m: 2}, what is the expected number of times the pattern 'v*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, x: 2, m: 1, v: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, m: 2, r: 1}. What is the expected number of occurrences of the pattern 'mg+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, e: 1, l: 1, u: 2, y: 1}, what is the expected number of times the pattern 'e+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, x: 3}, what is the expected number of times the pattern 'x.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, v: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'v*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, m: 1, y: 3, l: 1} to form a word, what is the expected number of matches of the pattern 'lm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, a: 4}, what is the expected number of times the pattern 'a+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, z: 1, f: 2, i: 1, q: 1}. What is the expected number of occurrences of the pattern 'q*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, u: 1, y: 2, b: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, o: 3}. What is the expected number of occurrences of the pattern 'o.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, s: 2, y: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 4, v: 2}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, k: 1, g: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, q: 1, m: 1, z: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'qa*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, b: 1, w: 1, i: 2}. What is the expected number of occurrences of the pattern 'i*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, z: 1, n: 2, v: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, b: 4, r: 1}, what is the expected number of times the pattern 'r+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, g: 2, r: 1, k: 1, n: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, o: 2, j: 3}. What is the expected number of occurrences of the pattern 'ju+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, j: 2, u: 1, l: 1}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, m: 1, x: 1, w: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'wc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, a: 2, o: 1, x: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'x*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 4, r: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'dm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, k: 3, h: 2}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, u: 2, t: 2}. What is the expected number of occurrences of the pattern 'u*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, i: 3, l: 1} to form a word, what is the expected number of matches of the pattern 'r*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, x: 4} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, s: 2, b: 2, r: 1}. What is the expected number of occurrences of the pattern 'fr+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, u: 1, w: 1, n: 1}. What is the expected number of occurrences of the pattern 'n.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, b: 2, i: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, x: 4}, what is the expected number of times the pattern 'e*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, a: 2, c: 2} to form a word, what is the expected number of matches of the pattern 'f+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 4, l: 2} to form a word, what is the expected number of matches of the pattern 'l+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, t: 4}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 4, d: 1, k: 1}. What is the expected number of occurrences of the pattern 'kd+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, v: 2, g: 1, k: 1, i: 1}. What is the expected number of occurrences of the pattern 'y.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, f: 2, q: 1, t: 1, y: 1}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, k: 4}. What is the expected number of occurrences of the pattern 'kl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, p: 1, g: 2, z: 1, w: 1}, what is the expected number of times the pattern 'n*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, z: 1, b: 2, t: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, y: 1, m: 1, d: 1, j: 1}, what is the expected number of times the pattern 'jd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, z: 2, r: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'fz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, m: 5}. What is the expected number of occurrences of the pattern 'm+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, k: 1, t: 2, x: 2}. What is the expected number of occurrences of the pattern 'at*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, k: 4}. What is the expected number of occurrences of the pattern 'kr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, b: 3}. What is the expected number of occurrences of the pattern 'c*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, u: 3, l: 2} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, x: 2, w: 2} to form a word, what is the expected number of matches of the pattern 'w+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, j: 2, l: 2} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, u: 1, c: 1, d: 2, k: 1}, what is the expected number of times the pattern 'c*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, p: 1, f: 2, u: 2}, what is the expected number of times the pattern 'u*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, i: 2, j: 1, r: 1, k: 1}. What is the expected number of occurrences of the pattern 'rk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, g: 1, v: 3, y: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 4, v: 2} to form a word, what is the expected number of matches of the pattern 'v*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, q: 2, w: 1, l: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, u: 2, v: 1}. What is the expected number of occurrences of the pattern 'vu+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, j: 3}, what is the expected number of times the pattern 'r+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, h: 1, q: 2, r: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, f: 3, w: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'f+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, q: 3}, what is the expected number of times the pattern 'k*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, l: 1, v: 3, g: 1}, what is the expected number of times the pattern 'v+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, n: 1, z: 1, d: 1, v: 2}. What is the expected number of occurrences of the pattern 'd*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 3, d: 3} to form a word, what is the expected number of matches of the pattern 'd.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, l: 1, c: 3}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, q: 2, u: 2, g: 1}. What is the expected number of occurrences of the pattern 'ug+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, c: 2, n: 2}. What is the expected number of occurrences of the pattern 'cn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, i: 1, m: 2}. What is the expected number of occurrences of the pattern 'k*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, p: 1, n: 2, g: 2} to form a word, what is the expected number of matches of the pattern 'gu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, j: 3, s: 2}, what is the expected number of times the pattern 's+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, i: 3, p: 1, j: 1}. What is the expected number of occurrences of the pattern 'p.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, j: 2, a: 1, r: 1, k: 1}. What is the expected number of occurrences of the pattern 'a+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, m: 3}, what is the expected number of times the pattern 'mi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, e: 3} to form a word, what is the expected number of matches of the pattern 'de+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, t: 1, x: 2, c: 2}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, v: 1, g: 1, c: 2, m: 1}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, a: 3, r: 1, q: 1}, what is the expected number of times the pattern 'r+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, s: 2, a: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, y: 3, h: 1} to form a word, what is the expected number of matches of the pattern 'hy+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, g: 1, n: 2, x: 1} to form a word, what is the expected number of matches of the pattern 'ne*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, r: 2, z: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'l*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 4, d: 2}, what is the expected number of times the pattern 'jd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, e: 1, s: 1, i: 2}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, t: 1, x: 2, j: 1}, what is the expected number of times the pattern 'xu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, z: 4}. What is the expected number of occurrences of the pattern 'f+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, r: 2, e: 1, k: 1, w: 1}, what is the expected number of times the pattern 'kw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, a: 1, q: 1, l: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'a*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, g: 3, u: 2} to form a word, what is the expected number of matches of the pattern 'u*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, c: 1, p: 2, k: 1, w: 1}. What is the expected number of occurrences of the pattern 'p*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, m: 4}. What is the expected number of occurrences of the pattern 'ml*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, a: 2, t: 3} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, h: 1, i: 1, v: 2, d: 1}, what is the expected number of times the pattern 'di*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, d: 1, p: 2, t: 1, h: 1}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, y: 1, q: 1, l: 2, x: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, o: 3, a: 1, h: 1}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 3, d: 3} to form a word, what is the expected number of matches of the pattern 'df*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 4, l: 2} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, x: 2, f: 1, p: 1, o: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, d: 2, b: 1, c: 1}. What is the expected number of occurrences of the pattern 'c+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, q: 1, s: 1, m: 1, z: 2}, what is the expected number of times the pattern 'm*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, v: 1, n: 3, d: 1} to form a word, what is the expected number of matches of the pattern 's.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, j: 4}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, m: 3, d: 2}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, y: 4} to form a word, what is the expected number of matches of the pattern 'z*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, j: 1, f: 1, w: 1, p: 1}. What is the expected number of occurrences of the pattern 'e+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, x: 4} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, c: 3}. What is the expected number of occurrences of the pattern 'c*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, o: 3} to form a word, what is the expected number of matches of the pattern 'o.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, o: 4}. What is the expected number of occurrences of the pattern 'o.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, r: 1, b: 1, j: 2, f: 1}, what is the expected number of times the pattern 'f+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, q: 2, n: 1}. What is the expected number of occurrences of the pattern 'ne*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, z: 2, l: 1, f: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'l+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, a: 2, i: 2}. What is the expected number of occurrences of the pattern 'a*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, l: 2, x: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'rg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, v: 2, h: 1, w: 1, b: 1}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, r: 1, j: 1, i: 2, u: 1}, what is the expected number of times the pattern 'r+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, b: 1, x: 1, r: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, x: 2, e: 2, c: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 4, w: 2} to form a word, what is the expected number of matches of the pattern 'w+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, m: 3, t: 2}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, z: 1, s: 1, e: 2}. What is the expected number of occurrences of the pattern 's*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, p: 3}. What is the expected number of occurrences of the pattern 'g.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, t: 1, c: 2, m: 1, l: 1}, what is the expected number of times the pattern 'l.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, h: 5} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, a: 4}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, e: 2, s: 1, u: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, v: 2, s: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, g: 1, p: 3} to form a word, what is the expected number of matches of the pattern 'p+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, l: 4} to form a word, what is the expected number of matches of the pattern 'lt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 4, n: 2} to form a word, what is the expected number of matches of the pattern 'n.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, y: 2, c: 1}, what is the expected number of times the pattern 'z+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, l: 1, y: 1, d: 1, p: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, n: 4}. What is the expected number of occurrences of the pattern 'nh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, e: 3} to form a word, what is the expected number of matches of the pattern 'g*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, n: 2, v: 3}. What is the expected number of occurrences of the pattern 'i.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, i: 3, l: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'ji+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, z: 1, f: 2, y: 1}. What is the expected number of occurrences of the pattern 'z*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, d: 2, n: 3} to form a word, what is the expected number of matches of the pattern 'nd+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, z: 1, o: 3}, what is the expected number of times the pattern 'ro+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, r: 1, t: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'e+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, o: 2, x: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'no+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, q: 2, c: 1, x: 1, y: 1}, what is the expected number of times the pattern 'c+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 5, d: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, q: 1, p: 4}, what is the expected number of times the pattern 'p*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, q: 1, r: 1, d: 1, g: 1}. What is the expected number of occurrences of the pattern 'e+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, a: 2, v: 1, j: 2}. What is the expected number of occurrences of the pattern 'q.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, g: 1, a: 2, r: 1}, what is the expected number of times the pattern 'rg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, p: 4} to form a word, what is the expected number of matches of the pattern 'p*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, s: 3}, what is the expected number of times the pattern 'w.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, r: 3, n: 2}. What is the expected number of occurrences of the pattern 'i+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, s: 1, p: 1, j: 1}. What is the expected number of occurrences of the pattern 'sp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, k: 1, q: 3}, what is the expected number of times the pattern 'qk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, j: 1, l: 1, g: 2}, what is the expected number of times the pattern 'jm+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, p: 1, q: 1, a: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 4, w: 2}, what is the expected number of times the pattern 'v.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, w: 4} to form a word, what is the expected number of matches of the pattern 'c*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, c: 2, s: 1, j: 1}. What is the expected number of occurrences of the pattern 'cj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, b: 1, c: 2, i: 1}. What is the expected number of occurrences of the pattern 'cb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 3, v: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'ed+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, g: 3}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, j: 2, t: 1, h: 1, z: 1}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, y: 1, f: 1, l: 1, j: 2} to form a word, what is the expected number of matches of the pattern 's*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, i: 1, a: 1, m: 1, y: 2}, what is the expected number of times the pattern 'a*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, k: 1, b: 1, y: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'k+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, a: 3, t: 1}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, r: 1, i: 2, n: 1}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, b: 1, m: 2, d: 1}. What is the expected number of occurrences of the pattern 'k.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, f: 1, k: 2, r: 1, a: 1}, what is the expected number of times the pattern 'f*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, n: 3}. What is the expected number of occurrences of the pattern 'q+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, p: 3, x: 2} to form a word, what is the expected number of matches of the pattern 'px+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, k: 3}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, a: 1, j: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'ra+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, a: 2, s: 1, f: 1, l: 1}. What is the expected number of occurrences of the pattern 'l.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, i: 1, r: 2}. What is the expected number of occurrences of the pattern 'rj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, s: 1, h: 1, a: 2, m: 1} to form a word, what is the expected number of matches of the pattern 'fh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, c: 1, n: 1, v: 3}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, v: 1, p: 1, i: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'pi*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, u: 1, r: 3, s: 1} to form a word, what is the expected number of matches of the pattern 'ur*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, e: 3}. What is the expected number of occurrences of the pattern 'f.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, i: 1, g: 1, s: 2} to form a word, what is the expected number of matches of the pattern 's+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, v: 1, h: 3} to form a word, what is the expected number of matches of the pattern 'h*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, u: 1, g: 2, y: 1}. What is the expected number of occurrences of the pattern 'yg+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, n: 2, m: 1, o: 1, t: 1}, what is the expected number of times the pattern 'o*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, v: 2, b: 3}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, u: 3, w: 2} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, h: 1, x: 2, z: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, w: 1, u: 1, f: 1}. What is the expected number of occurrences of the pattern 'wh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, v: 2, w: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, r: 3} to form a word, what is the expected number of matches of the pattern 't+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, d: 3, f: 2}, what is the expected number of times the pattern 'd*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, v: 4}, what is the expected number of times the pattern 'qv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, r: 1, u: 1, z: 1, h: 2}. What is the expected number of occurrences of the pattern 'zr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, y: 2, l: 2, p: 1}. What is the expected number of occurrences of the pattern 'pl+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, n: 3} to form a word, what is the expected number of matches of the pattern 'nj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, y: 1, h: 3, d: 1}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, p: 1, o: 2, x: 1, u: 1}, what is the expected number of times the pattern 'u*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, g: 1, i: 1, d: 1, u: 1}, what is the expected number of times the pattern 'yi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, y: 1, v: 1, l: 1, q: 2} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, l: 1, s: 1, b: 1, d: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, r: 1, b: 2, y: 1}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, l: 3, d: 2}. What is the expected number of occurrences of the pattern 'ln+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, t: 2, k: 1, g: 2}. What is the expected number of occurrences of the pattern 'k*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, x: 1, n: 1, c: 2}, what is the expected number of times the pattern 'c+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, x: 1, r: 2, h: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, p: 1, n: 2, s: 1}, what is the expected number of times the pattern 'p+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, x: 1, j: 3} to form a word, what is the expected number of matches of the pattern 'x.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, n: 1, q: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'e*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, z: 2, p: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'z+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 3, y: 1, h: 2}. What is the expected number of occurrences of the pattern 'hy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, l: 1, b: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'j+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, f: 2, p: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'f*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, c: 1, e: 2, z: 1}. What is the expected number of occurrences of the pattern 'g*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, s: 1, r: 1, p: 1, j: 1}. What is the expected number of occurrences of the pattern 'j+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, i: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'is*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, j: 1, f: 1, y: 1, t: 2}, what is the expected number of times the pattern 's*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, w: 2, c: 1, i: 1}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, s: 1, n: 2, q: 2}, what is the expected number of times the pattern 'l*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, h: 2, l: 1, m: 1, a: 1}. What is the expected number of occurrences of the pattern 'mp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, h: 2, q: 1}, what is the expected number of times the pattern 'qh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, m: 2, r: 1}, what is the expected number of times the pattern 'rm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, p: 2, c: 3}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, s: 4}. What is the expected number of occurrences of the pattern 's.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, g: 1, n: 2, d: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, y: 2, o: 1, e: 1}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, b: 1, y: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 4, w: 1, v: 1}. What is the expected number of occurrences of the pattern 'mw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 4, d: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, l: 3}. What is the expected number of occurrences of the pattern 'lk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, u: 2, m: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, g: 2, j: 1}. What is the expected number of occurrences of the pattern 'f.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, m: 3, j: 2}, what is the expected number of times the pattern 'k+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, q: 2, c: 1}. What is the expected number of occurrences of the pattern 'aq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 4, d: 2}, what is the expected number of times the pattern 'a+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, a: 1, q: 3}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, z: 1, q: 1, d: 1, r: 1}. What is the expected number of occurrences of the pattern 't.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, k: 1, j: 2, u: 1, o: 1}. What is the expected number of occurrences of the pattern 'pu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, z: 2, y: 2}. What is the expected number of occurrences of the pattern 'y+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, f: 1, m: 2}. What is the expected number of occurrences of the pattern 'fu+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, o: 1, f: 1, i: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, d: 1, b: 3, k: 1}. What is the expected number of occurrences of the pattern 'dt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 4, i: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 4, e: 1, j: 1}, what is the expected number of times the pattern 'o+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, q: 1, w: 3, u: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, i: 2, z: 1, k: 1, u: 1}. What is the expected number of occurrences of the pattern 'uo*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, v: 3}, what is the expected number of times the pattern 'm+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, t: 1, a: 2, k: 2}. What is the expected number of occurrences of the pattern 'gt+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 3, h: 1, f: 1, a: 1}, what is the expected number of times the pattern 'la*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, j: 2, d: 2}, what is the expected number of times the pattern 'j+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, h: 1, w: 1, u: 1, q: 1}. What is the expected number of occurrences of the pattern 'x*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, x: 1, r: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, q: 1, f: 1, j: 3}. What is the expected number of occurrences of the pattern 'fj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, r: 1, d: 1, y: 1, w: 1}, what is the expected number of times the pattern 'r*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 4, i: 2}, what is the expected number of times the pattern 'x*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, q: 1, y: 1, c: 2, h: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, y: 3} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, f: 3} to form a word, what is the expected number of matches of the pattern 'f*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 3, f: 3}, what is the expected number of times the pattern 'f.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, n: 3, p: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'ni+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, o: 4}, what is the expected number of times the pattern 'ok*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, f: 4}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, v: 2, t: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'c+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, y: 4} to form a word, what is the expected number of matches of the pattern 'hy*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, i: 1, h: 1, g: 3} to form a word, what is the expected number of matches of the pattern 'r+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, k: 1, d: 1, q: 2, r: 1}, what is the expected number of times the pattern 'qd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, v: 3, h: 1}, what is the expected number of times the pattern 'hc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, g: 2, b: 2}, what is the expected number of times the pattern 'pb+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, w: 2, v: 1}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, i: 2, n: 1, e: 1, w: 1}, what is the expected number of times the pattern 'i.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, t: 1, u: 3, y: 1} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, u: 3, a: 1}, what is the expected number of times the pattern 'u.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, x: 1, s: 1, t: 1, k: 1}. What is the expected number of occurrences of the pattern 'ty*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'uh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, z: 1, m: 3}. What is the expected number of occurrences of the pattern 'm+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, m: 1, c: 2, q: 2} to form a word, what is the expected number of matches of the pattern 'qm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, a: 2, q: 2} to form a word, what is the expected number of matches of the pattern 'aq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, a: 1, s: 2, m: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, g: 2, y: 2, k: 1}, what is the expected number of times the pattern 'k+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, f: 1, p: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, k: 1, f: 1, i: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 4, e: 2}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, l: 1, m: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, h: 1, t: 1, j: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'jt+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 3, s: 3}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, o: 3}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, y: 2, w: 1, z: 1}. What is the expected number of occurrences of the pattern 'y+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, a: 2, i: 2, r: 1}. What is the expected number of occurrences of the pattern 'g*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, i: 1, d: 4}, what is the expected number of times the pattern 'iq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, c: 3}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, b: 2, p: 1, v: 2}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, z: 1, q: 1, b: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'q+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, f: 2, n: 1, i: 1, u: 1}. What is the expected number of occurrences of the pattern 'i*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, x: 2, v: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'r*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 4, p: 2} to form a word, what is the expected number of matches of the pattern 'p*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, m: 1, v: 1, i: 1, w: 2}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, h: 2, j: 1}, what is the expected number of times the pattern 'hj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, a: 1, n: 1, k: 1, i: 2}, what is the expected number of times the pattern 'q+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'g.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, d: 1, p: 1, v: 1, m: 2}. What is the expected number of occurrences of the pattern 'mp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, u: 1, o: 1, z: 1, c: 2}. What is the expected number of occurrences of the pattern 'u*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 4, w: 2}. What is the expected number of occurrences of the pattern 'w.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, p: 2, o: 3}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, h: 1, q: 3}, what is the expected number of times the pattern 'dh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, c: 1, y: 3}. What is the expected number of occurrences of the pattern 'c+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 4, q: 2}. What is the expected number of occurrences of the pattern 'e.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, b: 2, x: 1, n: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'wx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, d: 2, q: 1, f: 2}. What is the expected number of occurrences of the pattern 'v*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, e: 3}, what is the expected number of times the pattern 'x.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, h: 1, l: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'lj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, d: 3}, what is the expected number of times the pattern 'dp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, m: 1, f: 1, j: 1, b: 2}. What is the expected number of occurrences of the pattern 'wb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, t: 1, a: 1, f: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'u+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, x: 1, c: 3, f: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, m: 1, p: 1, z: 2}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, x: 2, a: 2}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, i: 1, e: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'ai+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, q: 1, l: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'l.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, e: 1, z: 1, h: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'c+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, j: 3, z: 2} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, q: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'n*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, d: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'a.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, f: 3, c: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, l: 1, j: 3}. What is the expected number of occurrences of the pattern 'lj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, f: 4} to form a word, what is the expected number of matches of the pattern 'f+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, t: 4}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, j: 4}, what is the expected number of times the pattern 'j*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, b: 3, r: 1}, what is the expected number of times the pattern 'q+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, r: 1, e: 1, w: 1, y: 1}, what is the expected number of times the pattern 'y.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, t: 2, v: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'v+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 4, o: 2}. What is the expected number of occurrences of the pattern 'ok+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, n: 2, e: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'e+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, i: 2, x: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, a: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'a+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 3, v: 3}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, z: 3} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, w: 2, y: 1, j: 2}. What is the expected number of occurrences of the pattern 'vy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, q: 1, k: 1, i: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'q+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, v: 4}, what is the expected number of times the pattern 'r.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, w: 2, f: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'f*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, t: 2, z: 1, w: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'wt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 4, l: 2}. What is the expected number of occurrences of the pattern 'p*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, n: 1, m: 1, i: 2}. What is the expected number of occurrences of the pattern 'z+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, r: 2, s: 1, f: 1, c: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, u: 2, g: 3} to form a word, what is the expected number of matches of the pattern 'gm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 4, e: 2}, what is the expected number of times the pattern 'e.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, d: 2, e: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'r.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, g: 1, r: 1, d: 2, i: 1}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 4, r: 2}, what is the expected number of times the pattern 'rc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, i: 1, g: 1, f: 1, m: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, w: 3}. What is the expected number of occurrences of the pattern 'wi*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, f: 5} to form a word, what is the expected number of matches of the pattern 'jf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, s: 2, u: 2}, what is the expected number of times the pattern 'j.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, z: 2, v: 2} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, f: 1, d: 1, o: 2}, what is the expected number of times the pattern 'dk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, g: 2, i: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'c+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, t: 4}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, n: 1, d: 1, l: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, s: 3}, what is the expected number of times the pattern 'd.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, y: 2, i: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'ci+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, u: 1, b: 1, d: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'el*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 4, t: 2} to form a word, what is the expected number of matches of the pattern 't.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, a: 3}. What is the expected number of occurrences of the pattern 'a+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, o: 1, e: 2, i: 1}, what is the expected number of times the pattern 'e.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, r: 4, y: 1} to form a word, what is the expected number of matches of the pattern 'r+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, j: 2, r: 1, a: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'o+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, z: 1, v: 1, j: 2} to form a word, what is the expected number of matches of the pattern 'jq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, w: 2, m: 1}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'a*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, f: 2, i: 1, m: 2}, what is the expected number of times the pattern 'fi+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, x: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'xf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, h: 2, a: 3}, what is the expected number of times the pattern 'a+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, t: 2, y: 1, i: 2}. What is the expected number of occurrences of the pattern 't+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, x: 3, f: 2}. What is the expected number of occurrences of the pattern 'qx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, u: 2, v: 3}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 4, l: 2}. What is the expected number of occurrences of the pattern 'ld*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, i: 1, l: 3}, what is the expected number of times the pattern 'i+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, g: 2, f: 3}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, b: 1, r: 1, n: 1, u: 1}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, n: 1, h: 1, c: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, i: 3, v: 1}. What is the expected number of occurrences of the pattern 'z+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, x: 2}. What is the expected number of occurrences of the pattern 'u.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, b: 1, n: 2}, what is the expected number of times the pattern 'o*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, z: 1, v: 3}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, q: 1, a: 1, o: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'q*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 4, k: 2}, what is the expected number of times the pattern 'k*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, x: 1, i: 1, a: 1, k: 1}. What is the expected number of occurrences of the pattern 'xt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, p: 3}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, x: 1, q: 1, k: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, h: 1, a: 1, t: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, g: 1, v: 1, n: 1}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, q: 3, h: 2}, what is the expected number of times the pattern 'u+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, t: 2, p: 1, f: 1}. What is the expected number of occurrences of the pattern 'pf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, r: 5}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, f: 2, i: 1, j: 1, e: 1}, what is the expected number of times the pattern 'ij*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, n: 4}, what is the expected number of times the pattern 'j+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, c: 2, j: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'f.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, j: 2, h: 2}. What is the expected number of occurrences of the pattern 'fh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, v: 3}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, s: 1, h: 2, g: 2}, what is the expected number of times the pattern 'f.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, x: 1, k: 2, z: 1, s: 1}, what is the expected number of times the pattern 'e.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 4, v: 2} to form a word, what is the expected number of matches of the pattern 'zv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, l: 1, t: 3}, what is the expected number of times the pattern 'xl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, m: 1, i: 4}, what is the expected number of times the pattern 'm*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, i: 1, r: 2, n: 1, o: 1}, what is the expected number of times the pattern 'ir*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, h: 2, f: 1, x: 1, d: 1}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, f: 1, o: 1, c: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, k: 2, t: 1, c: 1, y: 1}, what is the expected number of times the pattern 'ck+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, t: 2, l: 3} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 4, f: 2}, what is the expected number of times the pattern 'qf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, s: 1, n: 2, u: 2}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, u: 1, r: 2, b: 1}, what is the expected number of times the pattern 'r+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, t: 3, o: 1, g: 1}. What is the expected number of occurrences of the pattern 'g+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'p.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, a: 1, e: 2, n: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, v: 3}, what is the expected number of times the pattern 't+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, g: 1, d: 2, w: 1, y: 1}. What is the expected number of occurrences of the pattern 'l+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, m: 1, b: 2, h: 1, i: 1}, what is the expected number of times the pattern 'mh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, w: 2}. What is the expected number of occurrences of the pattern 'uw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 4, e: 2} to form a word, what is the expected number of matches of the pattern 'ez+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, h: 1, v: 2}. What is the expected number of occurrences of the pattern 'hv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, u: 1, a: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, u: 1, x: 3}, what is the expected number of times the pattern 'l*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, h: 1, p: 2, k: 1, s: 1}, what is the expected number of times the pattern 's*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 4, i: 2}, what is the expected number of times the pattern 'iz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, b: 1, x: 3}, what is the expected number of times the pattern 'l+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, e: 1, m: 1, i: 2}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, m: 1, j: 1, y: 1}. What is the expected number of occurrences of the pattern 'yj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, d: 1, y: 3, r: 1}, what is the expected number of times the pattern 'vd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, q: 1, t: 2, z: 1}, what is the expected number of times the pattern 'qt*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, y: 1, s: 1, e: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, b: 1, l: 1, c: 3}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, w: 1, f: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'f+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, t: 2, q: 1, g: 2}. What is the expected number of occurrences of the pattern 't.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, t: 2, b: 2, x: 1} to form a word, what is the expected number of matches of the pattern 't.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, q: 2, w: 2}, what is the expected number of times the pattern 'w.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 4, x: 2} to form a word, what is the expected number of matches of the pattern 'hx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, c: 2, q: 1, r: 1}. What is the expected number of occurrences of the pattern 'h+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, y: 4, i: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, s: 2, t: 1}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, t: 2, r: 1, p: 1}. What is the expected number of occurrences of the pattern 'pt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 5, h: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, h: 2, i: 2}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, o: 1, x: 1, z: 1, k: 1}, what is the expected number of times the pattern 'xd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, w: 2, v: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, z: 1, j: 1, p: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'p*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, o: 1, e: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'e*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, l: 2, o: 1, v: 1, i: 1}, what is the expected number of times the pattern 'l*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, f: 1, w: 1, d: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, c: 3, b: 1}, what is the expected number of times the pattern 'c.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, p: 2, r: 2}, what is the expected number of times the pattern 'r+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, b: 1, i: 1, u: 1, n: 2}. What is the expected number of occurrences of the pattern 'i*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, m: 2, n: 3}, what is the expected number of times the pattern 'am+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, p: 1, v: 1, c: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'px+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, h: 3, e: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, c: 3, j: 1, w: 1}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, v: 1, z: 2, i: 2}, what is the expected number of times the pattern 'z.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, x: 1, b: 3, o: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, n: 1, a: 1, e: 2, h: 1} to form a word, what is the expected number of matches of the pattern 'he+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, g: 1, p: 1, i: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, c: 2, o: 1, x: 2}. What is the expected number of occurrences of the pattern 'vo+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, m: 1, v: 2, g: 1, b: 1}. What is the expected number of occurrences of the pattern 'm.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, g: 1, q: 3}. What is the expected number of occurrences of the pattern 'q*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, f: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'vf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, c: 2, q: 1, w: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, f: 1, q: 2, w: 1, n: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, y: 1, c: 1, l: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'u.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, h: 3, c: 1, q: 1}. What is the expected number of occurrences of the pattern 'qh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, p: 1, i: 2, q: 1, n: 1}. What is the expected number of occurrences of the pattern 'yq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, f: 1, i: 2, a: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'p*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 3, p: 3}, what is the expected number of times the pattern 'a.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, s: 2, y: 1, p: 1}. What is the expected number of occurrences of the pattern 'y.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, k: 1, z: 2, m: 1, o: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, y: 2, j: 1, r: 1, k: 1}, what is the expected number of times the pattern 'r.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, a: 3} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, c: 1, w: 3, e: 1}, what is the expected number of times the pattern 'ew*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, h: 4}, what is the expected number of times the pattern 'h*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, c: 2, e: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'ce*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 4, t: 2}, what is the expected number of times the pattern 'yt+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, r: 1, j: 1, f: 2}. What is the expected number of occurrences of the pattern 'r+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, d: 1, f: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, j: 1, f: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'sf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, w: 1, h: 1, d: 1, j: 1}, what is the expected number of times the pattern 'j+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, s: 1, b: 2, j: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, f: 2, a: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, h: 1, i: 2, o: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, z: 2, v: 1, h: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, c: 2, f: 3} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, v: 1, s: 3, h: 1}. What is the expected number of occurrences of the pattern 'v.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 4, m: 2} to form a word, what is the expected number of matches of the pattern 'f.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, x: 1, v: 1, d: 2, c: 1}, what is the expected number of times the pattern 'x*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, n: 3, h: 2}. What is the expected number of occurrences of the pattern 'h+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, u: 1, y: 1, e: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'e*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, v: 1, w: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, q: 1, v: 4}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, d: 3, u: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'z.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, r: 4} to form a word, what is the expected number of matches of the pattern 'rb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 5, q: 1} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, u: 2, f: 2}. What is the expected number of occurrences of the pattern 'f.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, u: 2, p: 1}. What is the expected number of occurrences of the pattern 'u*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, a: 2, n: 2}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, p: 1, d: 2, v: 2}, what is the expected number of times the pattern 'vp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, c: 1, v: 3}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, h: 1, t: 2, k: 2}, what is the expected number of times the pattern 't.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, t: 1, m: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'm+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, z: 1, h: 1, s: 1, e: 1} to form a word, what is the expected number of matches of the pattern 's.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, e: 1, y: 2, o: 2}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, d: 4}. What is the expected number of occurrences of the pattern 'a.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, v: 4}, what is the expected number of times the pattern 'v+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 5, i: 1}, what is the expected number of times the pattern 'vi+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, c: 3, w: 2} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, q: 1, t: 2, c: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'f*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, q: 1, j: 1, i: 1, x: 1}. What is the expected number of occurrences of the pattern 'y*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, b: 1, i: 1, k: 2, n: 1}, what is the expected number of times the pattern 'n*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 4, k: 2}. What is the expected number of occurrences of the pattern 'e*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, k: 3}. What is the expected number of occurrences of the pattern 'z*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, d: 3}, what is the expected number of times the pattern 'd.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, n: 2, o: 2, i: 1}, what is the expected number of times the pattern 'h.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, x: 3, m: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, j: 2, k: 1, v: 2}. What is the expected number of occurrences of the pattern 'j.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 3, s: 2, e: 1}, what is the expected number of times the pattern 'ey*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, s: 2, h: 2}. What is the expected number of occurrences of the pattern 's+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, d: 2, z: 1, u: 1, y: 1}, what is the expected number of times the pattern 'yd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, f: 1, o: 2, s: 1}. What is the expected number of occurrences of the pattern 'sf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, c: 1, h: 1, k: 1, o: 1}. What is the expected number of occurrences of the pattern 'e+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, s: 2, k: 2, x: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, a: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'o.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, m: 3, s: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, f: 1, s: 1, p: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'f.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, m: 1, e: 1, d: 1, v: 2}, what is the expected number of times the pattern 'vd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, z: 2, t: 1, e: 2}. What is the expected number of occurrences of the pattern 'te*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 5, c: 1}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, e: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'e.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, w: 3, u: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'u+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, w: 1, j: 1, a: 2, b: 1} to form a word, what is the expected number of matches of the pattern 'a.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, l: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'h*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, s: 1, p: 1, u: 2, q: 1}. What is the expected number of occurrences of the pattern 'ps+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, l: 1, x: 2, k: 1}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, j: 1, i: 3} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, c: 2, x: 2, g: 1}. What is the expected number of occurrences of the pattern 'l.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 4, d: 2}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, c: 1, e: 1, x: 2}. What is the expected number of occurrences of the pattern 'c+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, v: 1, z: 1, u: 1, j: 2}. What is the expected number of occurrences of the pattern 'z+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, j: 1, x: 1, s: 2, i: 1}. What is the expected number of occurrences of the pattern 'ij*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, w: 1, c: 1, n: 2}, what is the expected number of times the pattern 'cz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 4, v: 2}. What is the expected number of occurrences of the pattern 'q*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, c: 2, d: 1, w: 1, j: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 4, x: 2}, what is the expected number of times the pattern 'x+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 4, j: 2}. What is the expected number of occurrences of the pattern 'zj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, s: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'sw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, r: 2, z: 2}, what is the expected number of times the pattern 'r.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, r: 1, w: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'w.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, p: 1, r: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'p+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, o: 2, n: 1}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, c: 1, h: 1, i: 1, l: 1}, what is the expected number of times the pattern 'h+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, y: 1, i: 1, j: 2, w: 1}, what is the expected number of times the pattern 'o*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, b: 1, p: 2, i: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'kz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, p: 4}. What is the expected number of occurrences of the pattern 'j+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, b: 2, p: 1, z: 1, a: 1}. What is the expected number of occurrences of the pattern 'z*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, n: 2, j: 1, i: 1, p: 1}. What is the expected number of occurrences of the pattern 'p.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, e: 3, s: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'ey+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, b: 1, c: 4}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, j: 1, t: 3} to form a word, what is the expected number of matches of the pattern 't+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 4, c: 1, t: 1}, what is the expected number of times the pattern 'v*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, o: 1, a: 2}. What is the expected number of occurrences of the pattern 'au+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, n: 2, r: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, n: 2, u: 1, i: 1, r: 1}. What is the expected number of occurrences of the pattern 'r+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, o: 3, s: 2} to form a word, what is the expected number of matches of the pattern 'so+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, t: 1, x: 1, d: 1, c: 1}. What is the expected number of occurrences of the pattern 'x+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 4, j: 2} to form a word, what is the expected number of matches of the pattern 'jo+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, u: 1, m: 3, x: 1} to form a word, what is the expected number of matches of the pattern 'f*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, d: 2, e: 3} to form a word, what is the expected number of matches of the pattern 'g+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, i: 2, h: 1, c: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, o: 1, c: 3, d: 1}. What is the expected number of occurrences of the pattern 'o*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'mm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, m: 3}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, d: 3}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, x: 2, s: 1, f: 1, k: 1}. What is the expected number of occurrences of the pattern 'x*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 4, k: 2} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, n: 1, r: 3}. What is the expected number of occurrences of the pattern 'e.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, y: 1, v: 2, b: 1, a: 1}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, x: 3, u: 1, i: 1}, what is the expected number of times the pattern 'x+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, g: 2, e: 1}. What is the expected number of occurrences of the pattern 'e+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, j: 1, q: 2, k: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, x: 1, y: 1, m: 1, n: 1}, what is the expected number of times the pattern 'n*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, w: 3}. What is the expected number of occurrences of the pattern 'w+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, s: 2, h: 1, q: 2}, what is the expected number of times the pattern 'sl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, i: 4, v: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, u: 4} to form a word, what is the expected number of matches of the pattern 'ux*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, t: 2, x: 2, z: 1}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, y: 1, b: 1, d: 1, n: 1}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, f: 2, b: 1} to form a word, what is the expected number of matches of the pattern 'fb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, z: 1, e: 1, j: 1, g: 1}, what is the expected number of times the pattern 'c.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, r: 4}, what is the expected number of times the pattern 'rb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, h: 3, p: 1} to form a word, what is the expected number of matches of the pattern 'e.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, l: 2, v: 3} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 4, v: 2} to form a word, what is the expected number of matches of the pattern 'w*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, k: 1, p: 1, n: 1, v: 2}. What is the expected number of occurrences of the pattern 'vn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, l: 3, o: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'o*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, r: 2, t: 2}, what is the expected number of times the pattern 'r+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, n: 1, c: 2}, what is the expected number of times the pattern 'nx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, i: 2, u: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'vl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, h: 3}. What is the expected number of occurrences of the pattern 'xh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, o: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 4, t: 2} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, n: 2, r: 2} to form a word, what is the expected number of matches of the pattern 'nr+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, c: 2, n: 2, z: 1}, what is the expected number of times the pattern 'nc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, z: 2, u: 3} to form a word, what is the expected number of matches of the pattern 'z*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, w: 4, y: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, r: 2, g: 3}, what is the expected number of times the pattern 'g*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, v: 2, r: 2}, what is the expected number of times the pattern 'rv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, g: 1, x: 2, t: 2} to form a word, what is the expected number of matches of the pattern 'xt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, y: 1, k: 1, z: 1, b: 2}, what is the expected number of times the pattern 'y*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, t: 1, e: 1, v: 2}. What is the expected number of occurrences of the pattern 'ze*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, y: 1, d: 2, v: 1, e: 1}. What is the expected number of occurrences of the pattern 'y.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 4, z: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'j+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, h: 1, m: 2, q: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, f: 2, t: 3} to form a word, what is the expected number of matches of the pattern 'f*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, y: 2, q: 2}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, y: 1, q: 2} to form a word, what is the expected number of matches of the pattern 'y+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, p: 1, u: 2, v: 1, y: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, c: 1, r: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, d: 1, c: 2, p: 2}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, u: 2, g: 1, x: 2}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, w: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, q: 2, y: 1, k: 2}, what is the expected number of times the pattern 's*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 3, r: 2, v: 1}. What is the expected number of occurrences of the pattern 'nv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, n: 2, r: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, k: 3, e: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, d: 4} to form a word, what is the expected number of matches of the pattern 'd.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, x: 2, f: 2}, what is the expected number of times the pattern 'x.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, o: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, a: 3, s: 1}. What is the expected number of occurrences of the pattern 'as*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, e: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'r.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, t: 2, x: 1, i: 1}, what is the expected number of times the pattern 'g.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, z: 1, i: 1, v: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'xv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, z: 1, r: 2, j: 1, f: 1}, what is the expected number of times the pattern 'r+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 4, e: 2}. What is the expected number of occurrences of the pattern 'e.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, m: 4}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, p: 1, z: 1, d: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'r*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, l: 2, b: 1, w: 1}. What is the expected number of occurrences of the pattern 'lw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, z: 2, t: 1, r: 1}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, b: 3}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, g: 1, q: 1, j: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, a: 2, b: 1}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 4, f: 2}. What is the expected number of occurrences of the pattern 'pf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, m: 2, d: 2}. What is the expected number of occurrences of the pattern 'p.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, p: 1, w: 1, k: 3} to form a word, what is the expected number of matches of the pattern 'fk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, b: 2, u: 2}. What is the expected number of occurrences of the pattern 'ui*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 4, j: 2} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, f: 1, o: 1, g: 3}. What is the expected number of occurrences of the pattern 'o*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, i: 1, v: 1, h: 1, f: 1}, what is the expected number of times the pattern 'j+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, u: 3, j: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'e*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, p: 1, b: 3} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, y: 4, l: 1}, what is the expected number of times the pattern 'y+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, b: 3}. What is the expected number of occurrences of the pattern 'eb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 4, t: 2}, what is the expected number of times the pattern 't+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, z: 2}. What is the expected number of occurrences of the pattern 'zu+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, c: 1, t: 1, m: 1, g: 2} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, p: 2, s: 2} to form a word, what is the expected number of matches of the pattern 'ep+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, e: 2, r: 1, g: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, n: 1, w: 1, m: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, n: 2, y: 3} to form a word, what is the expected number of matches of the pattern 'n.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, o: 1, t: 1, d: 1}, what is the expected number of times the pattern 'd.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, v: 2, r: 1, j: 2} to form a word, what is the expected number of matches of the pattern 'gv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, l: 2, i: 3}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, l: 3}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, d: 1, i: 1, u: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'dz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 4, j: 2} to form a word, what is the expected number of matches of the pattern 'j.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, w: 1, i: 1, l: 1, p: 1}. What is the expected number of occurrences of the pattern 'l.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, l: 4}, what is the expected number of times the pattern 'z.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, i: 3, k: 1}, what is the expected number of times the pattern 'k*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, i: 3}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, k: 5}. What is the expected number of occurrences of the pattern 'k.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, t: 1, o: 1, x: 2}. What is the expected number of occurrences of the pattern 'co+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, i: 3, k: 1} to form a word, what is the expected number of matches of the pattern 'si+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, c: 3} to form a word, what is the expected number of matches of the pattern 'd*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, v: 4, i: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, y: 1, x: 3} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, f: 1, u: 2, c: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'xu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, x: 2, z: 2, f: 1}, what is the expected number of times the pattern 'f*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, b: 1, i: 2, t: 2}. What is the expected number of occurrences of the pattern 's*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, q: 1, d: 2, h: 1, w: 1}, what is the expected number of times the pattern 'h.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, x: 1, u: 1, w: 1, t: 2}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, z: 1, w: 1, a: 2, t: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, y: 4}, what is the expected number of times the pattern 'cy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 3, j: 2, m: 1}, what is the expected number of times the pattern 'j.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, g: 2, h: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, t: 2, r: 1}, what is the expected number of times the pattern 't*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'o+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, u: 3, l: 2}, what is the expected number of times the pattern 'u+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'v.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, k: 1, r: 1, e: 2}, what is the expected number of times the pattern 'rk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 4, y: 2}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, g: 3}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, f: 2, e: 1, c: 1, b: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, l: 3}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, y: 4}, what is the expected number of times the pattern 'a*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, j: 3}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, k: 1, b: 2, p: 1, f: 1}. What is the expected number of occurrences of the pattern 'fb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, o: 2, b: 3} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, e: 2, x: 1, k: 1, t: 1} to form a word, what is the expected number of matches of the pattern 't+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'g*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, q: 1, a: 3, k: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, j: 3}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, e: 1, j: 1, m: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'j+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, v: 2, l: 1, t: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'r+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, i: 2, a: 1, j: 2}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 4, c: 2}. What is the expected number of occurrences of the pattern 'cb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, a: 1, n: 1, q: 2, m: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, a: 1, i: 1, n: 1, w: 1}, what is the expected number of times the pattern 'na+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, g: 3} to form a word, what is the expected number of matches of the pattern 'w.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, z: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'gm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, o: 2, x: 1, d: 1}, what is the expected number of times the pattern 'jo*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, s: 1, r: 2, c: 1}, what is the expected number of times the pattern 's*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, j: 1, u: 1, d: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'dr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, d: 3, e: 1}, what is the expected number of times the pattern 'd+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, j: 1, l: 1, n: 1, t: 2}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, d: 2, g: 1}, what is the expected number of times the pattern 'g+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, d: 2, j: 2}, what is the expected number of times the pattern 'dj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, h: 1, q: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'qx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, u: 1, q: 2, k: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'k+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, w: 1, g: 2, p: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'w.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, b: 1, o: 1, a: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, c: 1, p: 1, m: 2, w: 1}, what is the expected number of times the pattern 'wp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, i: 1, y: 1, v: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'y*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, a: 1, r: 1, p: 2, m: 1}. What is the expected number of occurrences of the pattern 'v*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, r: 2, o: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, q: 1, s: 2, u: 1, y: 1}. What is the expected number of occurrences of the pattern 'y*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, d: 1, h: 2, p: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'wh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, b: 1, o: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'yy*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, e: 2, a: 3} to form a word, what is the expected number of matches of the pattern 'ea+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, l: 2, c: 1, e: 1}. What is the expected number of occurrences of the pattern 'ez*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 4, e: 2}, what is the expected number of times the pattern 'ce*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, t: 3, j: 2} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, x: 3}. What is the expected number of occurrences of the pattern 'lx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, b: 3, t: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, i: 3}. What is the expected number of occurrences of the pattern 'i*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, l: 1, u: 2, y: 1, i: 1}, what is the expected number of times the pattern 'yl*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 4, h: 2}. What is the expected number of occurrences of the pattern 'jh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, k: 2, d: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, w: 1, a: 3} to form a word, what is the expected number of matches of the pattern 'wa*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, e: 4}. What is the expected number of occurrences of the pattern 'c*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, m: 2, o: 2}. What is the expected number of occurrences of the pattern 'm.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, b: 1, d: 1, u: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'u*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, r: 2, d: 1}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, l: 3} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, d: 3}, what is the expected number of times the pattern 'di+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, w: 1, e: 1, k: 3} to form a word, what is the expected number of matches of the pattern 'we+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, v: 1, g: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'n+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, m: 1, a: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, w: 1, l: 2, b: 2}. What is the expected number of occurrences of the pattern 'm*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, c: 2, b: 1, j: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'db*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, k: 2, y: 1, r: 1, q: 1}, what is the expected number of times the pattern 'k.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, g: 1, p: 1, z: 2, c: 1}, what is the expected number of times the pattern 'zg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, p: 1, z: 2, b: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'zz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, d: 1, x: 1, y: 1, k: 2}. What is the expected number of occurrences of the pattern 'xd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, b: 2, h: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'pz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, r: 2, w: 1, c: 1}. What is the expected number of occurrences of the pattern 'h.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, v: 2, q: 2, x: 1}, what is the expected number of times the pattern 'xq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 4, a: 1, o: 1}. What is the expected number of occurrences of the pattern 'o+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, q: 2, f: 2} to form a word, what is the expected number of matches of the pattern 'k.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, p: 1, e: 2, h: 1}, what is the expected number of times the pattern 'p.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, a: 4}, what is the expected number of times the pattern 'a*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 5, y: 1}. What is the expected number of occurrences of the pattern 'ny+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, t: 1, h: 1, k: 2}, what is the expected number of times the pattern 'kh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, m: 3, d: 1, a: 1}. What is the expected number of occurrences of the pattern 'dn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, l: 4} to form a word, what is the expected number of matches of the pattern 'l+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, p: 2, e: 1, s: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, n: 2, j: 1, u: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'u*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, f: 1, m: 1, b: 2, n: 1}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, t: 1, u: 1, y: 1, x: 2}, what is the expected number of times the pattern 'y.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, p: 1, g: 2, i: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'iq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 4, z: 2} to form a word, what is the expected number of matches of the pattern 'zk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, n: 2, i: 1, y: 2}. What is the expected number of occurrences of the pattern 'n+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, f: 2, a: 1, w: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, t: 1, r: 2, p: 1}. What is the expected number of occurrences of the pattern 'd.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, k: 1, g: 2, b: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, v: 1, q: 1, k: 2, o: 1}, what is the expected number of times the pattern 'o.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, l: 1, n: 1, r: 1, c: 1}. What is the expected number of occurrences of the pattern 'cl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, l: 2, i: 2, t: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, l: 1, t: 1, j: 1, c: 2}, what is the expected number of times the pattern 'c*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, b: 2, o: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'o*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, i: 1, t: 3, a: 1} to form a word, what is the expected number of matches of the pattern 't.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, f: 4} to form a word, what is the expected number of matches of the pattern 'f+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, z: 2, s: 3}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, q: 1, a: 1, o: 2}. What is the expected number of occurrences of the pattern 'a.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 4, k: 2} to form a word, what is the expected number of matches of the pattern 'kt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, w: 1, h: 1, p: 3} to form a word, what is the expected number of matches of the pattern 'p.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, e: 1, j: 1, k: 1, c: 2} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, m: 1, y: 1, w: 1, p: 2}. What is the expected number of occurrences of the pattern 'yp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, p: 4}. What is the expected number of occurrences of the pattern 'p.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, v: 3}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, o: 1, r: 1, y: 1, s: 2}. What is the expected number of occurrences of the pattern 's*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, t: 3, e: 1}, what is the expected number of times the pattern 'e*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, k: 5}. What is the expected number of occurrences of the pattern 'nk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, d: 4}, what is the expected number of times the pattern 'db+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, q: 1, o: 1, c: 2, a: 1}, what is the expected number of times the pattern 'w*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 4, p: 1, z: 1}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, h: 3, b: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'ii*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, f: 1, p: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'vf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, z: 1, c: 1, w: 2}, what is the expected number of times the pattern 'z.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, j: 2, h: 2, x: 1} to form a word, what is the expected number of matches of the pattern 'uh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, i: 1, k: 1, n: 1, u: 1}. What is the expected number of occurrences of the pattern 'k*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 4, b: 2}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, j: 1, f: 1, k: 2, i: 1}. What is the expected number of occurrences of the pattern 'j*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, z: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, p: 2, e: 1, a: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'e.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, b: 2, c: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, x: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'qx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, p: 1, e: 3, s: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, m: 2, f: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'st+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, f: 3, v: 1}. What is the expected number of occurrences of the pattern 'v*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, g: 1, x: 1, r: 1, m: 1}. What is the expected number of occurrences of the pattern 'm+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, i: 1, f: 3, d: 1}, what is the expected number of times the pattern 'i.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, b: 3}, what is the expected number of times the pattern 'wb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, q: 3, y: 2}. What is the expected number of occurrences of the pattern 'yd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'hc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, h: 1, g: 1, t: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'sh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, l: 1, k: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'x.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, u: 2, a: 1, r: 1, p: 1}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, x: 3, d: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 4, z: 2}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, q: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'aq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, u: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'ke*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, j: 1, m: 1, p: 2}, what is the expected number of times the pattern 'np*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, w: 1, b: 2, d: 1, z: 1}, what is the expected number of times the pattern 'll+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, d: 2, a: 2, n: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, s: 4} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, z: 1, x: 3}. What is the expected number of occurrences of the pattern 'e.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, o: 3, w: 2}, what is the expected number of times the pattern 'nw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 4, o: 2}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, z: 1, v: 2, y: 2}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, s: 2, b: 1, g: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'x+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, b: 2, x: 1, o: 1, m: 1}. What is the expected number of occurrences of the pattern 'm.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, i: 3}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, t: 2, v: 3} to form a word, what is the expected number of matches of the pattern 'vs+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, s: 2, m: 3} to form a word, what is the expected number of matches of the pattern 'm+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, g: 2, d: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'z.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, v: 1, k: 2, h: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'ka+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, u: 2, f: 1, k: 1}, what is the expected number of times the pattern 'dk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, f: 1, p: 1, q: 3} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, j: 2, w: 1}, what is the expected number of times the pattern 'e*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, l: 1, i: 1, p: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'ku*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, o: 4}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, y: 1, b: 1, c: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'q+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, n: 1, r: 2, w: 1}, what is the expected number of times the pattern 'w*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, h: 4} to form a word, what is the expected number of matches of the pattern 'w*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, e: 2, w: 1, a: 1, y: 1}. What is the expected number of occurrences of the pattern 'rw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, z: 2, o: 1, t: 2}. What is the expected number of occurrences of the pattern 'o*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, g: 1, d: 3}. What is the expected number of occurrences of the pattern 'ig*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, u: 1, p: 2, e: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, f: 2, g: 2} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, w: 1, a: 1, k: 2, h: 1}. What is the expected number of occurrences of the pattern 'a*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, r: 2, d: 2}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, v: 2, j: 1, o: 2}, what is the expected number of times the pattern 'o.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, s: 1, h: 2, v: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, s: 3, a: 1} to form a word, what is the expected number of matches of the pattern 'd+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, n: 1, f: 1, a: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'n+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, h: 3}, what is the expected number of times the pattern 'w*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, k: 2, a: 1, p: 2}, what is the expected number of times the pattern 'pk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, r: 4} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, p: 2, u: 1, z: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, h: 2, i: 3} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, g: 3, t: 2}, what is the expected number of times the pattern 't*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, z: 3, n: 2}, what is the expected number of times the pattern 'c+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, q: 3} to form a word, what is the expected number of matches of the pattern 'q+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, q: 1, z: 2, v: 1, d: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, m: 1, k: 1, l: 3}, what is the expected number of times the pattern 'lm+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, l: 1, m: 3, o: 1}, what is the expected number of times the pattern 't.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, v: 1, t: 2, w: 1, r: 1}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, f: 3, x: 1, j: 1}, what is the expected number of times the pattern 'mx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, i: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, b: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, y: 1, v: 1, g: 1, d: 2}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, o: 3}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, z: 3}, what is the expected number of times the pattern 'iz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, q: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'n*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, y: 3, u: 2} to form a word, what is the expected number of matches of the pattern 'u+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, u: 3}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 4, y: 2} to form a word, what is the expected number of matches of the pattern 'my*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, y: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, q: 1, a: 1, o: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'aq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, q: 2, s: 2} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, s: 1, a: 1, h: 1, l: 1}. What is the expected number of occurrences of the pattern 'as+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, y: 1, t: 4}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, r: 1, m: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'ds*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, m: 1, t: 2, c: 1, n: 1}, what is the expected number of times the pattern 'm.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, e: 3, s: 1}, what is the expected number of times the pattern 'es*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, g: 5}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, r: 2, n: 1, d: 1, v: 1}, what is the expected number of times the pattern 'r*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'v+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, z: 1, e: 2, i: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'i.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 3, v: 1, j: 1, r: 1}, what is the expected number of times the pattern 'r*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, u: 2, n: 3}, what is the expected number of times the pattern 'd.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, p: 3}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, i: 1, w: 3} to form a word, what is the expected number of matches of the pattern 'w.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, r: 2, y: 1, b: 2}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, d: 1, j: 1, r: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'dr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, v: 2, d: 1, h: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'vh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, n: 3}, what is the expected number of times the pattern 'z*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, c: 3} to form a word, what is the expected number of matches of the pattern 'vc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, b: 1, m: 3, o: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, t: 1, o: 1, a: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'o*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, d: 3}. What is the expected number of occurrences of the pattern 'c+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, v: 1, i: 4}. What is the expected number of occurrences of the pattern 'iv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, f: 3} to form a word, what is the expected number of matches of the pattern 'df*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, v: 2, h: 2}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, y: 2, b: 2}. What is the expected number of occurrences of the pattern 'n.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, o: 2, p: 1, h: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, l: 1, a: 1, b: 2, p: 1}. What is the expected number of occurrences of the pattern 'p.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, g: 2, b: 2, e: 1}. What is the expected number of occurrences of the pattern 'x*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, o: 1, q: 1, z: 1, f: 1}. What is the expected number of occurrences of the pattern 'fg*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, t: 2, d: 2, o: 1}. What is the expected number of occurrences of the pattern 'o.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, b: 3, m: 2}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, s: 3, u: 2} to form a word, what is the expected number of matches of the pattern 's*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, d: 2, e: 1, q: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'qe+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 4, v: 2}. What is the expected number of occurrences of the pattern 'vb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, c: 2, s: 2}, what is the expected number of times the pattern 's+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, a: 1, z: 1, b: 1}, what is the expected number of times the pattern 'j*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, s: 3}. What is the expected number of occurrences of the pattern 's+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 5, p: 1}. What is the expected number of occurrences of the pattern 'pc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, u: 1, n: 1, z: 2, m: 1}, what is the expected number of times the pattern 'wu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 4, l: 2}, what is the expected number of times the pattern 'pl*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, m: 2, c: 1, l: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, j: 4} to form a word, what is the expected number of matches of the pattern 'fj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, f: 2, n: 1, p: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'n+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, s: 3}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 5, f: 1}, what is the expected number of times the pattern 'zf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, q: 1, h: 1, b: 1, j: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, y: 4} to form a word, what is the expected number of matches of the pattern 'j*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, w: 1, u: 2, x: 1, v: 1}. What is the expected number of occurrences of the pattern 'd*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, y: 2, u: 2}. What is the expected number of occurrences of the pattern 'y*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, t: 2, x: 1, g: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, c: 2, x: 1, j: 1}, what is the expected number of times the pattern 'cx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, z: 2, d: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'i.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, r: 1, k: 4}. What is the expected number of occurrences of the pattern 'ok*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, p: 2, f: 1, z: 1, e: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, e: 4}. What is the expected number of occurrences of the pattern 'xe+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, p: 1, y: 3, x: 1}. What is the expected number of occurrences of the pattern 'y.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, f: 1, x: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'yf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, w: 2, h: 1, v: 1, s: 1}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, h: 1, w: 1, p: 2, a: 1}. What is the expected number of occurrences of the pattern 'ah+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, z: 3, x: 2}, what is the expected number of times the pattern 'vx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 4, x: 2}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, o: 2, a: 1, d: 1, x: 1}, what is the expected number of times the pattern 'o*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, m: 2, o: 2}, what is the expected number of times the pattern 'pm+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, c: 1, x: 1, l: 2, r: 1}, what is the expected number of times the pattern 'fr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 4, p: 2}. What is the expected number of occurrences of the pattern 'i*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, v: 3}, what is the expected number of times the pattern 'gv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, e: 2, n: 1, t: 1} to form a word, what is the expected number of matches of the pattern 't.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, r: 2, n: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'r*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, f: 2, j: 2}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, m: 2, u: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'ri+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, s: 1, y: 1, c: 2}. What is the expected number of occurrences of the pattern 'cy*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, j: 2, t: 1, r: 2}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, z: 5} to form a word, what is the expected number of matches of the pattern 'z.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, g: 3, o: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'o+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, t: 2, e: 3} to form a word, what is the expected number of matches of the pattern 't*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, i: 3, y: 1}, what is the expected number of times the pattern 'di*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, z: 1, t: 2, r: 1, b: 1}. What is the expected number of occurrences of the pattern 'r*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, b: 1, o: 3}. What is the expected number of occurrences of the pattern 'p*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, t: 2, e: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'n.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, p: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'px+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, q: 1, s: 1, k: 2, p: 1}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, f: 2, u: 2}. What is the expected number of occurrences of the pattern 'f+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, y: 1, d: 1, a: 2, c: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, r: 2, v: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'vo+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, h: 1, a: 2, o: 1}, what is the expected number of times the pattern 'o+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, n: 1, a: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'n.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, c: 1, m: 1, z: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, v: 2, d: 1, y: 1, s: 1}. What is the expected number of occurrences of the pattern 'dy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, n: 1, o: 1, l: 1, m: 1}. What is the expected number of occurrences of the pattern 'mm+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 4, y: 2} to form a word, what is the expected number of matches of the pattern 'q*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, u: 1, v: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'e.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, l: 4, m: 1}. What is the expected number of occurrences of the pattern 'm+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, l: 2, g: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'a*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, x: 1, y: 3}, what is the expected number of times the pattern 'y*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, m: 2, z: 1, n: 2}, what is the expected number of times the pattern 'hm+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, b: 1, d: 1, u: 2, s: 1}. What is the expected number of occurrences of the pattern 'u+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, i: 1, w: 2, k: 1}, what is the expected number of times the pattern 'k+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, d: 2, u: 1, x: 1, a: 1}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, t: 2, e: 1, q: 1, f: 1}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, g: 3}, what is the expected number of times the pattern 'gu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, i: 2, q: 3}, what is the expected number of times the pattern 'iq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 4, k: 2} to form a word, what is the expected number of matches of the pattern 'uk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, m: 1, b: 1, o: 2}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, n: 1, z: 3}, what is the expected number of times the pattern 'n+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, p: 2, w: 2}. What is the expected number of occurrences of the pattern 'f+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, a: 5} to form a word, what is the expected number of matches of the pattern 'a.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, a: 2, s: 1, c: 2}, what is the expected number of times the pattern 'a.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, y: 2, f: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'a+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, j: 1, a: 4} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, g: 1, v: 3}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, b: 2, i: 1, q: 2}, what is the expected number of times the pattern 'iq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, x: 1, k: 1, g: 1, t: 2}. What is the expected number of occurrences of the pattern 'k*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, u: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'nu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, s: 2, b: 1, k: 1}, what is the expected number of times the pattern 'k+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, s: 3}. What is the expected number of occurrences of the pattern 'f*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, d: 1, u: 3} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, h: 1, z: 1, c: 1, o: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, m: 2, k: 3} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, m: 1, i: 3}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, d: 1, g: 2, b: 2}, what is the expected number of times the pattern 'd.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, r: 3}. What is the expected number of occurrences of the pattern 'rg+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, h: 2, d: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'dr+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, n: 3, e: 1, z: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, d: 1, i: 2, a: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'u+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, y: 2, b: 1}. What is the expected number of occurrences of the pattern 'y+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, x: 1, b: 3}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 4, n: 2}, what is the expected number of times the pattern 'o+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, b: 2, s: 1, l: 1}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, n: 2, u: 1, w: 1, r: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, l: 2, r: 1, a: 2}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, c: 2, g: 1}. What is the expected number of occurrences of the pattern 'gt+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, h: 4}. What is the expected number of occurrences of the pattern 'c.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, b: 3, o: 2} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, h: 3}. What is the expected number of occurrences of the pattern 'ht+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, z: 3}, what is the expected number of times the pattern 'zb+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, u: 1, a: 1, m: 1, i: 2}. What is the expected number of occurrences of the pattern 'ia+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, o: 1, e: 2, j: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, l: 2, g: 1, r: 2}, what is the expected number of times the pattern 'z*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, u: 1, p: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, p: 3, d: 1}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, m: 3, t: 1} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, d: 1, v: 2}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, v: 2, a: 1, m: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, w: 2, b: 1, q: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 5, n: 1}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, p: 3, m: 2} to form a word, what is the expected number of matches of the pattern 'm*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, s: 3, a: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, b: 1, n: 2, z: 2}. What is the expected number of occurrences of the pattern 'u.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, u: 2, t: 1, w: 1, j: 1}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, z: 2, e: 1, o: 1, y: 1}. What is the expected number of occurrences of the pattern 'e*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, d: 1, o: 2, b: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, u: 1, c: 2, d: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, o: 1, m: 2, j: 1, r: 1}, what is the expected number of times the pattern 'wo*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, i: 2, m: 1} to form a word, what is the expected number of matches of the pattern 'iq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, v: 1, m: 2}, what is the expected number of times the pattern 'm*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 4, z: 2} to form a word, what is the expected number of matches of the pattern 'z*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, c: 1, h: 2, o: 1, i: 1}, what is the expected number of times the pattern 'i*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, o: 1, n: 1, d: 2, s: 1}. What is the expected number of occurrences of the pattern 'qn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 4, j: 2} to form a word, what is the expected number of matches of the pattern 'k+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, l: 2, a: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'sj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, e: 2, d: 2, k: 1}. What is the expected number of occurrences of the pattern 'ek*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 4, k: 2} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, w: 3} to form a word, what is the expected number of matches of the pattern 'w*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, y: 3}. What is the expected number of occurrences of the pattern 'yl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, a: 1, k: 1, x: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, j: 2, n: 3}, what is the expected number of times the pattern 'a+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, i: 1, q: 3, z: 1} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, s: 1, d: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'r*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, u: 3, m: 2}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, y: 2, s: 1, u: 2}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 4, d: 2}. What is the expected number of occurrences of the pattern 'd.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, h: 3, l: 2} to form a word, what is the expected number of matches of the pattern 'hl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, h: 1, c: 1, s: 2, y: 1}. What is the expected number of occurrences of the pattern 'hy*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, m: 1, z: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'zn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, k: 1, z: 1, u: 1, n: 2}. What is the expected number of occurrences of the pattern 'ck*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, m: 1, l: 1, a: 2, q: 1}, what is the expected number of times the pattern 'z*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, n: 1, h: 2, i: 1, b: 1}. What is the expected number of occurrences of the pattern 'e*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, i: 1, v: 3, z: 1}, what is the expected number of times the pattern 'vz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, j: 1, f: 3}, what is the expected number of times the pattern 'fj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 4, z: 2}. What is the expected number of occurrences of the pattern 'pz*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, g: 2, t: 2, y: 1} to form a word, what is the expected number of matches of the pattern 't.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 4, d: 2} to form a word, what is the expected number of matches of the pattern 'ad+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, o: 2, c: 3}, what is the expected number of times the pattern 'oc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, t: 2, l: 1, y: 1}. What is the expected number of occurrences of the pattern 't*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 5, d: 1} to form a word, what is the expected number of matches of the pattern 'zd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 3, w: 1, i: 1, f: 1}. What is the expected number of occurrences of the pattern 'w+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, c: 1, f: 2, e: 2}, what is the expected number of times the pattern 'fe+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, q: 3} to form a word, what is the expected number of matches of the pattern 'wq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, a: 1, b: 3} to form a word, what is the expected number of matches of the pattern 'a*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, d: 1, o: 1, r: 1, j: 1} to form a word, what is the expected number of matches of the pattern 's+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, o: 3}, what is the expected number of times the pattern 'o.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, j: 2, k: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'k+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, y: 1, m: 2, w: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, p: 1, j: 2, r: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, b: 2, e: 2}, what is the expected number of times the pattern 'eb+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, y: 3}. What is the expected number of occurrences of the pattern 'y.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, a: 3, e: 2} to form a word, what is the expected number of matches of the pattern 'ev+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, d: 3, f: 1}, what is the expected number of times the pattern 'fd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, b: 2, t: 1, u: 1, p: 1}. What is the expected number of occurrences of the pattern 'tb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, r: 1, i: 2, t: 1} to form a word, what is the expected number of matches of the pattern 't*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, d: 1, q: 1, z: 2}, what is the expected number of times the pattern 'zi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, f: 1, w: 2, t: 1, u: 1}, what is the expected number of times the pattern 'w*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, y: 1, m: 1, q: 1}. What is the expected number of occurrences of the pattern 'y+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, t: 1, l: 2, y: 1, u: 1}. What is the expected number of occurrences of the pattern 't+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, m: 1, b: 1, j: 2}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, w: 1, l: 1, d: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'l*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, u: 1, y: 2, x: 1, g: 1}. What is the expected number of occurrences of the pattern 'g.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 4, j: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, q: 1, t: 1, y: 1, a: 1}. What is the expected number of occurrences of the pattern 't+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, k: 3}. What is the expected number of occurrences of the pattern 'sk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, k: 1, w: 1, f: 1, i: 1}, what is the expected number of times the pattern 'rf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, y: 3}, what is the expected number of times the pattern 'y*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, j: 2, u: 1, l: 1}. What is the expected number of occurrences of the pattern 'lu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, l: 3}. What is the expected number of occurrences of the pattern 'f+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, r: 2, p: 2}. What is the expected number of occurrences of the pattern 'r.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, z: 2, r: 1, e: 1, o: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, f: 1, o: 1, n: 2, x: 1}, what is the expected number of times the pattern 'no+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, f: 5} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, m: 3}. What is the expected number of occurrences of the pattern 'mx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, z: 2, y: 1, x: 1}, what is the expected number of times the pattern 'zy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, f: 3, u: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, z: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'zl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, n: 1, v: 1, f: 2, j: 1}. What is the expected number of occurrences of the pattern 'vf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, e: 1, n: 1, a: 1, k: 2}, what is the expected number of times the pattern 'ke+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, r: 2, g: 2}, what is the expected number of times the pattern 'gw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, y: 2, c: 2}, what is the expected number of times the pattern 'w+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 4, t: 2}, what is the expected number of times the pattern 'a+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, s: 2, f: 2, c: 1} to form a word, what is the expected number of matches of the pattern 'f*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, j: 3} to form a word, what is the expected number of matches of the pattern 'u*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, n: 1, e: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'v.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, w: 3}, what is the expected number of times the pattern 'vw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, u: 1, w: 3, z: 1}. What is the expected number of occurrences of the pattern 'zw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, a: 2, t: 3} to form a word, what is the expected number of matches of the pattern 'fa+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, a: 2, y: 1, f: 2}, what is the expected number of times the pattern 'ya*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, q: 3}. What is the expected number of occurrences of the pattern 'q+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, b: 1, n: 3} to form a word, what is the expected number of matches of the pattern 'w.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, n: 1, t: 4} to form a word, what is the expected number of matches of the pattern 'n.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, q: 3} to form a word, what is the expected number of matches of the pattern 's*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, t: 1, f: 1, e: 2, m: 1}, what is the expected number of times the pattern 'tu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, t: 1, b: 3} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, d: 3} to form a word, what is the expected number of matches of the pattern 'id+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, x: 2, k: 1}. What is the expected number of occurrences of the pattern 'ax*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, w: 2, j: 1, o: 1, b: 1}, what is the expected number of times the pattern 'w*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, e: 1, n: 4}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, q: 3}, what is the expected number of times the pattern 'q*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, e: 1, a: 4}. What is the expected number of occurrences of the pattern 'v*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, p: 4}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, d: 2, i: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, k: 2, z: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'gw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, g: 1, c: 3}. What is the expected number of occurrences of the pattern 'gw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, b: 1, r: 3}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, g: 2, v: 1, c: 1}. What is the expected number of occurrences of the pattern 'q*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 4, s: 2}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, f: 4} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, g: 1, p: 1, i: 2, f: 1}, what is the expected number of times the pattern 'gf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, b: 1, a: 2, n: 1, s: 1}. What is the expected number of occurrences of the pattern 'ss*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, y: 1, n: 1, l: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, h: 1, n: 1, k: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, k: 1, t: 1, i: 1, a: 2}. What is the expected number of occurrences of the pattern 'ai*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, f: 4} to form a word, what is the expected number of matches of the pattern 'fy*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, w: 2, d: 1, e: 1, m: 1}. What is the expected number of occurrences of the pattern 'n.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, s: 3}, what is the expected number of times the pattern 's*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, c: 3, g: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'g+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, r: 1, k: 3}, what is the expected number of times the pattern 'r+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, i: 2, c: 1, f: 1, g: 1}. What is the expected number of occurrences of the pattern 'if*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, s: 1, g: 2, x: 1, j: 1}. What is the expected number of occurrences of the pattern 'x+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, i: 1, p: 2, y: 1, f: 1}. What is the expected number of occurrences of the pattern 'yp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, p: 2, j: 1, l: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'l.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, i: 1, d: 1, y: 1}, what is the expected number of times the pattern 'i*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, s: 1, h: 2, m: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, p: 4}, what is the expected number of times the pattern 'p+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, f: 3, z: 2}, what is the expected number of times the pattern 'z*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, z: 3} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, m: 3, z: 2} to form a word, what is the expected number of matches of the pattern 'tm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, c: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'zr+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, v: 1, m: 2, h: 1}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, b: 1, j: 1, y: 2, n: 1}, what is the expected number of times the pattern 'c*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, q: 3}, what is the expected number of times the pattern 'k*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, d: 1, o: 3, r: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, r: 1, o: 1, d: 3}. What is the expected number of occurrences of the pattern 'r*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, k: 3, h: 2} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'h.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, c: 3} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, a: 1, l: 1, i: 1, q: 1}. What is the expected number of occurrences of the pattern 'ja*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 4, l: 2}. What is the expected number of occurrences of the pattern 'yl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, e: 3, m: 2}. What is the expected number of occurrences of the pattern 'l*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, a: 1, m: 1, b: 3} to form a word, what is the expected number of matches of the pattern 'a*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, d: 3}, what is the expected number of times the pattern 'de*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 5, n: 1}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, r: 3, z: 2}. What is the expected number of occurrences of the pattern 'z.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, v: 1, t: 1, z: 2, x: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, e: 2, r: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, r: 2, q: 2}. What is the expected number of occurrences of the pattern 'qr+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, y: 2, w: 1, k: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, o: 1, x: 1, n: 3}. What is the expected number of occurrences of the pattern 'o.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, i: 1, t: 3, r: 1} to form a word, what is the expected number of matches of the pattern 'p.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 3, h: 3}. What is the expected number of occurrences of the pattern 'n*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 4, s: 2}. What is the expected number of occurrences of the pattern 'y*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, a: 5}, what is the expected number of times the pattern 'a+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, l: 2, z: 2}. What is the expected number of occurrences of the pattern 'z+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, s: 4}. What is the expected number of occurrences of the pattern 'y*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, u: 2, t: 1, b: 1, k: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, s: 1, i: 3}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, g: 5} to form a word, what is the expected number of matches of the pattern 'g+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, y: 1, j: 2}. What is the expected number of occurrences of the pattern 'j+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 5, d: 1} to form a word, what is the expected number of matches of the pattern 'd.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, n: 2, l: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, c: 2, b: 2}. What is the expected number of occurrences of the pattern 'db+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, w: 1, u: 3}, what is the expected number of times the pattern 'n.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, n: 1, a: 2, k: 2}, what is the expected number of times the pattern 'n.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, x: 1, o: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, t: 2, o: 1, h: 2}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, q: 1, d: 1, n: 1, h: 1}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, i: 2, n: 1, h: 2}, what is the expected number of times the pattern 'na*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, s: 4}. What is the expected number of occurrences of the pattern 's.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, c: 1, a: 1, v: 1, y: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, t: 1, q: 3}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 4, f: 2}, what is the expected number of times the pattern 'f*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, e: 1, d: 2, n: 1, m: 1}. What is the expected number of occurrences of the pattern 'e*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, l: 1, b: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'oo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, j: 2, m: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, n: 2, r: 2} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, l: 1, k: 2, b: 2}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, l: 2, d: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, a: 1, h: 3, c: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, l: 3}. What is the expected number of occurrences of the pattern 'lx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, i: 4}, what is the expected number of times the pattern 'ie*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'x+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, e: 1, t: 1, g: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'wt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, u: 4}. What is the expected number of occurrences of the pattern 'uj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 3, d: 3}, what is the expected number of times the pattern 'ad+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, k: 2, j: 1, r: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'r.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, c: 3} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, t: 1, b: 3, x: 1}, what is the expected number of times the pattern 'xx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, j: 4}. What is the expected number of occurrences of the pattern 'jy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 4, q: 2}, what is the expected number of times the pattern 'o.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, u: 1, i: 1, l: 1}, what is the expected number of times the pattern 'ji+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, y: 2, j: 2} to form a word, what is the expected number of matches of the pattern 'y.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, y: 2, v: 2, h: 1} to form a word, what is the expected number of matches of the pattern 'h+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, t: 1, f: 2, a: 1}. What is the expected number of occurrences of the pattern 'tf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, s: 1, k: 1, a: 1, g: 2}, what is the expected number of times the pattern 'k*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, h: 1, r: 4} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, g: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, t: 4} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 4, j: 2}. What is the expected number of occurrences of the pattern 'ji+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 4, i: 2} to form a word, what is the expected number of matches of the pattern 'k+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, g: 2, v: 1}, what is the expected number of times the pattern 'vg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, n: 1, l: 1, s: 1, d: 1}. What is the expected number of occurrences of the pattern 'l+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, h: 2, b: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'wa*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, e: 1, m: 1, u: 1, w: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, q: 1, p: 2, x: 1, e: 1}, what is the expected number of times the pattern 'k*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, c: 2, j: 2}. What is the expected number of occurrences of the pattern 'jc+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 4, q: 2}, what is the expected number of times the pattern 'lq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, z: 2, t: 2}, what is the expected number of times the pattern 't+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, l: 2, g: 2}, what is the expected number of times the pattern 'l*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, p: 3, u: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, p: 4}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, j: 1, g: 1, t: 1, u: 2}, what is the expected number of times the pattern 'gr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, t: 4}. What is the expected number of occurrences of the pattern 'et*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, v: 2, a: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, j: 3}, what is the expected number of times the pattern 'j+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, k: 3}. What is the expected number of occurrences of the pattern 'k*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, l: 4} to form a word, what is the expected number of matches of the pattern 'w.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, z: 2, y: 1, i: 1}, what is the expected number of times the pattern 'i+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, l: 3, i: 2}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, e: 2, i: 3} to form a word, what is the expected number of matches of the pattern 'z*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, h: 2, y: 1, w: 1, n: 1}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, a: 3}. What is the expected number of occurrences of the pattern 'o+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, d: 5}. What is the expected number of occurrences of the pattern 'd.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, y: 2, e: 3} to form a word, what is the expected number of matches of the pattern 'ye*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, d: 1, b: 2}. What is the expected number of occurrences of the pattern 'd*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, a: 2, l: 1, h: 1, y: 1}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, b: 1, v: 1, y: 2}. What is the expected number of occurrences of the pattern 'c+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, x: 3}, what is the expected number of times the pattern 'xp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, z: 4}. What is the expected number of occurrences of the pattern 'zv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, c: 3, b: 1} to form a word, what is the expected number of matches of the pattern 'yy+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, s: 2, r: 2}. What is the expected number of occurrences of the pattern 'r*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, e: 4} to form a word, what is the expected number of matches of the pattern 'e+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, m: 1, u: 1, h: 3} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 4, x: 2} to form a word, what is the expected number of matches of the pattern 'lx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, g: 1, a: 2, z: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'av+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, k: 2, q: 2} to form a word, what is the expected number of matches of the pattern 'k+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, g: 1, m: 1, p: 1, c: 2}. What is the expected number of occurrences of the pattern 'p*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, u: 4} to form a word, what is the expected number of matches of the pattern 'u.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, i: 3, r: 1, j: 1}, what is the expected number of times the pattern 'i+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, j: 1, h: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'c.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, f: 5}, what is the expected number of times the pattern 'j*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, o: 3}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, h: 2, t: 1, d: 1}, what is the expected number of times the pattern 'h*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, a: 3}, what is the expected number of times the pattern 'aa+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, t: 1, s: 1, c: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, j: 4} to form a word, what is the expected number of matches of the pattern 'm+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 4, w: 2}. What is the expected number of occurrences of the pattern 'w*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, m: 3, x: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'x+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, c: 3}. What is the expected number of occurrences of the pattern 'wc+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 4, t: 2}. What is the expected number of occurrences of the pattern 'y.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, s: 1, f: 1, g: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, z: 3} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, r: 2, k: 2}. What is the expected number of occurrences of the pattern 'r*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, e: 1, q: 1, m: 1, g: 1}. What is the expected number of occurrences of the pattern 't.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, x: 1, m: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'tm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, x: 2, t: 2, k: 1}, what is the expected number of times the pattern 'kt+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, p: 2, d: 1, q: 2}. What is the expected number of occurrences of the pattern 'd+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, b: 2, o: 2}, what is the expected number of times the pattern 'qq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, z: 1, n: 1, b: 1, v: 1} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, r: 1, e: 3, w: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, r: 3}. What is the expected number of occurrences of the pattern 'r*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, t: 2, g: 1, a: 1, m: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, u: 3, c: 2}. What is the expected number of occurrences of the pattern 'u.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 4, n: 2}, what is the expected number of times the pattern 'd*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, t: 1, b: 1, f: 1, p: 1}. What is the expected number of occurrences of the pattern 'fb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, b: 4}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, x: 3}. What is the expected number of occurrences of the pattern 'x+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, s: 4}, what is the expected number of times the pattern 's+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 3, h: 1, o: 2}, what is the expected number of times the pattern 's+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, u: 3, z: 1}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, j: 1, o: 1, b: 2}, what is the expected number of times the pattern 'o*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, j: 2, d: 2, s: 1}. What is the expected number of occurrences of the pattern 'as*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, y: 4}, what is the expected number of times the pattern 'g+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, n: 1, d: 1, s: 2, h: 1}, what is the expected number of times the pattern 'h+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, e: 1, t: 3}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, v: 1, n: 2, x: 2}. What is the expected number of occurrences of the pattern 'x+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, j: 1, t: 2, f: 1} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, m: 2, h: 2, r: 1}, what is the expected number of times the pattern 'a+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, y: 3}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, j: 1, k: 1, q: 1, t: 2}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, r: 1, s: 1, e: 1, b: 2}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, i: 2, b: 2, a: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, f: 2, d: 1, c: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'af+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, a: 2, k: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, i: 1, k: 4}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, y: 1, m: 4}, what is the expected number of times the pattern 'm+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, u: 1, p: 1, x: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'r*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, c: 2, v: 1, w: 1, j: 1}, what is the expected number of times the pattern 'wc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, z: 2, s: 1, t: 1, l: 1}, what is the expected number of times the pattern 't+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, b: 1, r: 1, g: 2, t: 1} to form a word, what is the expected number of matches of the pattern 'kg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, o: 2, r: 1, b: 1, f: 1}. What is the expected number of occurrences of the pattern 'r+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, w: 3, r: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, h: 1, z: 1, y: 2, f: 1}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, n: 1, l: 2, s: 1}, what is the expected number of times the pattern 'lx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, h: 5}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, z: 1, g: 1, k: 1, f: 1}. What is the expected number of occurrences of the pattern 'f*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, q: 2, n: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'nx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, f: 1, p: 1, l: 2}, what is the expected number of times the pattern 'f+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, k: 2, s: 2} to form a word, what is the expected number of matches of the pattern 'e+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, g: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'gl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, o: 1, w: 2, a: 1, n: 1}, what is the expected number of times the pattern 'n+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, i: 5} to form a word, what is the expected number of matches of the pattern 'ti+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, d: 1, e: 1, p: 1, g: 2}, what is the expected number of times the pattern 'g*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, u: 2, z: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'g+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, c: 4, r: 1} to form a word, what is the expected number of matches of the pattern 'c.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, p: 1, a: 2, r: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'r.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, o: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'no*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, v: 4, h: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, c: 1, y: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'c.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, h: 2, q: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, u: 1, n: 2, b: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, g: 1, b: 1, z: 3}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, e: 1, t: 1, a: 1, w: 2}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, k: 3}. What is the expected number of occurrences of the pattern 'k.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'xu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, d: 4}. What is the expected number of occurrences of the pattern 'p+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, k: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'k.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, y: 2, r: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'r*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, h: 2, q: 1, a: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'q.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, y: 2, h: 2, p: 1}. What is the expected number of occurrences of the pattern 'p+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 4, r: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'k*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, w: 1, m: 1, p: 1, l: 2}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, v: 3}. What is the expected number of occurrences of the pattern 'vm*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, i: 3}, what is the expected number of times the pattern 'q+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, e: 4} to form a word, what is the expected number of matches of the pattern 'xe*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, b: 1, p: 1, q: 3} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, j: 2, x: 2, o: 1}, what is the expected number of times the pattern 'o+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, y: 1, x: 1, w: 1, u: 2}. What is the expected number of occurrences of the pattern 'y*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, s: 1, x: 2, k: 1}. What is the expected number of occurrences of the pattern 'ak+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, c: 3} to form a word, what is the expected number of matches of the pattern 'c.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, v: 3}. What is the expected number of occurrences of the pattern 'z+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, x: 1, i: 1, w: 1, k: 2}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, b: 1, f: 1, c: 1, g: 1}. What is the expected number of occurrences of the pattern 'fl+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, d: 2, b: 2, j: 1}, what is the expected number of times the pattern 'd.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, i: 4} to form a word, what is the expected number of matches of the pattern 'ki*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, s: 1, m: 3} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, y: 2, s: 1, z: 1, u: 1}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, g: 2, d: 2}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, c: 1, z: 2, m: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'y+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, n: 1, x: 2, c: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'h+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, s: 1, a: 1, i: 1, g: 2}. What is the expected number of occurrences of the pattern 'gi+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, s: 1, k: 1, x: 1, o: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, q: 2, s: 2} to form a word, what is the expected number of matches of the pattern 'js*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, i: 3, p: 1, l: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, n: 1, a: 2}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, i: 1, l: 2, a: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 4, q: 2}, what is the expected number of times the pattern 'f*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, k: 1, z: 1, e: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'er*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 4, z: 2}, what is the expected number of times the pattern 'u*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, w: 2, f: 1, t: 1}, what is the expected number of times the pattern 'f+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, f: 3} to form a word, what is the expected number of matches of the pattern 'fp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, f: 1, h: 1, p: 1, b: 1}, what is the expected number of times the pattern 'f+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, n: 2, d: 2}. What is the expected number of occurrences of the pattern 'j+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, r: 2, n: 1, y: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'cr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, u: 1, k: 1, o: 1, v: 2}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, b: 1, f: 1, g: 3} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, n: 1, q: 2, s: 2}, what is the expected number of times the pattern 'y*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, n: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'n.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, q: 1, z: 2, c: 1, m: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, m: 1, e: 2, d: 1}. What is the expected number of occurrences of the pattern 'e.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, g: 1, u: 1, j: 1, w: 2}, what is the expected number of times the pattern 'wg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, p: 3, s: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, i: 2, j: 2}, what is the expected number of times the pattern 'i.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, o: 2, g: 3}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, n: 1, p: 2, i: 1}. What is the expected number of occurrences of the pattern 'pn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, u: 2, t: 1, w: 1, z: 1}. What is the expected number of occurrences of the pattern 'ru*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, x: 2, e: 3} to form a word, what is the expected number of matches of the pattern 'x+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, s: 1, c: 2, x: 2}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 4, l: 2} to form a word, what is the expected number of matches of the pattern 'l+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, a: 2, h: 2}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, f: 3} to form a word, what is the expected number of matches of the pattern 's+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, w: 2, u: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'r*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, k: 1, h: 3}, what is the expected number of times the pattern 'n.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, o: 4, q: 1}, what is the expected number of times the pattern 'on+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, h: 2, y: 1, s: 1, j: 1}, what is the expected number of times the pattern 'y+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, g: 3}. What is the expected number of occurrences of the pattern 'a*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, c: 5}. What is the expected number of occurrences of the pattern 'dc+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 4, j: 2}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, d: 1, o: 3, l: 1}. What is the expected number of occurrences of the pattern 'od*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, o: 3, y: 1, v: 1}, what is the expected number of times the pattern 'do+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, m: 3} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, x: 2, c: 1}. What is the expected number of occurrences of the pattern 'cj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, w: 1, q: 1, n: 1, d: 1}. What is the expected number of occurrences of the pattern 'w*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, f: 4}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, r: 3}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 4, n: 2}, what is the expected number of times the pattern 'j*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, d: 3} to form a word, what is the expected number of matches of the pattern 'ds*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, q: 2, k: 2}. What is the expected number of occurrences of the pattern 'uk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, i: 2, t: 2, b: 1}, what is the expected number of times the pattern 'pb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, h: 4}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, q: 1, w: 2, s: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'w+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, b: 1, t: 1, k: 2}. What is the expected number of occurrences of the pattern 'j+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, p: 2, j: 1, a: 1, g: 1}, what is the expected number of times the pattern 'a+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, x: 2, d: 1, n: 1}. What is the expected number of occurrences of the pattern 'x+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, y: 1, h: 1, m: 2, j: 1}, what is the expected number of times the pattern 'm.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, x: 1, f: 1, a: 2, c: 1} to form a word, what is the expected number of matches of the pattern 'x.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, l: 3, m: 1, u: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, u: 1, t: 1, z: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'z.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, j: 4}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, u: 5} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, p: 4} to form a word, what is the expected number of matches of the pattern 'm*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, e: 3, t: 1}, what is the expected number of times the pattern 'k.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, a: 2, e: 2}. What is the expected number of occurrences of the pattern 'h+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, a: 3, n: 1}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, q: 2, k: 1, d: 2}, what is the expected number of times the pattern 'p.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 4, a: 2}. What is the expected number of occurrences of the pattern 'l*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, h: 2, y: 2}. What is the expected number of occurrences of the pattern 'f*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, f: 3}, what is the expected number of times the pattern 'f+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, d: 1, l: 1, p: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, n: 2, t: 2} to form a word, what is the expected number of matches of the pattern 'n.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, v: 3}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, r: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'r.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, p: 1, q: 1, a: 1, c: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 4, w: 1, f: 1}. What is the expected number of occurrences of the pattern 'f.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 4, b: 2}, what is the expected number of times the pattern 'q*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, v: 1, t: 2, w: 1, h: 1}. What is the expected number of occurrences of the pattern 't+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, b: 1, x: 3, i: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, d: 1, u: 2, w: 2}. What is the expected number of occurrences of the pattern 'dg*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, i: 4}, what is the expected number of times the pattern 'i+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, b: 1, o: 1, k: 2}. What is the expected number of occurrences of the pattern 'km*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, d: 1, f: 3}, what is the expected number of times the pattern 'ud+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, k: 3, x: 1}, what is the expected number of times the pattern 'n*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, x: 5}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, p: 1, k: 1, c: 1, h: 1}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, i: 2, g: 1, x: 1}. What is the expected number of occurrences of the pattern 'i*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, w: 1, z: 2, y: 1, x: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, z: 2, b: 1}. What is the expected number of occurrences of the pattern 'mb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, h: 1, z: 1, o: 2}. What is the expected number of occurrences of the pattern 'o.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, m: 1, p: 2, d: 2}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, e: 1, y: 3, j: 1}, what is the expected number of times the pattern 'j+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, j: 2, v: 2, h: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, r: 1, j: 2, m: 2}. What is the expected number of occurrences of the pattern 'j+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, d: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, b: 3, g: 2} to form a word, what is the expected number of matches of the pattern 'g.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, t: 2, f: 1, z: 1}, what is the expected number of times the pattern 'af+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 5, s: 1} to form a word, what is the expected number of matches of the pattern 'xs*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, n: 4, e: 1}. What is the expected number of occurrences of the pattern 'e*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, v: 2, d: 1, i: 1, f: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, f: 2, y: 2, i: 1}. What is the expected number of occurrences of the pattern 'f+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, h: 3}. What is the expected number of occurrences of the pattern 'hx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, n: 4} to form a word, what is the expected number of matches of the pattern 'nr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, l: 1, y: 3}. What is the expected number of occurrences of the pattern 'f*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, j: 1, k: 1, t: 1, o: 1}. What is the expected number of occurrences of the pattern 'tc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, r: 2, p: 1, m: 2}. What is the expected number of occurrences of the pattern 'r.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, o: 2, u: 2}, what is the expected number of times the pattern 'eu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, l: 2, u: 3}, what is the expected number of times the pattern 'p*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, b: 2, h: 1, t: 1}, what is the expected number of times the pattern 'hh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, x: 2, l: 1}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, v: 1, f: 1, m: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'v.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, p: 1, f: 2, y: 1, q: 1}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, i: 1, h: 1, q: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'fv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, k: 1, t: 2, z: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, j: 1, x: 1, z: 1, i: 1}, what is the expected number of times the pattern 'j*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, j: 1, u: 1, h: 2, b: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, u: 1, t: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'u*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, l: 1, u: 3}. What is the expected number of occurrences of the pattern 'f*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, s: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'lb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 4, e: 2} to form a word, what is the expected number of matches of the pattern 'de*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, d: 2, b: 1, w: 1}, what is the expected number of times the pattern 'f+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, f: 2, w: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, o: 3}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, i: 1, r: 1, k: 2, l: 1}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, i: 1, y: 2}, what is the expected number of times the pattern 'qi+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, y: 1, z: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'y*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, r: 3, a: 1, k: 1}. What is the expected number of occurrences of the pattern 'ra*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, f: 2, c: 1, v: 2}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, o: 1, v: 2, u: 1, b: 1}. What is the expected number of occurrences of the pattern 'u.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, w: 2, l: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'lb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, y: 1, a: 1, i: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'd+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, i: 1, h: 2, b: 1, z: 1}. What is the expected number of occurrences of the pattern 'hb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, p: 2, t: 1, w: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 5, s: 1}. What is the expected number of occurrences of the pattern 's*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, z: 1, b: 1, x: 2, n: 1}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, n: 1, u: 1, m: 2}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, j: 1, r: 3} to form a word, what is the expected number of matches of the pattern 'rj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 4, u: 2} to form a word, what is the expected number of matches of the pattern 'uy+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, p: 2, k: 3} to form a word, what is the expected number of matches of the pattern 'kp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, i: 1, m: 1, e: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'e*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, r: 1, p: 1, h: 1, o: 2}. What is the expected number of occurrences of the pattern 'o.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, r: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'ga+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, d: 4}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, c: 1, u: 1, g: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'uw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, y: 1, h: 1, q: 2, i: 1}. What is the expected number of occurrences of the pattern 'q.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, q: 2, t: 1}. What is the expected number of occurrences of the pattern 'qv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, i: 3}. What is the expected number of occurrences of the pattern 'i+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, p: 4} to form a word, what is the expected number of matches of the pattern 'p+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, o: 1, x: 1, n: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, p: 2, y: 1, a: 1, d: 1}, what is the expected number of times the pattern 'py*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, h: 3, z: 2} to form a word, what is the expected number of matches of the pattern 'z.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, p: 1, r: 1, s: 1, k: 1}, what is the expected number of times the pattern 'k*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, i: 2, d: 2}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, s: 1, c: 2, o: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'c.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 4, g: 2}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, u: 1, y: 1, i: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'yi*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, l: 2, d: 1, h: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, n: 1, j: 2, o: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, m: 2, u: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'm*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, n: 3}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, g: 1, v: 1, c: 1, q: 1}. What is the expected number of occurrences of the pattern 'v*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, c: 1, n: 1, q: 2, z: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 4, v: 2}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, l: 2, q: 1, i: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'mq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, f: 1, o: 3, x: 1}. What is the expected number of occurrences of the pattern 'f*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, c: 3, m: 2}, what is the expected number of times the pattern 'ma+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, b: 1, d: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'd+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, i: 2, a: 1, j: 2}. What is the expected number of occurrences of the pattern 'wi+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, d: 3, l: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, h: 4}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, k: 1, f: 1, e: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, j: 4}, what is the expected number of times the pattern 'nj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, f: 1, h: 3} to form a word, what is the expected number of matches of the pattern 'f+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, y: 3, a: 2}, what is the expected number of times the pattern 'yr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, v: 1, c: 2, q: 1}. What is the expected number of occurrences of the pattern 'd.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, p: 1, n: 1, h: 2}. What is the expected number of occurrences of the pattern 'hp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, u: 1, w: 2, a: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'u+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, r: 1, g: 1, z: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'r+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, j: 2, n: 3} to form a word, what is the expected number of matches of the pattern 'n+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, l: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'd.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, u: 2, t: 1, h: 1}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, r: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, j: 1, u: 2, y: 1, i: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, u: 1, a: 1, s: 2}. What is the expected number of occurrences of the pattern 'h.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, u: 2, k: 2, l: 1}, what is the expected number of times the pattern 'k*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, m: 1, s: 3} to form a word, what is the expected number of matches of the pattern 'fm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, q: 1, e: 1, a: 1, w: 1}, what is the expected number of times the pattern 'te*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, r: 2, d: 1, e: 1}, what is the expected number of times the pattern 'ea*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, c: 2, y: 1, q: 1, n: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, n: 1, c: 2, h: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, r: 3, k: 2}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 4, f: 1, m: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, g: 2, w: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'x+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, s: 1, i: 1, v: 3}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, l: 1, d: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'pd+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, u: 2, o: 1, z: 1, y: 1}, what is the expected number of times the pattern 'z*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, v: 3}, what is the expected number of times the pattern 'e*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, y: 1, t: 1, g: 2, p: 1}, what is the expected number of times the pattern 'ty*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, u: 1, f: 2}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, b: 4}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, i: 2, x: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'wx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, n: 1, f: 1, j: 1, h: 2}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, b: 1, d: 4}, what is the expected number of times the pattern 'db+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, c: 1, p: 1, u: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'z+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, z: 1, j: 1, u: 1, n: 1}. What is the expected number of occurrences of the pattern 'jn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 4, z: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 4, d: 2} to form a word, what is the expected number of matches of the pattern 'd*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 4, i: 2}, what is the expected number of times the pattern 'in*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, s: 1, z: 3, n: 1}, what is the expected number of times the pattern 'sn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, n: 2, l: 2, p: 1}, what is the expected number of times the pattern 'o+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, z: 3}. What is the expected number of occurrences of the pattern 'zi+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, a: 4}, what is the expected number of times the pattern 'ma*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, v: 4, w: 1}, what is the expected number of times the pattern 'sv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, p: 1, f: 1, t: 2}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, l: 1, b: 2, a: 1, i: 1}, what is the expected number of times the pattern 'a.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, f: 2, c: 1, h: 2}, what is the expected number of times the pattern 'f+k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 4, n: 2} to form a word, what is the expected number of matches of the pattern 'nb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, x: 1, d: 1, e: 1, c: 1}. What is the expected number of occurrences of the pattern 'ce+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, g: 1, e: 1, i: 1, q: 2}. What is the expected number of occurrences of the pattern 'e*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, w: 5}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, p: 2, j: 1, b: 2}, what is the expected number of times the pattern 'l+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, m: 2, o: 2}. What is the expected number of occurrences of the pattern 'o.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, j: 1, w: 1, e: 3}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, t: 1, j: 1, v: 2, k: 1}. What is the expected number of occurrences of the pattern 't+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, e: 1, m: 2}. What is the expected number of occurrences of the pattern 'e+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, s: 2, y: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'p+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, i: 3, p: 2} to form a word, what is the expected number of matches of the pattern 'ip+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, j: 1, v: 2}, what is the expected number of times the pattern 'jv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, k: 3, q: 1} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, z: 4}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, c: 1, r: 2, h: 1}, what is the expected number of times the pattern 'hr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, g: 2, v: 2}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, l: 3, p: 1}, what is the expected number of times the pattern 'ps+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, h: 1, k: 1, v: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'z.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, a: 3}. What is the expected number of occurrences of the pattern 'w.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, o: 1, x: 1, d: 1, r: 1}. What is the expected number of occurrences of the pattern 'r.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, g: 1, n: 2, x: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'gx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, d: 2, v: 2, q: 1}. What is the expected number of occurrences of the pattern 'vq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, u: 2, g: 3}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, d: 4} to form a word, what is the expected number of matches of the pattern 'qd+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'u*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, o: 1, d: 1, n: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, o: 1, d: 2, i: 2}. What is the expected number of occurrences of the pattern 'i+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, a: 1, t: 1, k: 1, h: 1}. What is the expected number of occurrences of the pattern 'a+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, w: 1, p: 3} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, g: 1, k: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'p*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, q: 3}. What is the expected number of occurrences of the pattern 'q.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, w: 3}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, a: 1, d: 1, f: 1, t: 1}, what is the expected number of times the pattern 'wf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, z: 1, g: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'hg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, c: 2, r: 1, w: 1}. What is the expected number of occurrences of the pattern 'rw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, q: 2, r: 1, a: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'a.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, k: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'v+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, s: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'd+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, m: 1, k: 1, d: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, c: 4}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, l: 4} to form a word, what is the expected number of matches of the pattern 'l+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, y: 2, o: 2}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, t: 2, b: 1, p: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, k: 1, q: 1, b: 1, d: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'k*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, q: 1, a: 2, o: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, w: 3, k: 2}. What is the expected number of occurrences of the pattern 'yw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, h: 1, w: 3} to form a word, what is the expected number of matches of the pattern 'l*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, l: 5} to form a word, what is the expected number of matches of the pattern 'l*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, e: 3, j: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, g: 3, x: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, c: 1, f: 1, d: 1, x: 2}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, l: 1, y: 1, u: 1, d: 1}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, w: 1, f: 1, e: 1, x: 1}, what is the expected number of times the pattern 'e+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, z: 1, w: 2, f: 1}. What is the expected number of occurrences of the pattern 'lf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, a: 1, e: 2, p: 2}. What is the expected number of occurrences of the pattern 'e.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, o: 1, s: 3} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, f: 4}, what is the expected number of times the pattern 'm.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, e: 2, u: 2}. What is the expected number of occurrences of the pattern 'uw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, c: 1, f: 1, a: 1, z: 1}. What is the expected number of occurrences of the pattern 'z*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, e: 2, m: 1, i: 2}, what is the expected number of times the pattern 'ie*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, w: 1, a: 1, i: 1, d: 1}, what is the expected number of times the pattern 'ca+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 4, d: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 5, a: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, a: 1, s: 1, j: 1, g: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, x: 5}, what is the expected number of times the pattern 'o+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, n: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, q: 2, o: 2}, what is the expected number of times the pattern 'f.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, k: 1, p: 1, n: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'gk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, o: 1, w: 1, b: 1}, what is the expected number of times the pattern 'w+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, t: 1, z: 4}. What is the expected number of occurrences of the pattern 't+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, i: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'iv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, l: 2, e: 1, k: 1}. What is the expected number of occurrences of the pattern 'e*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, b: 1, s: 1, x: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'xx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, g: 1, l: 1, d: 1, f: 2}. What is the expected number of occurrences of the pattern 'd.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, g: 2, e: 1, t: 2}. What is the expected number of occurrences of the pattern 'e+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, j: 1, w: 2, y: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'jw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, t: 3} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, f: 2, s: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'fv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, r: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'yr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, i: 1, p: 1, c: 2, y: 1}. What is the expected number of occurrences of the pattern 'p+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, l: 2, s: 1}. What is the expected number of occurrences of the pattern 'sb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, z: 4}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, x: 2, u: 3}, what is the expected number of times the pattern 'v+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, x: 1, r: 2, s: 1, a: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 4, m: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, a: 2, x: 1, s: 1, t: 1}. What is the expected number of occurrences of the pattern 'sa+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, q: 3} to form a word, what is the expected number of matches of the pattern 'qv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 3, q: 3}, what is the expected number of times the pattern 'l*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, y: 1, r: 2, p: 1, i: 1}, what is the expected number of times the pattern 'p+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, x: 3, s: 1}. What is the expected number of occurrences of the pattern 'xv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, m: 1, d: 1, a: 1, o: 1}, what is the expected number of times the pattern 'da*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, b: 2, a: 2, h: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 4, r: 2}. What is the expected number of occurrences of the pattern 'gr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, i: 1, f: 1, l: 3} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, e: 1, x: 4} to form a word, what is the expected number of matches of the pattern 'e+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, r: 1, s: 1, v: 1, d: 2}. What is the expected number of occurrences of the pattern 'sx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 4, h: 1, c: 1}, what is the expected number of times the pattern 'c.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, d: 4}. What is the expected number of occurrences of the pattern 'd*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, k: 4}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, m: 3, t: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, p: 1, k: 1, l: 1, w: 1}, what is the expected number of times the pattern 'wl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, d: 4} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, i: 2, y: 3}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, c: 3} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, p: 3, t: 2} to form a word, what is the expected number of matches of the pattern 'jp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, v: 1, d: 3, w: 1}. What is the expected number of occurrences of the pattern 'wv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, s: 2, m: 3}, what is the expected number of times the pattern 'm.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, y: 1, b: 1, t: 2}, what is the expected number of times the pattern 'at*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, g: 3, i: 1}. What is the expected number of occurrences of the pattern 'i+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, t: 3}, what is the expected number of times the pattern 'qt*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 5, o: 1}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, l: 4}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, t: 1, z: 1, r: 3}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, i: 2, u: 1, t: 1, j: 1}, what is the expected number of times the pattern 'j*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, y: 1, r: 2, k: 1, e: 1}, what is the expected number of times the pattern 'k.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, w: 3}. What is the expected number of occurrences of the pattern 'w.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 4, d: 1, s: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, e: 1, j: 1, a: 3}, what is the expected number of times the pattern 'aj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 3, w: 3}, what is the expected number of times the pattern 'sw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, z: 1, w: 1, x: 2}, what is the expected number of times the pattern 'wx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, c: 1, h: 1, b: 2, t: 1} to form a word, what is the expected number of matches of the pattern 'hc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 4, u: 2}, what is the expected number of times the pattern 'ju*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, f: 1, d: 3} to form a word, what is the expected number of matches of the pattern 'f.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, l: 2, e: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'l.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 4, v: 2}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, z: 2, f: 2}, what is the expected number of times the pattern 'zo*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, q: 3, w: 2} to form a word, what is the expected number of matches of the pattern 'xq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, v: 1, n: 2, a: 1, h: 1}, what is the expected number of times the pattern 'v.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, v: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'zb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, t: 1, m: 2, o: 1, l: 1}, what is the expected number of times the pattern 'lr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, b: 1, q: 1, d: 1, k: 2}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, j: 1, c: 1, q: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'cj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, j: 1, g: 1, v: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'vb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 4, p: 2}. What is the expected number of occurrences of the pattern 'zp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, x: 1, a: 1, d: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'x*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, p: 1, d: 2, n: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, b: 2, s: 1, f: 1, m: 1}, what is the expected number of times the pattern 'mf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, x: 3, f: 1}. What is the expected number of occurrences of the pattern 'fx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, d: 3} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, x: 3}, what is the expected number of times the pattern 'd.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, h: 1, a: 1, k: 1, o: 1}, what is the expected number of times the pattern 'k.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, d: 4}. What is the expected number of occurrences of the pattern 'dn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, j: 1, y: 2, d: 2}, what is the expected number of times the pattern 'p.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, e: 3}, what is the expected number of times the pattern 'u*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'ui+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, c: 2, z: 1}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 4, y: 2}, what is the expected number of times the pattern 'yt+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, y: 1, f: 1, m: 2}. What is the expected number of occurrences of the pattern 'ym*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, j: 2, p: 1, z: 2}, what is the expected number of times the pattern 'z*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, s: 1, o: 2, m: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, z: 3, c: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'u.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, t: 2, l: 1, s: 1, x: 1}, what is the expected number of times the pattern 'l.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, j: 2, t: 1, o: 1, z: 1}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, g: 2, b: 1, e: 1, w: 1}, what is the expected number of times the pattern 'xb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, v: 3, d: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 4, d: 2}. What is the expected number of occurrences of the pattern 'fd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, e: 2, a: 2, l: 1}, what is the expected number of times the pattern 'j.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, z: 2, j: 1}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 4, e: 2}, what is the expected number of times the pattern 'e+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, u: 2, y: 1, h: 1, d: 1}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, l: 2, f: 2, v: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, t: 1, z: 2, s: 1}. What is the expected number of occurrences of the pattern 'z.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 4, m: 2} to form a word, what is the expected number of matches of the pattern 'm.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, j: 2, f: 2}. What is the expected number of occurrences of the pattern 'gj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, b: 1, s: 1, n: 2}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, p: 2, w: 1}. What is the expected number of occurrences of the pattern 'pw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, x: 4}, what is the expected number of times the pattern 'ax+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, r: 2, w: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'n+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, c: 1, n: 1, e: 1}. What is the expected number of occurrences of the pattern 'q+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, j: 1, x: 3, i: 1}. What is the expected number of occurrences of the pattern 'c*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, f: 1, x: 1, i: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'ji*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, v: 3, e: 2} to form a word, what is the expected number of matches of the pattern 'i+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, q: 2, p: 1, v: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, h: 1, c: 1, g: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'i.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 4, y: 2} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, u: 1, m: 2, q: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, q: 2, k: 2, i: 1}. What is the expected number of occurrences of the pattern 'i.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, r: 2, f: 1, a: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'r+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, e: 2, z: 2}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, g: 1, s: 3, u: 1}. What is the expected number of occurrences of the pattern 'g*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, e: 2, v: 3}, what is the expected number of times the pattern 't.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, z: 1, s: 1, y: 1, n: 1}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, z: 1, y: 1, u: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'u*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, p: 1, d: 1, o: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'po*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, p: 4} to form a word, what is the expected number of matches of the pattern 'h*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, z: 1, y: 2}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, u: 4}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, j: 1, n: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, u: 1, o: 1, e: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'o+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, w: 1, o: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'o*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 4, f: 2} to form a word, what is the expected number of matches of the pattern 'fl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, w: 4, r: 1}, what is the expected number of times the pattern 'w.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, m: 1, u: 1, s: 3}. What is the expected number of occurrences of the pattern 'a*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, v: 1, g: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'eg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, v: 1, b: 1, s: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, f: 1, v: 3, p: 1}. What is the expected number of occurrences of the pattern 'o.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 4, g: 2} to form a word, what is the expected number of matches of the pattern 'gq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 4, e: 2}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, m: 3, i: 2}. What is the expected number of occurrences of the pattern 'im*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, o: 1, d: 1, v: 3} to form a word, what is the expected number of matches of the pattern 'o*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, r: 1, u: 1, q: 3}, what is the expected number of times the pattern 'i*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 4, x: 2}, what is the expected number of times the pattern 'x.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, v: 1, a: 1, l: 1, b: 2}. What is the expected number of occurrences of the pattern 'a.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, o: 3}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 4, e: 2}. What is the expected number of occurrences of the pattern 'v*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, v: 1, w: 2, k: 1, s: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, x: 1, n: 1, o: 1, i: 1}. What is the expected number of occurrences of the pattern 'no*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, p: 2, c: 1}, what is the expected number of times the pattern 'q*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 3, a: 1, y: 1, j: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, v: 1, t: 1, d: 2, x: 1}, what is the expected number of times the pattern 'xd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, b: 2, o: 3} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, q: 4} to form a word, what is the expected number of matches of the pattern 'q.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, y: 2, f: 3}, what is the expected number of times the pattern 'd+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 4, c: 1, r: 1} to form a word, what is the expected number of matches of the pattern 's*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, v: 1, o: 1, x: 1, k: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, y: 2}. What is the expected number of occurrences of the pattern 'yt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, s: 4}, what is the expected number of times the pattern 'ys*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, g: 1, u: 1, b: 1, x: 1}. What is the expected number of occurrences of the pattern 'g*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, y: 1, w: 2, t: 1}, what is the expected number of times the pattern 'y*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, l: 1, p: 1, h: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 4, e: 2}, what is the expected number of times the pattern 'u*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, m: 2, s: 2} to form a word, what is the expected number of matches of the pattern 's+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, t: 2, i: 2}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, k: 1, f: 2}. What is the expected number of occurrences of the pattern 'lk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, s: 2, z: 2}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, n: 2, w: 1, u: 1}, what is the expected number of times the pattern 'p*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, i: 2, e: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, h: 2, f: 3}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, o: 2, f: 1, t: 1, y: 1}. What is the expected number of occurrences of the pattern 'p*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, v: 1, z: 1, w: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'w+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, l: 2, w: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'lg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 3, c: 3} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, s: 1, c: 2, l: 2}. What is the expected number of occurrences of the pattern 'dl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, c: 1, j: 2, n: 1}. What is the expected number of occurrences of the pattern 'n+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, a: 2, k: 1, d: 1, o: 1}, what is the expected number of times the pattern 'ka*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, a: 1, e: 3, h: 1} to form a word, what is the expected number of matches of the pattern 'n+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, c: 1, u: 1, w: 2, h: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, w: 5}. What is the expected number of occurrences of the pattern 'o.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, b: 1, s: 2, m: 2}. What is the expected number of occurrences of the pattern 'm+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, p: 4}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, v: 1, f: 4} to form a word, what is the expected number of matches of the pattern 'v*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, w: 3} to form a word, what is the expected number of matches of the pattern 'iw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, c: 1, d: 2}. What is the expected number of occurrences of the pattern 'dc+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, s: 2, p: 2}. What is the expected number of occurrences of the pattern 'ps+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, q: 3, y: 1}. What is the expected number of occurrences of the pattern 'xq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, r: 4} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 4, w: 2}, what is the expected number of times the pattern 'w+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, o: 1, h: 2, w: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'wg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, v: 2, d: 1, j: 1, q: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, z: 1, w: 1, r: 1, i: 1}. What is the expected number of occurrences of the pattern 'i*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, s: 1, r: 2}, what is the expected number of times the pattern 'is*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, m: 1, q: 2, z: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, b: 1, e: 1, m: 1}. What is the expected number of occurrences of the pattern 'eb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, e: 2, a: 2}. What is the expected number of occurrences of the pattern 'e+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 4, y: 2}. What is the expected number of occurrences of the pattern 'r*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, u: 2, q: 1, a: 1, t: 1}, what is the expected number of times the pattern 't*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, p: 1, v: 3} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, w: 1, r: 3} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, m: 3}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, j: 1, x: 2, y: 2}, what is the expected number of times the pattern 'j*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, w: 1, q: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, y: 2, m: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'm.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, m: 1, l: 1, w: 3}. What is the expected number of occurrences of the pattern 'l+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, y: 4}. What is the expected number of occurrences of the pattern 'yb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, q: 3}. What is the expected number of occurrences of the pattern 'q*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, e: 1, p: 1, o: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, x: 1, l: 3}, what is the expected number of times the pattern 'dl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, r: 1, b: 2, m: 1, u: 1}, what is the expected number of times the pattern 'rr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, h: 1, i: 1, d: 2, z: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, o: 2, p: 1, c: 2}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, v: 1, g: 2, q: 2}, what is the expected number of times the pattern 'v*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, q: 2, a: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, q: 1, c: 1, a: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, d: 1, l: 1, c: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'l*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, e: 3}. What is the expected number of occurrences of the pattern 'el*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, s: 1, m: 1, r: 1, t: 2} to form a word, what is the expected number of matches of the pattern 'rt+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'x*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, o: 1, c: 3} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, r: 3, q: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'a+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, s: 1, h: 1, q: 2} to form a word, what is the expected number of matches of the pattern 's+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, t: 3}, what is the expected number of times the pattern 'r+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, d: 4}. What is the expected number of occurrences of the pattern 'ds+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, g: 1, e: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'm+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, v: 2, j: 1}. What is the expected number of occurrences of the pattern 'v*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, a: 4}, what is the expected number of times the pattern 'at*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, s: 1, q: 1, y: 1, z: 2}. What is the expected number of occurrences of the pattern 'zs*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, p: 2, h: 1, s: 1, e: 1}, what is the expected number of times the pattern 'h+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, z: 1, y: 1, a: 1, p: 2}. What is the expected number of occurrences of the pattern 'z.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, t: 2, c: 2} to form a word, what is the expected number of matches of the pattern 't.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, v: 2, m: 1, i: 1, c: 1}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, y: 1, u: 2, a: 1}, what is the expected number of times the pattern 'u.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, x: 1, f: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'xr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, a: 2, m: 1, q: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, r: 3}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 4, d: 2} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, g: 4}. What is the expected number of occurrences of the pattern 'd.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, c: 4} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, v: 2, o: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'v*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, e: 1, t: 1, o: 2, q: 1}. What is the expected number of occurrences of the pattern 'u.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, q: 1, b: 2, x: 1, w: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 5, s: 1}. What is the expected number of occurrences of the pattern 's.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, v: 2, f: 1, m: 2}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, m: 1, r: 3}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, y: 2, e: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'de+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, s: 1, u: 2, v: 2}. What is the expected number of occurrences of the pattern 'z.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, s: 1, g: 1, w: 2, q: 1}, what is the expected number of times the pattern 'qw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, p: 1, k: 1, s: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'v*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, x: 3, k: 2}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, i: 1, j: 2} to form a word, what is the expected number of matches of the pattern 'ik*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, s: 4}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'u+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, i: 1, j: 1, o: 1, x: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, h: 1, f: 1, x: 2, z: 1}, what is the expected number of times the pattern 'fx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, e: 2, u: 3}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 4, k: 2}, what is the expected number of times the pattern 'u+k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, v: 1, o: 1, m: 2, e: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 3, q: 3} to form a word, what is the expected number of matches of the pattern 'qf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, l: 1, p: 1, y: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'p*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, o: 4}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, i: 1, h: 2}. What is the expected number of occurrences of the pattern 'i*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 5, o: 1}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, a: 2, v: 2}. What is the expected number of occurrences of the pattern 'l*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, y: 2, t: 2}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, s: 2, f: 2, u: 1}, what is the expected number of times the pattern 'c*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, n: 1, m: 3} to form a word, what is the expected number of matches of the pattern 'm.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, l: 2, n: 1, a: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, i: 1, d: 1, t: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'j+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, u: 1, w: 3}. What is the expected number of occurrences of the pattern 'wq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, k: 1, p: 1, m: 1, o: 2}, what is the expected number of times the pattern 'p.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, t: 2, a: 2}. What is the expected number of occurrences of the pattern 'a+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, j: 2, n: 1, d: 1}, what is the expected number of times the pattern 'jp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, f: 1, s: 1, l: 2, y: 1}, what is the expected number of times the pattern 'lo+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, x: 1, r: 1, j: 2} to form a word, what is the expected number of matches of the pattern 'xi*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, j: 2, c: 2} to form a word, what is the expected number of matches of the pattern 'c+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, w: 1, j: 2, l: 1, m: 1}. What is the expected number of occurrences of the pattern 'm*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, w: 1, g: 1, d: 2, n: 1}, what is the expected number of times the pattern 'h.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, c: 3}, what is the expected number of times the pattern 'co+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, g: 1, n: 1, r: 3}. What is the expected number of occurrences of the pattern 'j.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, s: 2, g: 3} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, y: 1, n: 2, o: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'n*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, p: 2, n: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'np+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, r: 1, b: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 4, s: 2}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, x: 4}. What is the expected number of occurrences of the pattern 'u+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, v: 1, b: 1, n: 1, q: 2}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, h: 2, l: 1, v: 1, r: 1}. What is the expected number of occurrences of the pattern 'l+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, p: 1, b: 2, f: 1}, what is the expected number of times the pattern 'p*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, b: 2, k: 1, o: 1, a: 1}. What is the expected number of occurrences of the pattern 'ab+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, i: 1, q: 2, z: 2}. What is the expected number of occurrences of the pattern 'qq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, g: 2, o: 2, m: 1}. What is the expected number of occurrences of the pattern 'io+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, h: 2, j: 2}, what is the expected number of times the pattern 'x.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, g: 2, h: 1, d: 1, r: 1}. What is the expected number of occurrences of the pattern 'wg*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, j: 3, u: 1}, what is the expected number of times the pattern 'x+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, w: 2, k: 2, c: 1}. What is the expected number of occurrences of the pattern 'k*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, z: 1, k: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 3, z: 3}. What is the expected number of occurrences of the pattern 'nz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, r: 2, g: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'x*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, e: 1, k: 1, r: 1, s: 1}. What is the expected number of occurrences of the pattern 'k+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, c: 4}, what is the expected number of times the pattern 'a+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, b: 4} to form a word, what is the expected number of matches of the pattern 'd.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, z: 1, n: 1, t: 2}. What is the expected number of occurrences of the pattern 'kz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, b: 2, d: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, y: 1, k: 2}. What is the expected number of occurrences of the pattern 'ak*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, t: 1, a: 1, q: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'ta*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, f: 1, y: 1, j: 2, v: 1}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, y: 3}, what is the expected number of times the pattern 'jy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, r: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, r: 2, d: 2}, what is the expected number of times the pattern 'r+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, u: 2, x: 1, v: 1, q: 1}. What is the expected number of occurrences of the pattern 'v*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, m: 2, c: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, c: 2, u: 1, q: 1, e: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 5, y: 1} to form a word, what is the expected number of matches of the pattern 'y+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, j: 3}. What is the expected number of occurrences of the pattern 'ej+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, z: 2, b: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'j+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, c: 3}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, u: 3, c: 2}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, o: 1, y: 1, u: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'o+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, i: 4, m: 1}, what is the expected number of times the pattern 'i*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 4, n: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'n.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, n: 3}. What is the expected number of occurrences of the pattern 'nb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, l: 1, c: 4} to form a word, what is the expected number of matches of the pattern 's+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, a: 2, o: 3}, what is the expected number of times the pattern 'w*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, r: 2, x: 1} to form a word, what is the expected number of matches of the pattern 'x+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, w: 1, r: 1, m: 2, h: 1}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, x: 2, z: 1, d: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, j: 2, x: 2}. What is the expected number of occurrences of the pattern 't*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, r: 1, e: 1, x: 1, o: 1}. What is the expected number of occurrences of the pattern 'xd+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, f: 2, l: 3}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, x: 1, q: 1, f: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'wo+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, s: 2, b: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, b: 3}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, d: 2, r: 2}. What is the expected number of occurrences of the pattern 'g+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, q: 1, d: 1, v: 1, f: 2}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 3, s: 3} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, l: 2, s: 1, r: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'ds+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, r: 1, p: 1, o: 1, j: 1}, what is the expected number of times the pattern 's+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, h: 3}. What is the expected number of occurrences of the pattern 'r.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, f: 1, y: 3} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, h: 5}. What is the expected number of occurrences of the pattern 'h*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, i: 4} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, m: 3}, what is the expected number of times the pattern 'm+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, o: 3, s: 1, t: 1}, what is the expected number of times the pattern 'o*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, c: 1, f: 1, j: 2, g: 1}. What is the expected number of occurrences of the pattern 'f.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, m: 1, v: 3}. What is the expected number of occurrences of the pattern 'v+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, o: 5} to form a word, what is the expected number of matches of the pattern 'q*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, p: 1, q: 3, k: 1}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'h+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, y: 3}. What is the expected number of occurrences of the pattern 'y+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, u: 2, o: 1, g: 1, y: 1}. What is the expected number of occurrences of the pattern 'j.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, i: 1, j: 1, l: 2, x: 1}. What is the expected number of occurrences of the pattern 'l.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, f: 3, d: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 4, k: 2}, what is the expected number of times the pattern 'h+k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, c: 2, w: 1, u: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'cu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 4, g: 2}. What is the expected number of occurrences of the pattern 'gi+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, u: 3, q: 2}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, j: 1, t: 2, g: 1}, what is the expected number of times the pattern 'g.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, z: 2, g: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'j.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, u: 1, p: 1, q: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, k: 3, x: 2}. What is the expected number of occurrences of the pattern 'ux+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, r: 1, x: 2}. What is the expected number of occurrences of the pattern 'r*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, y: 3, u: 2}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, v: 1, p: 1, t: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, o: 4}, what is the expected number of times the pattern 'q+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, j: 1, l: 3, m: 1}, what is the expected number of times the pattern 'q.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, u: 2, c: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, z: 1, h: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'z.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, g: 5} to form a word, what is the expected number of matches of the pattern 'ig+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 4, f: 2}, what is the expected number of times the pattern 'f+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, x: 1, v: 1, t: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'xt+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, x: 3, m: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, v: 1, b: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'a*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, a: 2, z: 1, p: 1, c: 1}, what is the expected number of times the pattern 'z*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, l: 1, q: 1, i: 2, y: 1}, what is the expected number of times the pattern 'yi+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, i: 2, k: 1, l: 1}, what is the expected number of times the pattern 'id*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, s: 1, b: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, o: 2, x: 1, k: 1, q: 1}. What is the expected number of occurrences of the pattern 'k+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, z: 1, x: 2, y: 2}, what is the expected number of times the pattern 'x*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, d: 2, t: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'd.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, l: 4} to form a word, what is the expected number of matches of the pattern 'rl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, x: 4}, what is the expected number of times the pattern 'x.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, v: 3}, what is the expected number of times the pattern 'v.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, k: 4}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, e: 2, r: 2} to form a word, what is the expected number of matches of the pattern 't+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, n: 2, o: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 5, x: 1}, what is the expected number of times the pattern 'hx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, p: 4}. What is the expected number of occurrences of the pattern 'hp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, e: 4} to form a word, what is the expected number of matches of the pattern 'er*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, l: 1, r: 1, e: 2, t: 1} to form a word, what is the expected number of matches of the pattern 'e+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, d: 1, q: 1, a: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'dv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, m: 1, v: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'ym+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, i: 2, f: 1, s: 2}, what is the expected number of times the pattern 'ui*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, i: 2, z: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 4, b: 2} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, e: 2, d: 2}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, h: 3, z: 2}. What is the expected number of occurrences of the pattern 'm.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, v: 1, p: 2}. What is the expected number of occurrences of the pattern 'p.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, f: 2, p: 1, t: 1, k: 1}, what is the expected number of times the pattern 'ft+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, q: 1, p: 2, l: 2}, what is the expected number of times the pattern 'i+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, v: 4}, what is the expected number of times the pattern 'j+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, o: 1, k: 3} to form a word, what is the expected number of matches of the pattern 'kr+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, q: 2, z: 3}. What is the expected number of occurrences of the pattern 'r.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, n: 1, p: 1, l: 2, y: 1}, what is the expected number of times the pattern 'w.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, s: 5}, what is the expected number of times the pattern 's+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, x: 1, q: 2, p: 2}. What is the expected number of occurrences of the pattern 'qx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, q: 2, o: 2}. What is the expected number of occurrences of the pattern 'oq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, l: 1, y: 1, m: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'n+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 4, r: 2}, what is the expected number of times the pattern 'q+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, q: 1, x: 2}. What is the expected number of occurrences of the pattern 'q*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, f: 1, o: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, w: 1, i: 1, f: 2, h: 1} to form a word, what is the expected number of matches of the pattern 'i.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, k: 1, h: 1, s: 2, g: 1}. What is the expected number of occurrences of the pattern 'w.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, n: 2, q: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'iq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, f: 2, b: 1, e: 1, y: 1}, what is the expected number of times the pattern 'zy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, t: 3, u: 1, s: 1} to form a word, what is the expected number of matches of the pattern 's*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, i: 1, u: 1, l: 1, f: 1}, what is the expected number of times the pattern 'lc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 5, c: 1} to form a word, what is the expected number of matches of the pattern 'mc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, p: 2, w: 1, e: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, u: 2, a: 1, j: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, d: 3} to form a word, what is the expected number of matches of the pattern 'l*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, m: 2, e: 3} to form a word, what is the expected number of matches of the pattern 'm+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, k: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'vk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, g: 4}, what is the expected number of times the pattern 'z*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, y: 4}. What is the expected number of occurrences of the pattern 'yp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 5, b: 1} to form a word, what is the expected number of matches of the pattern 'w*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 4, m: 2}, what is the expected number of times the pattern 'xm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, n: 2, o: 1, g: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'eo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, c: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'n*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, e: 2, w: 3}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 5, v: 1}, what is the expected number of times the pattern 'v+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 4, r: 2}. What is the expected number of occurrences of the pattern 's.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, d: 3, s: 1, m: 1}. What is the expected number of occurrences of the pattern 'm.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, h: 2, q: 3}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 4, d: 2} to form a word, what is the expected number of matches of the pattern 'd*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, r: 4}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, m: 2, l: 2}. What is the expected number of occurrences of the pattern 'l*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 4, i: 2} to form a word, what is the expected number of matches of the pattern 'hi+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, q: 1, y: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, y: 1, x: 2, e: 1, v: 1}, what is the expected number of times the pattern 'et*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, o: 2, p: 2}. What is the expected number of occurrences of the pattern 'po+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, i: 1, f: 1, k: 2, s: 1}, what is the expected number of times the pattern 'mf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, l: 1, c: 1, q: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'ce+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, a: 1, p: 1, g: 2, t: 1}. What is the expected number of occurrences of the pattern 'ap*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, o: 2, i: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'i*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, h: 3, s: 2} to form a word, what is the expected number of matches of the pattern 'h*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, d: 1, z: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'jq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, c: 4}, what is the expected number of times the pattern 'nc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, j: 1, p: 2, f: 2}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, k: 1, w: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, l: 3}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, p: 1, b: 1, c: 1, o: 2}. What is the expected number of occurrences of the pattern 'c*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, f: 2, b: 1}. What is the expected number of occurrences of the pattern 'c.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, j: 1, m: 1, u: 1, o: 2}, what is the expected number of times the pattern 'u.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, a: 3} to form a word, what is the expected number of matches of the pattern 'ai+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, j: 4} to form a word, what is the expected number of matches of the pattern 'jj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 3, k: 3}, what is the expected number of times the pattern 'k.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, f: 1, n: 1, z: 2}. What is the expected number of occurrences of the pattern 'ni+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, b: 2, p: 1, r: 1, i: 1}. What is the expected number of occurrences of the pattern 'p+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, x: 1, w: 2, i: 1, d: 1}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, v: 1, f: 2, c: 1, u: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, o: 2, p: 3}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, r: 2, z: 2, x: 1}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, q: 1, m: 3}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, t: 3, r: 2}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, a: 4, o: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, x: 2, r: 1, k: 1, s: 1}, what is the expected number of times the pattern 'x+k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, u: 2, g: 1, p: 2}. What is the expected number of occurrences of the pattern 'u+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, g: 4, a: 1}. What is the expected number of occurrences of the pattern 'pa*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, k: 1, e: 1, h: 2}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, q: 3, d: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, n: 2, p: 3}, what is the expected number of times the pattern 't+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, f: 4} to form a word, what is the expected number of matches of the pattern 'f.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, a: 4}, what is the expected number of times the pattern 'oa*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, b: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, f: 1, k: 1, j: 1, z: 2}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, j: 1, m: 1, x: 1, w: 2}. What is the expected number of occurrences of the pattern 'wx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, g: 1, p: 1, z: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'pq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, o: 4} to form a word, what is the expected number of matches of the pattern 'f.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, b: 1, u: 1, n: 1, k: 2}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, o: 1, y: 2, f: 1}, what is the expected number of times the pattern 'f+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, v: 1, a: 1, u: 1, s: 2} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 4, j: 1, b: 1}, what is the expected number of times the pattern 'j*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, s: 1, i: 2, h: 1, l: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 4, l: 2}, what is the expected number of times the pattern 'dl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, y: 2, i: 3}. What is the expected number of occurrences of the pattern 'y+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, y: 3, c: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'c*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, t: 1, r: 3}, what is the expected number of times the pattern 'r+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 4, s: 2}. What is the expected number of occurrences of the pattern 's*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, b: 4} to form a word, what is the expected number of matches of the pattern 'y*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, s: 3, n: 1, o: 1}. What is the expected number of occurrences of the pattern 'o+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, t: 1, p: 1, h: 3}. What is the expected number of occurrences of the pattern 'h*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 4, v: 2} to form a word, what is the expected number of matches of the pattern 'v.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, e: 2, a: 2, j: 1}. What is the expected number of occurrences of the pattern 'j*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, x: 1, w: 1, i: 1}. What is the expected number of occurrences of the pattern 'xi+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, v: 1, o: 2, g: 2}. What is the expected number of occurrences of the pattern 'gv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, h: 2, d: 1, i: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, d: 1, g: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, f: 4, e: 1} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'ox+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, d: 4} to form a word, what is the expected number of matches of the pattern 'sd+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, x: 1, h: 1, g: 3} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, h: 1, c: 1, q: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'eu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 4, s: 2}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, h: 1, v: 3}. What is the expected number of occurrences of the pattern 'h*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, m: 2, w: 1, d: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'yu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, v: 2, l: 2}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 4, c: 2}, what is the expected number of times the pattern 'gc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, t: 2, h: 2}, what is the expected number of times the pattern 'h*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, l: 2, p: 1, q: 1}. What is the expected number of occurrences of the pattern 'p+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, m: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'm*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, n: 4} to form a word, what is the expected number of matches of the pattern 'nz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, l: 2, c: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'qa+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, l: 2, z: 1, x: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'l*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 3, j: 3}, what is the expected number of times the pattern 'j.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, o: 2, n: 2, m: 1} to form a word, what is the expected number of matches of the pattern 'm+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, u: 3}. What is the expected number of occurrences of the pattern 'u*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, g: 3} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, j: 1, p: 2, m: 1, c: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, j: 1, q: 2, f: 2}, what is the expected number of times the pattern 'j*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, d: 1, o: 3, h: 1} to form a word, what is the expected number of matches of the pattern 'd+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, b: 1, n: 1, w: 1, z: 2}, what is the expected number of times the pattern 'k.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, f: 3, v: 2}. What is the expected number of occurrences of the pattern 'v*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, y: 3} to form a word, what is the expected number of matches of the pattern 'y*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, g: 2, e: 1}. What is the expected number of occurrences of the pattern 'ge+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 4, g: 2}, what is the expected number of times the pattern 'g.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, s: 5}, what is the expected number of times the pattern 's+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, w: 2, i: 3}, what is the expected number of times the pattern 'id*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, b: 2, j: 2}, what is the expected number of times the pattern 'wj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, v: 2, a: 3}, what is the expected number of times the pattern 'm.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, x: 1, a: 1, m: 3}, what is the expected number of times the pattern 'xf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, l: 2, x: 1, w: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, k: 1, s: 1, q: 1, i: 2}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, q: 3}, what is the expected number of times the pattern 'q+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, c: 3}. What is the expected number of occurrences of the pattern 'a.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, l: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, f: 4}. What is the expected number of occurrences of the pattern 't.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, x: 1, r: 1, y: 1, g: 1}, what is the expected number of times the pattern 'xy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, f: 2, n: 1, l: 1, b: 1}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, s: 4, z: 1}, what is the expected number of times the pattern 'y.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, x: 5}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 3, y: 2, g: 1}. What is the expected number of occurrences of the pattern 'gp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, u: 1, p: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'p+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, t: 2, m: 3} to form a word, what is the expected number of matches of the pattern 'tm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, r: 3, v: 2} to form a word, what is the expected number of matches of the pattern 'v+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, q: 1, p: 2, r: 2} to form a word, what is the expected number of matches of the pattern 'pq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, i: 2, n: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'nv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, l: 4}, what is the expected number of times the pattern 'n.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, r: 1, v: 1, y: 1, d: 1}, what is the expected number of times the pattern 'y+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, s: 3}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, t: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'to+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, c: 1, v: 1, g: 2}. What is the expected number of occurrences of the pattern 'g.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, k: 2, h: 1, d: 1, y: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, p: 1, w: 1, f: 1}, what is the expected number of times the pattern 'jw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, z: 1, d: 1, b: 2, h: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, b: 1, a: 2, o: 1}, what is the expected number of times the pattern 'a*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, r: 2, o: 1, f: 1, i: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, f: 2, o: 1, h: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'xo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 4, a: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, f: 4, t: 1}, what is the expected number of times the pattern 'tf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, q: 1, s: 1, n: 1, z: 2} to form a word, what is the expected number of matches of the pattern 's*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, y: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'a.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, k: 1, b: 1, v: 1, f: 2}, what is the expected number of times the pattern 'f+k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, r: 1, s: 1, e: 3}, what is the expected number of times the pattern 'r+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, a: 1, c: 1, k: 1, v: 2}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, z: 1, o: 1, m: 1, k: 2}. What is the expected number of occurrences of the pattern 'k.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, g: 2, a: 1, d: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, v: 4}. What is the expected number of occurrences of the pattern 'v*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, n: 1, a: 2, u: 1}. What is the expected number of occurrences of the pattern 'au*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, r: 3}, what is the expected number of times the pattern 'r+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, x: 3, q: 1}. What is the expected number of occurrences of the pattern 'q.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 4, i: 2}, what is the expected number of times the pattern 'yi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, p: 4}, what is the expected number of times the pattern 'g*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, g: 4} to form a word, what is the expected number of matches of the pattern 'o*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 4, m: 1, p: 1}. What is the expected number of occurrences of the pattern 'm.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, p: 4}, what is the expected number of times the pattern 'p+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, n: 3, l: 1} to form a word, what is the expected number of matches of the pattern 'h*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, i: 3}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, t: 1, i: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'lt+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 4, i: 2}. What is the expected number of occurrences of the pattern 'i*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, b: 1, y: 2, p: 1}. What is the expected number of occurrences of the pattern 'c*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, t: 2, j: 2, o: 1} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'q*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, n: 2, c: 1, x: 1, f: 1}. What is the expected number of occurrences of the pattern 'n+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, n: 3, k: 1, e: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, w: 1, r: 3, s: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, f: 1, b: 1, t: 2, w: 1}, what is the expected number of times the pattern 'w*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, g: 1, r: 1, t: 1, j: 1}. What is the expected number of occurrences of the pattern 'j.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 4, i: 2} to form a word, what is the expected number of matches of the pattern 'yi+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, e: 2, o: 2, f: 1}. What is the expected number of occurrences of the pattern 'jf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, i: 1, p: 1, f: 1, g: 2}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, u: 1, h: 3} to form a word, what is the expected number of matches of the pattern 'y+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, q: 2, h: 2}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, i: 1, c: 1, v: 2, p: 1}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, l: 1, p: 2, v: 1}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 5, g: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, m: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 5, r: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, z: 3}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, m: 1, q: 1, c: 2, p: 1}. What is the expected number of occurrences of the pattern 'q*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, i: 1, p: 2, r: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, r: 2, j: 3}. What is the expected number of occurrences of the pattern 'r.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, t: 2, m: 2}. What is the expected number of occurrences of the pattern 'tm+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, f: 1, v: 3, d: 1} to form a word, what is the expected number of matches of the pattern 'av+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, i: 4}. What is the expected number of occurrences of the pattern 'g+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, h: 2}. What is the expected number of occurrences of the pattern 'uh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, f: 3, s: 2} to form a word, what is the expected number of matches of the pattern 's+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, l: 1, d: 1, u: 1, p: 2}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, r: 1, o: 2, d: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'oz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, m: 1, e: 1, b: 1, y: 2}, what is the expected number of times the pattern 'e.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 4, m: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'dm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, v: 1, u: 1, g: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'u.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, n: 2, p: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, c: 4} to form a word, what is the expected number of matches of the pattern 'j+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, o: 4}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 4, u: 2}. What is the expected number of occurrences of the pattern 'u.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, n: 3, h: 1}. What is the expected number of occurrences of the pattern 'ht*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, m: 1, r: 1, l: 1, t: 1} to form a word, what is the expected number of matches of the pattern 't.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, b: 2, v: 1, r: 2}. What is the expected number of occurrences of the pattern 'a*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, d: 1, g: 1, l: 1}. What is the expected number of occurrences of the pattern 'l.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, q: 1, k: 2, l: 1, s: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, e: 2, g: 1, z: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'ne*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 4, u: 2}. What is the expected number of occurrences of the pattern 'h+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 5, n: 1}. What is the expected number of occurrences of the pattern 'cn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 4, e: 2} to form a word, what is the expected number of matches of the pattern 'pe*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, a: 2, r: 1, w: 1}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 4, a: 2} to form a word, what is the expected number of matches of the pattern 'ac+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, k: 2, v: 2}, what is the expected number of times the pattern 'dk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, i: 3} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, f: 2, b: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'a+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, f: 1, e: 2, p: 1, k: 1}. What is the expected number of occurrences of the pattern 'ek+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, c: 2, t: 1} to form a word, what is the expected number of matches of the pattern 'tc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, p: 2, b: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, d: 3, w: 2}. What is the expected number of occurrences of the pattern 'wt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, x: 5}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, x: 2, q: 3}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, n: 2, i: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'iu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 4, r: 2}, what is the expected number of times the pattern 'e.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, w: 1, b: 1, s: 1, e: 2}, what is the expected number of times the pattern 'nn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, q: 1, y: 2, i: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'h+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, j: 3}. What is the expected number of occurrences of the pattern 'c+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, d: 4}, what is the expected number of times the pattern 'q+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, f: 2, d: 2}, what is the expected number of times the pattern 'jd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, b: 2, v: 2}, what is the expected number of times the pattern 'vv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, h: 1, v: 1, b: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, y: 1, t: 2, c: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, z: 1, f: 3}, what is the expected number of times the pattern 'qf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, w: 3, q: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, i: 4}. What is the expected number of occurrences of the pattern 'i.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, j: 2, s: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 4, b: 2} to form a word, what is the expected number of matches of the pattern 'n+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, v: 2, c: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'vc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, o: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'ow+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 5, h: 1}. What is the expected number of occurrences of the pattern 'h.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, u: 1, z: 2, r: 1}. What is the expected number of occurrences of the pattern 'z+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, h: 4}. What is the expected number of occurrences of the pattern 'z*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, u: 1, m: 2, r: 1}, what is the expected number of times the pattern 'uk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, i: 2, j: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'j.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, e: 1, l: 2, g: 1}. What is the expected number of occurrences of the pattern 'el+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, l: 1, f: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'fs+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, q: 1, e: 2}. What is the expected number of occurrences of the pattern 'q*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, x: 1, y: 1, j: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'j*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, l: 3, t: 1, e: 1}, what is the expected number of times the pattern 'tl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, q: 2, s: 2} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, p: 1, e: 1, n: 2}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, z: 1, h: 3, c: 1} to form a word, what is the expected number of matches of the pattern 'h.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, q: 2, f: 1, y: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'g*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 4, c: 2}, what is the expected number of times the pattern 'cy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, m: 5} to form a word, what is the expected number of matches of the pattern 'm+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, d: 1, k: 2}, what is the expected number of times the pattern 'dk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, c: 2, s: 1, h: 2}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 4, x: 2} to form a word, what is the expected number of matches of the pattern 'wx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, s: 1, v: 1, t: 1} to form a word, what is the expected number of matches of the pattern 't+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, t: 1, r: 2, c: 1, u: 1}. What is the expected number of occurrences of the pattern 'jt+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, x: 1, r: 2, c: 2}. What is the expected number of occurrences of the pattern 'x.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, j: 1, x: 2, b: 1, a: 1}, what is the expected number of times the pattern 'a*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, r: 1, c: 1, q: 2}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, p: 2, l: 1, i: 1, u: 1}. What is the expected number of occurrences of the pattern 'pl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, x: 1, h: 1, i: 1}. What is the expected number of occurrences of the pattern 'x+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 4, r: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, k: 1, x: 2}, what is the expected number of times the pattern 'x.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, x: 2, u: 1, v: 2}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, d: 5} to form a word, what is the expected number of matches of the pattern 'dg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, u: 3, y: 1}, what is the expected number of times the pattern 'u+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, p: 1, a: 3} to form a word, what is the expected number of matches of the pattern 'py+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, n: 1, v: 3, m: 1}. What is the expected number of occurrences of the pattern 'm*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 4, z: 2} to form a word, what is the expected number of matches of the pattern 'zi*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, o: 2, n: 3}. What is the expected number of occurrences of the pattern 'n.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 3, e: 3} to form a word, what is the expected number of matches of the pattern 'r+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, s: 1, y: 1, i: 2, l: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, v: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'vx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, d: 1, k: 1, r: 2, h: 1}, what is the expected number of times the pattern 'k*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, s: 2, r: 1, j: 1, a: 1}. What is the expected number of occurrences of the pattern 'r+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 4, n: 2} to form a word, what is the expected number of matches of the pattern 'n+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, u: 2, f: 2, k: 1}. What is the expected number of occurrences of the pattern 'f+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, y: 1, x: 1, b: 1, u: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, k: 1, q: 2, t: 1, u: 1} to form a word, what is the expected number of matches of the pattern 't+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, y: 2, d: 2}, what is the expected number of times the pattern 'dy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, z: 1, x: 1, s: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'si+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, k: 3}. What is the expected number of occurrences of the pattern 'k*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, d: 4}. What is the expected number of occurrences of the pattern 'w+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, f: 3, p: 1} to form a word, what is the expected number of matches of the pattern 'pf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 4, a: 2} to form a word, what is the expected number of matches of the pattern 'z+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, d: 3, y: 1}, what is the expected number of times the pattern 'i+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 4, r: 1, j: 1}. What is the expected number of occurrences of the pattern 'jf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, c: 4}. What is the expected number of occurrences of the pattern 'c.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, u: 1, b: 1, m: 2, v: 1}. What is the expected number of occurrences of the pattern 'p*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, v: 1, b: 1, k: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'v*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, w: 3}. What is the expected number of occurrences of the pattern 'o.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, a: 2, c: 1, d: 1, e: 1}. What is the expected number of occurrences of the pattern 'ea*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 5, w: 1}, what is the expected number of times the pattern 'h*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, z: 2, j: 2}, what is the expected number of times the pattern 'ja+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, s: 2, y: 3}, what is the expected number of times the pattern 'l.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, p: 3}. What is the expected number of occurrences of the pattern 'p+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, i: 5} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, s: 4}, what is the expected number of times the pattern 'se*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 5, w: 1}, what is the expected number of times the pattern 's.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, y: 3} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, o: 3}. What is the expected number of occurrences of the pattern 'o*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, k: 4} to form a word, what is the expected number of matches of the pattern 'hk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, c: 3} to form a word, what is the expected number of matches of the pattern 'cn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, z: 4}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, o: 3, m: 2}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, a: 1, f: 1, k: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, r: 2, p: 1, q: 2} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, d: 1, i: 1, l: 1, k: 2}. What is the expected number of occurrences of the pattern 'i.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, u: 1, z: 2, o: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, b: 1, j: 1, o: 2, v: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, g: 1, n: 2, y: 2}, what is the expected number of times the pattern 'sy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, d: 2, u: 2}, what is the expected number of times the pattern 'ud+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, d: 1, a: 1, i: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, t: 1, z: 1, n: 3}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, h: 1, m: 3}, what is the expected number of times the pattern 'h+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, l: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'am+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, u: 1, a: 1, w: 1, v: 1}, what is the expected number of times the pattern 'a+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, r: 1, s: 1, c: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'cs+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, s: 3, i: 1}, what is the expected number of times the pattern 'i+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, u: 2, s: 2, a: 1}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, h: 4}, what is the expected number of times the pattern 'h*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, x: 2, m: 1, a: 2}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, j: 2, o: 1, i: 1}, what is the expected number of times the pattern 'o+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, f: 1, a: 1, v: 2, k: 1}. What is the expected number of occurrences of the pattern 'vf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, w: 3, k: 1}, what is the expected number of times the pattern 'wi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 4, q: 2}. What is the expected number of occurrences of the pattern 'rq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 4, b: 2} to form a word, what is the expected number of matches of the pattern 'cc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, g: 1, w: 2, y: 1, i: 1}, what is the expected number of times the pattern 'g.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, i: 3, b: 2} to form a word, what is the expected number of matches of the pattern 'il*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, b: 1, n: 1, q: 1, c: 1}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, y: 1, v: 2}, what is the expected number of times the pattern 'yv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, k: 3} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, t: 2, r: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, u: 3}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, v: 3, x: 1, r: 1}. What is the expected number of occurrences of the pattern 'rc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, u: 2, r: 1, x: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, u: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'u*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, q: 5}. What is the expected number of occurrences of the pattern 'd+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, p: 2, a: 1}, what is the expected number of times the pattern 'q.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, h: 3, x: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, p: 2, b: 1, x: 1, z: 1}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, u: 1, q: 1, s: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'j+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, a: 3, h: 2}, what is the expected number of times the pattern 'a*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 5, c: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, o: 1, u: 1, j: 2}, what is the expected number of times the pattern 'u*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, p: 1, j: 1, f: 2, z: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, q: 3} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 4, t: 2}. What is the expected number of occurrences of the pattern 'tx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, n: 2, j: 1}, what is the expected number of times the pattern 'g.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'r*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, c: 3, w: 1}, what is the expected number of times the pattern 'c+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, q: 1, r: 1, y: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'q.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, u: 1, i: 2}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, v: 2, x: 1, w: 1}. What is the expected number of occurrences of the pattern 'v*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, z: 3, a: 2} to form a word, what is the expected number of matches of the pattern 'a+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, l: 1, j: 1, m: 1, y: 1}, what is the expected number of times the pattern 'rl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, b: 1, x: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'n.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, w: 4}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, y: 1, s: 2, c: 1, q: 1}, what is the expected number of times the pattern 'y*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, c: 2, p: 1, w: 1, a: 1}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, t: 3}. What is the expected number of occurrences of the pattern 't*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, s: 3}. What is the expected number of occurrences of the pattern 'es+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, a: 2, z: 1, h: 1}, what is the expected number of times the pattern 'v.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, t: 2, i: 1, y: 1, s: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, d: 3} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, k: 2, j: 2}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 4, l: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, c: 3, i: 2}. What is the expected number of occurrences of the pattern 'i*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, q: 1, i: 2, d: 1, o: 1}. What is the expected number of occurrences of the pattern 'q*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, n: 1, e: 2, s: 1, h: 1}, what is the expected number of times the pattern 'j.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, i: 1, v: 2, r: 1, x: 1}. What is the expected number of occurrences of the pattern 'i.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, f: 2, x: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, u: 2, b: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, n: 1, k: 2, a: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, g: 1, q: 1, i: 2, x: 1} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, w: 3}. What is the expected number of occurrences of the pattern 'h+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, p: 1, o: 1, r: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'r+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, n: 2, l: 1, x: 1}. What is the expected number of occurrences of the pattern 'n*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, b: 1, n: 1, l: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'ab*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, w: 1, i: 2, e: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'eu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, y: 1, o: 1, e: 1, u: 1}, what is the expected number of times the pattern 'u.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, o: 2, z: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'g*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, x: 3}, what is the expected number of times the pattern 'f+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, q: 3}. What is the expected number of occurrences of the pattern 's.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, t: 1, y: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, u: 4}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 5, t: 1} to form a word, what is the expected number of matches of the pattern 't.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, c: 1, p: 1, v: 2}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, g: 1, r: 1, k: 1, o: 1}. What is the expected number of occurrences of the pattern 'g*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, e: 1, w: 2}. What is the expected number of occurrences of the pattern 'we+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, x: 1, h: 2, n: 2}, what is the expected number of times the pattern 'x.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 4, o: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'x.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, y: 1, e: 2, b: 1}, what is the expected number of times the pattern 'r*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, v: 1, b: 1, c: 1}, what is the expected number of times the pattern 'c+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, c: 1, x: 1, o: 2, v: 1}, what is the expected number of times the pattern 'x*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, q: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'zm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, s: 1, j: 1, t: 1, w: 2}. What is the expected number of occurrences of the pattern 'zt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, o: 1, s: 2, a: 2} to form a word, what is the expected number of matches of the pattern 's+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, d: 1, r: 1, g: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'rt+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, a: 5}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, j: 3, o: 2}, what is the expected number of times the pattern 'jh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, m: 1, s: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'y.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, m: 1, l: 1, w: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'lw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, e: 3}. What is the expected number of occurrences of the pattern 'o+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, t: 3} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, n: 2, b: 2}. What is the expected number of occurrences of the pattern 't*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 4, v: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, t: 2, o: 3}. What is the expected number of occurrences of the pattern 't+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 4, n: 2}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, c: 1, m: 3}. What is the expected number of occurrences of the pattern 'm+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 4, x: 2}. What is the expected number of occurrences of the pattern 'ox+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, d: 1, o: 1, t: 1, b: 1}. What is the expected number of occurrences of the pattern 'to*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, y: 1, n: 2, c: 1, k: 1}, what is the expected number of times the pattern 'y.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, n: 1, m: 1, z: 2, t: 1} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, b: 3, m: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, b: 2, q: 2}. What is the expected number of occurrences of the pattern 'qq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, a: 2, r: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, w: 1, z: 3, j: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, i: 1, c: 1, p: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, p: 1, h: 1, c: 1, i: 1}. What is the expected number of occurrences of the pattern 'c+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, b: 2, u: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, g: 1, q: 3}, what is the expected number of times the pattern 'e.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, e: 3}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, u: 1, p: 2, o: 2}, what is the expected number of times the pattern 'u+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, z: 1, l: 2, x: 1, f: 1}. What is the expected number of occurrences of the pattern 'x.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, v: 1, t: 3}, what is the expected number of times the pattern 'f+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, g: 3}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, y: 2, b: 2, k: 1}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, u: 1, c: 1, t: 1, v: 1}. What is the expected number of occurrences of the pattern 'k*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, f: 1, o: 2, u: 1, p: 1}. What is the expected number of occurrences of the pattern 'v.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, k: 2, g: 1, u: 1}, what is the expected number of times the pattern 'iu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, a: 4} to form a word, what is the expected number of matches of the pattern 'fa*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, s: 2, f: 2, u: 1}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, z: 2, y: 1}, what is the expected number of times the pattern 'k*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, s: 1, q: 1, y: 2, x: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, l: 1, d: 2, t: 2}, what is the expected number of times the pattern 'td*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, j: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, y: 2, p: 2, m: 1} to form a word, what is the expected number of matches of the pattern 'pk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, h: 3, x: 1, i: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, v: 1, q: 1, y: 1, b: 1}, what is the expected number of times the pattern 'y+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, y: 3, t: 2} to form a word, what is the expected number of matches of the pattern 'k+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, m: 1, o: 1, l: 1}, what is the expected number of times the pattern 'w+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, s: 3}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, n: 4} to form a word, what is the expected number of matches of the pattern 'n+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, j: 1, y: 1, f: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'y.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, j: 3}. What is the expected number of occurrences of the pattern 'j+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, k: 1, e: 1, q: 1, m: 1}, what is the expected number of times the pattern 'k+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 3, o: 3}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, d: 1, g: 2}, what is the expected number of times the pattern 'r*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, z: 3, d: 1}. What is the expected number of occurrences of the pattern 'z.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, t: 3, p: 1}. What is the expected number of occurrences of the pattern 't.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, u: 5}, what is the expected number of times the pattern 'k*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 4, c: 2}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 3, k: 3}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, l: 2, d: 2}. What is the expected number of occurrences of the pattern 'sd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, o: 1, e: 4} to form a word, what is the expected number of matches of the pattern 'ef+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, d: 1, u: 1, e: 1}, what is the expected number of times the pattern 'u*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, e: 2, q: 1, w: 1}. What is the expected number of occurrences of the pattern 'd*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, y: 1, h: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'hy*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, w: 3, y: 2}. What is the expected number of occurrences of the pattern 'u+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, u: 1, v: 1, r: 2}. What is the expected number of occurrences of the pattern 'y+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, g: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'a.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, g: 2, u: 3} to form a word, what is the expected number of matches of the pattern 'u*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, a: 3, l: 2}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, a: 2, t: 1, e: 1}, what is the expected number of times the pattern 'ae*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, r: 3}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, t: 1, x: 2, y: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'f*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'oh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, w: 1, y: 1, m: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'yw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, f: 1, p: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, d: 1, a: 1, v: 2, o: 1}. What is the expected number of occurrences of the pattern 'ud*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, i: 2, h: 3} to form a word, what is the expected number of matches of the pattern 'qi+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, g: 1, d: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'ga+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, o: 2, a: 2}. What is the expected number of occurrences of the pattern 'a.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 4, m: 2}, what is the expected number of times the pattern 'm*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, d: 2, x: 1, z: 2}, what is the expected number of times the pattern 'g*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, d: 2, a: 1}, what is the expected number of times the pattern 'ad+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, l: 3, q: 1}. What is the expected number of occurrences of the pattern 'lq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, n: 3}. What is the expected number of occurrences of the pattern 'nq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, w: 1, u: 3} to form a word, what is the expected number of matches of the pattern 'uf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, i: 1, v: 2, x: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, t: 1, z: 1, o: 2}. What is the expected number of occurrences of the pattern 'o.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 5, e: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, d: 1, l: 1, g: 1, y: 1}, what is the expected number of times the pattern 'y+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, l: 3, g: 1}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, h: 1, o: 2, s: 2} to form a word, what is the expected number of matches of the pattern 'io*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 4, a: 1, k: 1}, what is the expected number of times the pattern 'kn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, p: 4}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, i: 2, a: 1, c: 2}, what is the expected number of times the pattern 'ac+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, d: 4}. What is the expected number of occurrences of the pattern 'dy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 3, o: 3}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 4, k: 2} to form a word, what is the expected number of matches of the pattern 'k*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, j: 2, y: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'p.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 4, i: 2}. What is the expected number of occurrences of the pattern 'i.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 5, d: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, n: 1, h: 3}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, q: 1, i: 1, h: 1, r: 2}, what is the expected number of times the pattern 'q.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, b: 1, e: 1, l: 1}. What is the expected number of occurrences of the pattern 'e+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, x: 3, e: 1, g: 1}. What is the expected number of occurrences of the pattern 'k+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, o: 1, e: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'oe+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, k: 1, y: 2, m: 1, q: 1}, what is the expected number of times the pattern 'r.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, m: 1, b: 2, q: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'q+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 4, k: 2}, what is the expected number of times the pattern 'kr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, j: 2, y: 1, q: 2} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, o: 3, i: 2}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, d: 2, j: 1, f: 2} to form a word, what is the expected number of matches of the pattern 't*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, x: 1, r: 1, m: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, a: 2, x: 3}. What is the expected number of occurrences of the pattern 'ay*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 3, f: 1, c: 2}. What is the expected number of occurrences of the pattern 'fn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, o: 1, p: 1, q: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'o.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, w: 2, o: 2, l: 1}, what is the expected number of times the pattern 'al*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, n: 1, z: 4} to form a word, what is the expected number of matches of the pattern 'z+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, z: 1, x: 1, d: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, b: 2, e: 1, i: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, n: 1, g: 2}. What is the expected number of occurrences of the pattern 'z*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, z: 3, a: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, z: 1, s: 1, t: 1, m: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, s: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'u+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, g: 2, p: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'gi+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, a: 2, l: 2, g: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, l: 1, u: 1, n: 2, a: 1}. What is the expected number of occurrences of the pattern 'a*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, z: 2, y: 1, g: 2}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, j: 2, k: 1, o: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, n: 4} to form a word, what is the expected number of matches of the pattern 'ng+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, b: 1, k: 2, w: 1, t: 1}. What is the expected number of occurrences of the pattern 'qq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, b: 1, r: 1, t: 3}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, u: 2, v: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, b: 3}. What is the expected number of occurrences of the pattern 'k+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, l: 2, h: 1} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, s: 2, w: 3}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, k: 2, l: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, p: 4, c: 1}. What is the expected number of occurrences of the pattern 'c+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 3, z: 3} to form a word, what is the expected number of matches of the pattern 'r+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 4, f: 2} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, w: 5}, what is the expected number of times the pattern 'aw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, u: 3, d: 1} to form a word, what is the expected number of matches of the pattern 'u.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 3, b: 3}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, k: 1, f: 1, r: 1, y: 2}. What is the expected number of occurrences of the pattern 'k.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 4, j: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, g: 2, j: 2, l: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, p: 3, f: 1} to form a word, what is the expected number of matches of the pattern 'm+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 5, k: 1}. What is the expected number of occurrences of the pattern 'k+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, p: 1, h: 4}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, v: 1, n: 2, t: 1, u: 1}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, f: 2, o: 1, j: 1}. What is the expected number of occurrences of the pattern 'o.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, l: 2, x: 1, g: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, t: 3}, what is the expected number of times the pattern 'th*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, z: 1, a: 1, d: 2}, what is the expected number of times the pattern 'av+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, i: 2, u: 1, e: 1, z: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, n: 4} to form a word, what is the expected number of matches of the pattern 'an+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, h: 1, o: 3}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 4, p: 2} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, x: 2, c: 2}, what is the expected number of times the pattern 'm.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, n: 1, p: 1, z: 2, t: 1}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, g: 1, p: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'v+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, m: 4, n: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, f: 4}, what is the expected number of times the pattern 'v*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, i: 2, m: 1, d: 1, z: 1}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, k: 1, u: 3}, what is the expected number of times the pattern 'k*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, z: 2, k: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, l: 1, p: 1, o: 1, g: 2}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 4, z: 2} to form a word, what is the expected number of matches of the pattern 'l.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, o: 1, i: 1, n: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'n.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, p: 3}. What is the expected number of occurrences of the pattern 'h*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, w: 1, j: 3, t: 1}, what is the expected number of times the pattern 'j+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, o: 3}. What is the expected number of occurrences of the pattern 'o*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, x: 1, k: 1, v: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, v: 1, r: 1, l: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, e: 1, n: 2, y: 1, h: 1}. What is the expected number of occurrences of the pattern 'y*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, v: 1, m: 1, p: 2}. What is the expected number of occurrences of the pattern 'p*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 4, v: 2}, what is the expected number of times the pattern 'd.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, p: 1, z: 1, i: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'p*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, d: 2, g: 2}, what is the expected number of times the pattern 'g*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, r: 1, h: 4} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, p: 2, n: 2}, what is the expected number of times the pattern 'p+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, e: 1, s: 2, y: 1, h: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, k: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'ik*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, y: 1, t: 3} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, j: 1, m: 2, q: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'd+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, r: 1, a: 1, w: 1, e: 2}. What is the expected number of occurrences of the pattern 'e+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, h: 1, t: 1, o: 1, q: 2}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, v: 2, a: 1, o: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, b: 1, i: 1, z: 1, x: 1}, what is the expected number of times the pattern 'x*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, g: 2, n: 1, y: 1, z: 1}, what is the expected number of times the pattern 'xz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, e: 1, h: 3}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, p: 3}, what is the expected number of times the pattern 'xp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, b: 1, y: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'yw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, s: 2, x: 1, m: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'sj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, q: 2, v: 3}. What is the expected number of occurrences of the pattern 'q*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, e: 2, k: 3}, what is the expected number of times the pattern 'ke+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, j: 1, g: 2, p: 1, b: 1}. What is the expected number of occurrences of the pattern 'wj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, d: 1, r: 1, v: 2, f: 1}. What is the expected number of occurrences of the pattern 'v*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, u: 1, s: 3}, what is the expected number of times the pattern 'ud+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, u: 1, j: 1, a: 2, b: 1}, what is the expected number of times the pattern 'ca*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, w: 2, q: 3} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, z: 3}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, e: 1, w: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, c: 1, j: 1, v: 2}, what is the expected number of times the pattern 'j.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, x: 2, p: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'd+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, k: 1, s: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'js*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, k: 3}. What is the expected number of occurrences of the pattern 'km*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, o: 2, e: 2}. What is the expected number of occurrences of the pattern 'oc+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, r: 1, a: 1, u: 2}, what is the expected number of times the pattern 'r+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, v: 3, k: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'e*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, j: 2, r: 3} to form a word, what is the expected number of matches of the pattern 'mj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, d: 2, f: 1, e: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, g: 1, c: 2, n: 1, o: 1}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, t: 1, r: 2, e: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'rt+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, j: 2, q: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, r: 1, p: 3}, what is the expected number of times the pattern 'r+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, m: 1, a: 1, o: 2}, what is the expected number of times the pattern 'ao+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 5, t: 1}, what is the expected number of times the pattern 'it+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, q: 1, b: 2}. What is the expected number of occurrences of the pattern 'q*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, s: 2, i: 3} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, k: 4}, what is the expected number of times the pattern 'k+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, v: 1, p: 3, s: 1}, what is the expected number of times the pattern 'rv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, p: 1, c: 1, e: 2, u: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, d: 3}, what is the expected number of times the pattern 'c.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, e: 3, o: 2}, what is the expected number of times the pattern 'e.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 4, b: 2} to form a word, what is the expected number of matches of the pattern 'ob+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, a: 2, d: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'e*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, j: 4}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, h: 1, m: 2, y: 1}. What is the expected number of occurrences of the pattern 'h+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, p: 1, m: 1, a: 3}, what is the expected number of times the pattern 'p.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 5, r: 1}. What is the expected number of occurrences of the pattern 'pr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, b: 1, e: 3} to form a word, what is the expected number of matches of the pattern 'j.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, n: 1, i: 1, j: 2} to form a word, what is the expected number of matches of the pattern 'nc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, b: 4}, what is the expected number of times the pattern 'n+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, b: 1, h: 2}. What is the expected number of occurrences of the pattern 'i+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, b: 1, g: 2}. What is the expected number of occurrences of the pattern 'c+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, q: 1, c: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'ok*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, w: 2, e: 3} to form a word, what is the expected number of matches of the pattern 'j*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 4, h: 1, f: 1}. What is the expected number of occurrences of the pattern 'mf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, z: 2, f: 1, j: 2}. What is the expected number of occurrences of the pattern 'fj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, l: 1, h: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'n.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 4, j: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, q: 1, l: 4}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 4, b: 2}. What is the expected number of occurrences of the pattern 'a*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, y: 2, t: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'y*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, g: 1, p: 1, h: 1, u: 2}. What is the expected number of occurrences of the pattern 'g+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, e: 1, p: 1, t: 1, y: 1}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, p: 3} to form a word, what is the expected number of matches of the pattern 'h.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, j: 1, r: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'jx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, f: 2, i: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, x: 4} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, c: 2, v: 1, g: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, b: 2, k: 1, x: 1, d: 1}. What is the expected number of occurrences of the pattern 'l.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, n: 4}, what is the expected number of times the pattern 'nw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, p: 1, k: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'vl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, p: 2, b: 1}, what is the expected number of times the pattern 'jp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, l: 2, f: 2}, what is the expected number of times the pattern 'wf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, b: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, z: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'e.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 5, z: 1} to form a word, what is the expected number of matches of the pattern 'zp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, b: 4}. What is the expected number of occurrences of the pattern 'e*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, w: 3} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, t: 1, i: 3}, what is the expected number of times the pattern 'li*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, b: 2, y: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'ib+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, q: 5} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, r: 1, o: 2, h: 1}. What is the expected number of occurrences of the pattern 'h*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, l: 1, g: 2, j: 1, p: 1}. What is the expected number of occurrences of the pattern 'pg+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, s: 1, v: 3}, what is the expected number of times the pattern 'sv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, z: 2, w: 3}, what is the expected number of times the pattern 'w*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 3, u: 3}. What is the expected number of occurrences of the pattern 'up*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 4, c: 2} to form a word, what is the expected number of matches of the pattern 'l*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, h: 2, d: 1, t: 1, q: 1} to form a word, what is the expected number of matches of the pattern 't.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, l: 3, e: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'x.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, r: 1, e: 2, x: 1}. What is the expected number of occurrences of the pattern 'e.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, g: 3} to form a word, what is the expected number of matches of the pattern 'l.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, z: 3} to form a word, what is the expected number of matches of the pattern 'iz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, c: 3} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, y: 2, z: 2}. What is the expected number of occurrences of the pattern 'g.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, u: 2, q: 2}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, e: 2, w: 2}, what is the expected number of times the pattern 'w*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, g: 1, m: 2}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, b: 3, t: 1, d: 1}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, g: 3}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, i: 1, k: 3, m: 1} to form a word, what is the expected number of matches of the pattern 'e.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, g: 1, k: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'gz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, x: 1, u: 3} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, t: 1, u: 1, s: 2} to form a word, what is the expected number of matches of the pattern 's.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, o: 1, h: 1, b: 2}, what is the expected number of times the pattern 'o.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, n: 1, i: 3, l: 1}, what is the expected number of times the pattern 'en*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, z: 3}. What is the expected number of occurrences of the pattern 'rz*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, n: 4} to form a word, what is the expected number of matches of the pattern 'ne+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, o: 3, z: 2} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, q: 2, o: 1, k: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'q*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, u: 1, f: 2, g: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'd*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, e: 1, d: 1, o: 1, m: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, o: 1, d: 1, u: 2}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, j: 1, i: 1, p: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'ai*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, h: 1, j: 1, d: 2, c: 1}, what is the expected number of times the pattern 'c+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, a: 2, p: 2}, what is the expected number of times the pattern 'pa+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 4, u: 2}. What is the expected number of occurrences of the pattern 'u+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, b: 2, u: 1, h: 1, m: 1}. What is the expected number of occurrences of the pattern 'vh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, h: 1, j: 1, q: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'i*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, l: 1, m: 3}. What is the expected number of occurrences of the pattern 'm+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, k: 2, g: 1, z: 1, q: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, h: 3, m: 1} to form a word, what is the expected number of matches of the pattern 'v*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, a: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'k+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, s: 3, q: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, d: 1, g: 1, l: 2, t: 1} to form a word, what is the expected number of matches of the pattern 'g+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, m: 1, i: 1, d: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, l: 1, i: 1, o: 3} to form a word, what is the expected number of matches of the pattern 'l*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, e: 1, u: 3}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, u: 1, z: 1, a: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, d: 2, f: 1, b: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 4, y: 2}. What is the expected number of occurrences of the pattern 'v.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, s: 4}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, y: 1, u: 2, z: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 4, t: 2}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, o: 4} to form a word, what is the expected number of matches of the pattern 'o+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, d: 2, k: 1, l: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, t: 4}, what is the expected number of times the pattern 't.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, z: 4, k: 1} to form a word, what is the expected number of matches of the pattern 'zk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 3, e: 3}, what is the expected number of times the pattern 'e*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, c: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'yc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, a: 1, i: 1, f: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, u: 1, i: 2, e: 2}, what is the expected number of times the pattern 'e*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, k: 5}. What is the expected number of occurrences of the pattern 'q.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, l: 2, f: 3}, what is the expected number of times the pattern 'lf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, y: 2, j: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'j*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, b: 1, i: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'd.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, n: 2, e: 3}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, s: 2, c: 1, q: 1, h: 1}, what is the expected number of times the pattern 'hc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, w: 4}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, b: 1, c: 1, l: 3}, what is the expected number of times the pattern 'lc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, s: 1, c: 1, r: 1}. What is the expected number of occurrences of the pattern 'd.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, t: 1, u: 2, x: 1, p: 1}. What is the expected number of occurrences of the pattern 'u*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, r: 3, l: 1} to form a word, what is the expected number of matches of the pattern 'l.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, o: 1, f: 1, i: 2}. What is the expected number of occurrences of the pattern 'if*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, d: 3}. What is the expected number of occurrences of the pattern 'i+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, s: 1, o: 1, l: 1, q: 2}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, g: 1, i: 1, l: 1}. What is the expected number of occurrences of the pattern 'l*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, i: 3, l: 2}. What is the expected number of occurrences of the pattern 'ip*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, e: 2, w: 1}, what is the expected number of times the pattern 'w.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, g: 1, k: 1, v: 2, u: 1}, what is the expected number of times the pattern 'v.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, p: 1, s: 1, k: 1, z: 1}, what is the expected number of times the pattern 'uk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'u.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, c: 1, e: 1, y: 1, t: 1}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, v: 1, s: 1, p: 1, n: 1}, what is the expected number of times the pattern 'p.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, e: 3}. What is the expected number of occurrences of the pattern 'f*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'th+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, p: 2, i: 3}. What is the expected number of occurrences of the pattern 'a+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, x: 2, k: 3}. What is the expected number of occurrences of the pattern 'x+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, a: 1, w: 1, h: 1, y: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, u: 1, a: 1, i: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, i: 3}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, l: 1, s: 1, o: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'od+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, h: 2, a: 3}, what is the expected number of times the pattern 'a+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, y: 1, b: 2, x: 1}, what is the expected number of times the pattern 'xm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, h: 1, k: 4} to form a word, what is the expected number of matches of the pattern 'km*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, f: 1, b: 3, i: 1}, what is the expected number of times the pattern 'i+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'h+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, n: 3}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, m: 1, j: 3, h: 1} to form a word, what is the expected number of matches of the pattern 'a+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, l: 2, t: 1, c: 1, g: 1} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, n: 3} to form a word, what is the expected number of matches of the pattern 'n.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, n: 2, a: 2, j: 1}, what is the expected number of times the pattern 'za*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 4, j: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'jk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, h: 2, l: 2}, what is the expected number of times the pattern 'fh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, j: 1, q: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, k: 3}, what is the expected number of times the pattern 'k+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, s: 1, j: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'sj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, o: 1, m: 3, c: 1}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, w: 1, e: 1, b: 1, n: 2}. What is the expected number of occurrences of the pattern 'e*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, v: 3, i: 1}. What is the expected number of occurrences of the pattern 'i+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, i: 1, y: 3, d: 1} to form a word, what is the expected number of matches of the pattern 'df*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, v: 1, e: 1, o: 1, i: 2}, what is the expected number of times the pattern 'v*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, f: 3} to form a word, what is the expected number of matches of the pattern 'lf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, s: 1, h: 1, o: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'o+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, y: 4} to form a word, what is the expected number of matches of the pattern 'x*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, i: 2, p: 1, z: 1, k: 1}, what is the expected number of times the pattern 'ik*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, g: 2, o: 1, l: 2}, what is the expected number of times the pattern 't*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, d: 1, i: 2, e: 1, v: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, n: 1, m: 2, c: 2}, what is the expected number of times the pattern 'c*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 4, l: 2}. What is the expected number of occurrences of the pattern 'li+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, s: 1, y: 1, a: 2}. What is the expected number of occurrences of the pattern 'ua+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, y: 1, n: 1, a: 3} to form a word, what is the expected number of matches of the pattern 'y*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, o: 1, r: 1, g: 2}, what is the expected number of times the pattern 'rg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 4, k: 2} to form a word, what is the expected number of matches of the pattern 'kj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, q: 4, e: 1}, what is the expected number of times the pattern 'z*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, k: 2, w: 1, g: 2}, what is the expected number of times the pattern 'k.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, n: 2, l: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, q: 1, j: 2, c: 1, e: 1}, what is the expected number of times the pattern 'qn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, s: 3}, what is the expected number of times the pattern 'w*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, x: 1, w: 1, m: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'kx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 4, d: 2}. What is the expected number of occurrences of the pattern 'ds+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, i: 1, f: 3} to form a word, what is the expected number of matches of the pattern 'i*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, j: 1, l: 1, c: 1}. What is the expected number of occurrences of the pattern 'cj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, v: 3, f: 2} to form a word, what is the expected number of matches of the pattern 'vs*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, s: 2, p: 1}, what is the expected number of times the pattern 's+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 4, z: 2} to form a word, what is the expected number of matches of the pattern 'z+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, e: 3} to form a word, what is the expected number of matches of the pattern 'ec*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, c: 3, p: 1}, what is the expected number of times the pattern 'pc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, i: 1, b: 2}. What is the expected number of occurrences of the pattern 'x.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, p: 1, m: 1, j: 1, b: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 5, r: 1}. What is the expected number of occurrences of the pattern 'r*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, r: 2, t: 1, e: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'ce*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, g: 2, z: 2}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, l: 3, s: 2}. What is the expected number of occurrences of the pattern 'l*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, t: 2, d: 3}, what is the expected number of times the pattern 't*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, q: 4}, what is the expected number of times the pattern 'a+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, j: 4}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 4, u: 2}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, c: 3}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, g: 1, e: 1, r: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'r*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 4, i: 2} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, q: 2, s: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'l.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, h: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'a.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, j: 1, t: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'j+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 4, z: 2}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, t: 1, h: 1, s: 1, g: 1}. What is the expected number of occurrences of the pattern 't*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, u: 2, n: 2}. What is the expected number of occurrences of the pattern 'u+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, t: 3, q: 2}. What is the expected number of occurrences of the pattern 'q.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, c: 4}, what is the expected number of times the pattern 'c+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, x: 1, r: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'xf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, f: 2}. What is the expected number of occurrences of the pattern 'f*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, t: 1, p: 1, v: 1, j: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, t: 1, k: 1, r: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'v*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, z: 1, a: 1, g: 1, b: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, a: 1, t: 3}, what is the expected number of times the pattern 't*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, x: 1, j: 1, i: 1, q: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, n: 2, p: 1}. What is the expected number of occurrences of the pattern 'pn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, g: 1, i: 2, c: 1, o: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, w: 3} to form a word, what is the expected number of matches of the pattern 'wi*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, h: 2, q: 2}, what is the expected number of times the pattern 'hz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, z: 2, o: 1, x: 1}. What is the expected number of occurrences of the pattern 'o+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, g: 2, f: 2, u: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, t: 2, w: 2} to form a word, what is the expected number of matches of the pattern 'rw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, d: 1, n: 3} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, u: 2, t: 3}. What is the expected number of occurrences of the pattern 'i+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, m: 2, t: 1, p: 1, f: 1}. What is the expected number of occurrences of the pattern 'hm*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 4, m: 2}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, d: 3} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, e: 2, r: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'rz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, m: 3, d: 2} to form a word, what is the expected number of matches of the pattern 'dm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, r: 4} to form a word, what is the expected number of matches of the pattern 'r+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, e: 4}. What is the expected number of occurrences of the pattern 'e.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, k: 2, u: 1, w: 1, g: 1}. What is the expected number of occurrences of the pattern 'uk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, h: 1, y: 2, k: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'r*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, m: 1, v: 2, x: 1}. What is the expected number of occurrences of the pattern 'a*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 4, f: 2}, what is the expected number of times the pattern 'fl*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, p: 1, l: 4} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, d: 4}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, o: 1, a: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'o.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 4, u: 1, o: 1}, what is the expected number of times the pattern 'e.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, i: 2, g: 3}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, g: 2, t: 3} to form a word, what is the expected number of matches of the pattern 'v*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 4, y: 2}. What is the expected number of occurrences of the pattern 'yc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, g: 1, i: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'q*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, i: 2, j: 2}, what is the expected number of times the pattern 'i.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, z: 1, u: 1, y: 1}. What is the expected number of occurrences of the pattern 'vz*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, h: 1, t: 1, o: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'ht+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, l: 5}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, f: 3}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, w: 3}. What is the expected number of occurrences of the pattern 'w.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, k: 2, j: 1, b: 1}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, e: 2, v: 2}. What is the expected number of occurrences of the pattern 'e*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, j: 3} to form a word, what is the expected number of matches of the pattern 'i+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, h: 5}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, i: 2, a: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, e: 1, v: 1, q: 2, t: 1}, what is the expected number of times the pattern 'ez+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, m: 3, k: 1, l: 1}. What is the expected number of occurrences of the pattern 'ck+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, y: 4} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, f: 2, j: 1, k: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'j+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, r: 1, z: 1, s: 3}, what is the expected number of times the pattern 'ms+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, b: 1, j: 1, u: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'j.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, w: 3}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, i: 1, u: 2, r: 2}. What is the expected number of occurrences of the pattern 'ri*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, t: 1, o: 1, w: 1, a: 2}, what is the expected number of times the pattern 'w*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, t: 1, z: 1, h: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'hs+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, o: 4}, what is the expected number of times the pattern 'o*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, e: 1, d: 1, h: 1, o: 2}, what is the expected number of times the pattern 'go+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, t: 4, d: 1} to form a word, what is the expected number of matches of the pattern 'n*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, r: 4}. What is the expected number of occurrences of the pattern 'jr+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, m: 2, a: 3}. What is the expected number of occurrences of the pattern 's.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, w: 1, x: 1, n: 2, a: 1}. What is the expected number of occurrences of the pattern 'ak+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, z: 1, l: 3, q: 1} to form a word, what is the expected number of matches of the pattern 'z+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, y: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, q: 3}. What is the expected number of occurrences of the pattern 'q.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 4, e: 2}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, l: 3, e: 1, s: 1}, what is the expected number of times the pattern 'sl*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, q: 2, n: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'nq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, v: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'f.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, b: 2, j: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, i: 2, k: 1, t: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'k+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, w: 3}, what is the expected number of times the pattern 'w+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, m: 2, i: 1, q: 2}. What is the expected number of occurrences of the pattern 'i.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 4, o: 2}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, c: 3, u: 1}, what is the expected number of times the pattern 'uc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, k: 2, i: 3}, what is the expected number of times the pattern 'nk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 4, a: 2} to form a word, what is the expected number of matches of the pattern 'a+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 4, x: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, r: 1, y: 1, l: 1, h: 1}, what is the expected number of times the pattern 'h.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, x: 2, q: 2, s: 1}. What is the expected number of occurrences of the pattern 'i+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, y: 3, v: 2}. What is the expected number of occurrences of the pattern 'v.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, k: 4} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, v: 2, e: 2}. What is the expected number of occurrences of the pattern 'v+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, o: 2, s: 3} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, q: 2, d: 3} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, z: 4}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 5, f: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, f: 2, s: 2, c: 1}. What is the expected number of occurrences of the pattern 'f*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, f: 1, i: 1, v: 1, x: 2}, what is the expected number of times the pattern 'x*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, t: 1, v: 1, n: 2, c: 1} to form a word, what is the expected number of matches of the pattern 'v+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, c: 2, r: 1, z: 1}, what is the expected number of times the pattern 'rz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, v: 1, q: 1, y: 1, n: 2}, what is the expected number of times the pattern 'qy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, n: 1, j: 1, t: 1, z: 1}, what is the expected number of times the pattern 'j*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, x: 1, f: 1, n: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'f*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, b: 2, u: 1, k: 2}. What is the expected number of occurrences of the pattern 'fu+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, t: 3} to form a word, what is the expected number of matches of the pattern 'ti*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, l: 1, b: 2, k: 1, a: 1}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, f: 1, q: 2, u: 1, h: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, b: 2, h: 1, l: 1, m: 1}. What is the expected number of occurrences of the pattern 'g*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, m: 1, x: 1, z: 1, e: 1}. What is the expected number of occurrences of the pattern 'm.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, h: 1, e: 1, y: 1}. What is the expected number of occurrences of the pattern 'q*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, g: 1, a: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, f: 5} to form a word, what is the expected number of matches of the pattern 'p.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, j: 2, r: 1, z: 1, c: 1}. What is the expected number of occurrences of the pattern 'r.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, l: 1, k: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, p: 3} to form a word, what is the expected number of matches of the pattern 'sp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, s: 1, f: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, y: 4, s: 1} to form a word, what is the expected number of matches of the pattern 'yh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, x: 5}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, t: 1, j: 1, q: 3} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, a: 1, u: 1, q: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'u.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, o: 2, i: 1, g: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, r: 3, j: 2} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'z*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, r: 1, d: 1, c: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'rj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 4, q: 2} to form a word, what is the expected number of matches of the pattern 'q*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, d: 3, s: 1}. What is the expected number of occurrences of the pattern 'u*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, m: 1, h: 2, e: 2}, what is the expected number of times the pattern 'm.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, l: 2, y: 3}, what is the expected number of times the pattern 'ym*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, m: 1, z: 1, g: 2, u: 1}. What is the expected number of occurrences of the pattern 'zm*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, m: 3} to form a word, what is the expected number of matches of the pattern 'm+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, y: 1, e: 3}. What is the expected number of occurrences of the pattern 'ya*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, c: 1, d: 1, p: 2, a: 1}, what is the expected number of times the pattern 'p.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, g: 1, x: 1, r: 1, m: 2}, what is the expected number of times the pattern 'cg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, l: 2, b: 1, j: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 4, a: 2} to form a word, what is the expected number of matches of the pattern 'a.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, j: 3}, what is the expected number of times the pattern 'jg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, m: 3, d: 2}, what is the expected number of times the pattern 'd*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, i: 1, j: 1, n: 2}, what is the expected number of times the pattern 'j+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, v: 4}. What is the expected number of occurrences of the pattern 't+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, c: 1, q: 2, x: 1, o: 1}. What is the expected number of occurrences of the pattern 'xo+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 3, j: 1, a: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, f: 2, z: 2}. What is the expected number of occurrences of the pattern 'z+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, x: 1, u: 3, k: 1} to form a word, what is the expected number of matches of the pattern 'uk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, s: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'x+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, y: 2, j: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, w: 5}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, k: 1, g: 1, d: 1, v: 1}. What is the expected number of occurrences of the pattern 'vk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 4, y: 2} to form a word, what is the expected number of matches of the pattern 'y*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, h: 4}, what is the expected number of times the pattern 'd+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 4, i: 1, f: 1}, what is the expected number of times the pattern 'fo+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, i: 1, q: 1, u: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'i.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, s: 2, w: 2, f: 1}. What is the expected number of occurrences of the pattern 'wf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, u: 1, h: 3, f: 1}, what is the expected number of times the pattern 'h*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, u: 1, e: 2, o: 1, v: 1}, what is the expected number of times the pattern 'o*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, t: 2, r: 2}, what is the expected number of times the pattern 't+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, k: 2, l: 1, f: 1, d: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, n: 3} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, g: 2, u: 1, k: 1, j: 1}, what is the expected number of times the pattern 'ik*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 4, s: 2}, what is the expected number of times the pattern 'sc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, w: 3, k: 1}. What is the expected number of occurrences of the pattern 'w.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, x: 2, q: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'dt+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, q: 3, l: 2} to form a word, what is the expected number of matches of the pattern 'l*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, x: 2, i: 1, e: 1, v: 1}, what is the expected number of times the pattern 'v+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, u: 3}, what is the expected number of times the pattern 'u.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, w: 3}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 4, j: 2} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, s: 1, i: 3}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, l: 2, z: 1, v: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'u*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, j: 1, s: 2}, what is the expected number of times the pattern 'j*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, h: 3, e: 1, n: 1}, what is the expected number of times the pattern 'h*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, y: 3}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, j: 1, u: 1, s: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, n: 1, x: 3}. What is the expected number of occurrences of the pattern 'n+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 4, x: 2}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, x: 1, s: 1, n: 1, m: 1}. What is the expected number of occurrences of the pattern 'l.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, q: 3}. What is the expected number of occurrences of the pattern 'x*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, o: 1, d: 4}, what is the expected number of times the pattern 'od*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, p: 1, e: 1, h: 1, a: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 4, e: 2}, what is the expected number of times the pattern 'm+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, k: 1, d: 1, u: 3} to form a word, what is the expected number of matches of the pattern 'y*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, d: 5}, what is the expected number of times the pattern 'd.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, x: 3, f: 1}. What is the expected number of occurrences of the pattern 'x*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, w: 2, h: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'w+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, y: 2, h: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, p: 1, u: 1, e: 2, i: 1}. What is the expected number of occurrences of the pattern 'e*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, l: 1, b: 1, y: 1, m: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, p: 2, h: 1, v: 1}, what is the expected number of times the pattern 'v*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, t: 1, e: 2, w: 1}, what is the expected number of times the pattern 'we*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, r: 2, t: 2}. What is the expected number of occurrences of the pattern 'ta+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, b: 1, z: 1, a: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'hb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, h: 1, i: 1, c: 2, j: 1}. What is the expected number of occurrences of the pattern 'r*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, b: 2, h: 1, s: 1}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, n: 2, u: 1, t: 1, q: 1} to form a word, what is the expected number of matches of the pattern 't.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, u: 2, z: 2, m: 1}, what is the expected number of times the pattern 'm*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, c: 2, k: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, w: 3}. What is the expected number of occurrences of the pattern 'w+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, u: 2, z: 1, m: 1}. What is the expected number of occurrences of the pattern 'zt+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, s: 2, k: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'k.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, u: 4} to form a word, what is the expected number of matches of the pattern 'u*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, q: 2, r: 3} to form a word, what is the expected number of matches of the pattern 'rv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 4, y: 2}, what is the expected number of times the pattern 'w+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, d: 1, t: 1, l: 1, s: 2}. What is the expected number of occurrences of the pattern 'c*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, c: 2, r: 1, m: 1, h: 1}. What is the expected number of occurrences of the pattern 'r+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, r: 4}, what is the expected number of times the pattern 'ir+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, y: 1, x: 3}. What is the expected number of occurrences of the pattern 'y*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, i: 1, t: 1, x: 1, d: 1}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 4, r: 2}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, d: 2, p: 1, w: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, h: 1, b: 1, n: 1, g: 2}. What is the expected number of occurrences of the pattern 'n*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, g: 1, r: 3}, what is the expected number of times the pattern 'rg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, a: 1, o: 2, r: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'rc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, d: 2, n: 2}. What is the expected number of occurrences of the pattern 'n+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 5, i: 1}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, v: 3}. What is the expected number of occurrences of the pattern 'v*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, p: 4} to form a word, what is the expected number of matches of the pattern 'f*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, s: 3} to form a word, what is the expected number of matches of the pattern 'z.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, q: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, f: 1, g: 2, u: 1, b: 1}, what is the expected number of times the pattern 'ef+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, b: 2, i: 3}, what is the expected number of times the pattern 'i*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, e: 1, r: 2, s: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'r+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, w: 1, d: 1, e: 2}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, n: 1, i: 2, z: 2}. What is the expected number of occurrences of the pattern 'i*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, l: 1, k: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'c.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, w: 3}. What is the expected number of occurrences of the pattern 'l+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, r: 2, x: 2}, what is the expected number of times the pattern 'rx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, y: 2, g: 1, x: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, a: 2, j: 1, n: 1}. What is the expected number of occurrences of the pattern 'a*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, z: 3, k: 1}. What is the expected number of occurrences of the pattern 'z+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, p: 1, s: 1, q: 2}, what is the expected number of times the pattern 'p.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, k: 1, v: 1, b: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'k.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, z: 1, g: 2, p: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'f+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, q: 2, v: 1}, what is the expected number of times the pattern 'v+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 4, p: 2}, what is the expected number of times the pattern 'pt+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, m: 3, f: 2} to form a word, what is the expected number of matches of the pattern 'm.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, y: 1, o: 2, x: 1}. What is the expected number of occurrences of the pattern 'x+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, y: 1, x: 3}, what is the expected number of times the pattern 'sy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, g: 3}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, k: 1, t: 1, f: 2}, what is the expected number of times the pattern 'k*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, j: 3, z: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'z*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 4, u: 2} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, a: 2, o: 1, d: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, p: 1, b: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'v+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, z: 2, w: 1, h: 2}. What is the expected number of occurrences of the pattern 'gw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, y: 2, c: 2, j: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, z: 3} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, f: 2, g: 1, s: 2}, what is the expected number of times the pattern 's+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, g: 1, x: 1, u: 1}, what is the expected number of times the pattern 'g+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, v: 1, d: 2, z: 1, c: 1}. What is the expected number of occurrences of the pattern 'vc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, s: 1, i: 2, p: 1}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, f: 1, g: 1}. What is the expected number of occurrences of the pattern 'ft*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, w: 2, p: 2}, what is the expected number of times the pattern 'pq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, p: 3, v: 1, w: 1}. What is the expected number of occurrences of the pattern 'p*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, b: 2, r: 1}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, c: 3}, what is the expected number of times the pattern 'd+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, l: 1, e: 2, g: 2}. What is the expected number of occurrences of the pattern 'ld+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, e: 2, r: 1, o: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, h: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, w: 1, h: 4} to form a word, what is the expected number of matches of the pattern 'wv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, w: 4}. What is the expected number of occurrences of the pattern 'w.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, t: 1, p: 1, z: 2, r: 1} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, g: 1, m: 1, h: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'g*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, k: 1, o: 1, x: 1, e: 2}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, q: 3} to form a word, what is the expected number of matches of the pattern 'qh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, f: 2, j: 2, i: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, z: 1, p: 2, f: 1}. What is the expected number of occurrences of the pattern 'f.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, c: 5}. What is the expected number of occurrences of the pattern 'c+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, m: 3, w: 1}, what is the expected number of times the pattern 'j*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, w: 2, c: 3} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, b: 2, i: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 4, k: 2} to form a word, what is the expected number of matches of the pattern 'kh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, d: 3, k: 2}. What is the expected number of occurrences of the pattern 'hd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, t: 1, e: 1, q: 1, p: 2}. What is the expected number of occurrences of the pattern 'q*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, b: 1, c: 1, t: 1, q: 2}, what is the expected number of times the pattern 'c*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 4, r: 2}. What is the expected number of occurrences of the pattern 'd*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, b: 4} to form a word, what is the expected number of matches of the pattern 'gg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, l: 4} to form a word, what is the expected number of matches of the pattern 'h.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, g: 1, v: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'pv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, g: 2, u: 1, f: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 4, v: 2} to form a word, what is the expected number of matches of the pattern 'k.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, y: 1, d: 1, o: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, w: 2, k: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'y+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, w: 1, u: 4}, what is the expected number of times the pattern 'nw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, a: 1, j: 3, x: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, q: 1, m: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'q+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, e: 1, v: 1, o: 1}. What is the expected number of occurrences of the pattern 'eo*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 4, r: 2}, what is the expected number of times the pattern 'r*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, s: 1, k: 1, w: 1, y: 1}, what is the expected number of times the pattern 'sw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, w: 1, m: 1, i: 2}. What is the expected number of occurrences of the pattern 'wm+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, u: 1, r: 1, w: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'ru+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, a: 1, n: 1, l: 3}. What is the expected number of occurrences of the pattern 'n*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 4, b: 2} to form a word, what is the expected number of matches of the pattern 'cc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, u: 1, b: 1, o: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, w: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'l+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, l: 2, j: 2}. What is the expected number of occurrences of the pattern 'j.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, q: 1, p: 2, c: 1, j: 1}. What is the expected number of occurrences of the pattern 'q+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, b: 4} to form a word, what is the expected number of matches of the pattern 'a*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, s: 3} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, w: 2, f: 3}. What is the expected number of occurrences of the pattern 'w*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 4, i: 2}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, v: 1, a: 2, o: 1, n: 1}. What is the expected number of occurrences of the pattern 'a+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, r: 1, b: 2, l: 1, z: 1}, what is the expected number of times the pattern 't+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, x: 1, u: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, m: 2, r: 1, a: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, h: 2, v: 1, z: 1}. What is the expected number of occurrences of the pattern 'l+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, u: 2, t: 1, m: 1, g: 1}, what is the expected number of times the pattern 'mq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, e: 4}. What is the expected number of occurrences of the pattern 'e*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, j: 1, a: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'j*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, t: 1, x: 2, a: 1, p: 1}. What is the expected number of occurrences of the pattern 'tx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, t: 1, v: 1, j: 1, g: 2}. What is the expected number of occurrences of the pattern 'j+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, m: 1, a: 1, w: 1, g: 2}. What is the expected number of occurrences of the pattern 'yw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, o: 5}. What is the expected number of occurrences of the pattern 'o.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, q: 2, t: 1, m: 1, b: 1}. What is the expected number of occurrences of the pattern 'qq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, b: 3}, what is the expected number of times the pattern 'qb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, j: 3, z: 1}. What is the expected number of occurrences of the pattern 'za*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, w: 3}. What is the expected number of occurrences of the pattern 'c+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, z: 1, q: 1, d: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'i*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, o: 1, c: 3}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, e: 4} to form a word, what is the expected number of matches of the pattern 'e*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, s: 1, e: 1, w: 2}, what is the expected number of times the pattern 's+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, t: 1, v: 1, j: 2, p: 1}, what is the expected number of times the pattern 'j.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, f: 1, a: 1, i: 2, y: 1}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, f: 3}. What is the expected number of occurrences of the pattern 'd*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, l: 1, g: 3} to form a word, what is the expected number of matches of the pattern 'lg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, y: 4} to form a word, what is the expected number of matches of the pattern 'a+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, u: 1, n: 3}. What is the expected number of occurrences of the pattern 'qn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, u: 1, r: 3, a: 1}, what is the expected number of times the pattern 'ar+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 3, i: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'e.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, e: 1, g: 2, o: 1, w: 1}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, o: 1, r: 2, b: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, e: 1, s: 2, t: 2}, what is the expected number of times the pattern 'lt+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, d: 4}. What is the expected number of occurrences of the pattern 'i*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, e: 2, o: 3}, what is the expected number of times the pattern 'e+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, a: 2, c: 3}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 4, c: 2} to form a word, what is the expected number of matches of the pattern 'vc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, d: 2, j: 1, o: 1, m: 1}, what is the expected number of times the pattern 'mg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, l: 1, r: 4} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, n: 2, f: 2} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'e.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, z: 2, m: 1, t: 1, q: 1}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, u: 1, a: 1, s: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'i*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, x: 2, y: 1, e: 1}. What is the expected number of occurrences of the pattern 'e+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, e: 1, y: 2, j: 1, r: 1}. What is the expected number of occurrences of the pattern 'rh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, b: 1, u: 1, p: 1, l: 2}, what is the expected number of times the pattern 'p+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, b: 1, i: 1, r: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'i+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, x: 4}. What is the expected number of occurrences of the pattern 'x.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, a: 3}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, h: 1, b: 2, z: 2}. What is the expected number of occurrences of the pattern 'hz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, x: 2, o: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, g: 1, v: 1, s: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, o: 1, c: 1, a: 2, s: 1}. What is the expected number of occurrences of the pattern 'f+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, e: 1, r: 1, s: 2, f: 1}. What is the expected number of occurrences of the pattern 'f+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, s: 1, o: 1, g: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, m: 3}. What is the expected number of occurrences of the pattern 'mh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, f: 2, p: 1, n: 1}. What is the expected number of occurrences of the pattern 'p.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, x: 1, o: 2, s: 1}. What is the expected number of occurrences of the pattern 'sx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, v: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'v+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, e: 2, t: 2, i: 1}. What is the expected number of occurrences of the pattern 't+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, i: 1, e: 3} to form a word, what is the expected number of matches of the pattern 'r*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, i: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'a+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, c: 3}. What is the expected number of occurrences of the pattern 'fc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, d: 1, f: 3}, what is the expected number of times the pattern 'jd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, t: 1, e: 1, s: 3} to form a word, what is the expected number of matches of the pattern 'e+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, f: 3, s: 1}. What is the expected number of occurrences of the pattern 'z.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, c: 1, h: 1, w: 2}. What is the expected number of occurrences of the pattern 'hx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, m: 2, c: 2}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, k: 1, v: 1, z: 1, m: 2}. What is the expected number of occurrences of the pattern 'm+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, f: 1, h: 2, g: 1, i: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, g: 1, s: 1, a: 2, x: 1}, what is the expected number of times the pattern 'xg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, t: 1, b: 1, d: 2} to form a word, what is the expected number of matches of the pattern 't+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, o: 1, x: 2}. What is the expected number of occurrences of the pattern 'l+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 5, k: 1}, what is the expected number of times the pattern 'ek+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, m: 1, d: 3}. What is the expected number of occurrences of the pattern 'm.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, f: 3}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 3, p: 3}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, o: 3} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 4, x: 2} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, r: 3}, what is the expected number of times the pattern 'nr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, p: 1, y: 1, d: 2}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, y: 2, f: 1, c: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'y*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, i: 3, b: 2} to form a word, what is the expected number of matches of the pattern 'i+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, n: 2, t: 3}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, l: 1, r: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'li+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, p: 1, j: 1, k: 1, w: 1}. What is the expected number of occurrences of the pattern 'p+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, i: 2, l: 2}, what is the expected number of times the pattern 'l.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, v: 3}, what is the expected number of times the pattern 'fv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, w: 1, z: 1, t: 1, i: 2}, what is the expected number of times the pattern 'i+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, y: 3} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, h: 3}. What is the expected number of occurrences of the pattern 'ah+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, a: 2, i: 1, d: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, p: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'pw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, j: 1, z: 3, q: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, l: 1, p: 2, w: 1, j: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, a: 1, x: 1, o: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'xa*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, y: 2, w: 1, j: 1, o: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, b: 2, a: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'u+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, i: 1, k: 3}. What is the expected number of occurrences of the pattern 'i+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, m: 1, h: 2, z: 1}, what is the expected number of times the pattern 'zo*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, w: 3, e: 1}. What is the expected number of occurrences of the pattern 've+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, n: 1, p: 1, h: 2, r: 1}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, j: 1, s: 1, c: 2, m: 1} to form a word, what is the expected number of matches of the pattern 'j*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, m: 3}. What is the expected number of occurrences of the pattern 'm.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, h: 2, w: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'w*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, l: 2, q: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, e: 3} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, b: 1, k: 1, i: 1, n: 2}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, f: 1, j: 2, y: 2}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, k: 4, n: 1}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, t: 1, g: 1, k: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'u+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, i: 1, v: 2}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, j: 3}, what is the expected number of times the pattern 'p.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 3, h: 1, f: 1, u: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, y: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'j.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, v: 1, i: 1, d: 2, p: 1}, what is the expected number of times the pattern 'd+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, s: 3} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, b: 1, h: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, o: 1, q: 1, s: 1, f: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, q: 1, n: 1, b: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'ff+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, p: 2, x: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'p.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, z: 1, x: 1, o: 1}. What is the expected number of occurrences of the pattern 'o*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 3, e: 3}. What is the expected number of occurrences of the pattern 'e.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 5, b: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, p: 1, x: 1, a: 2}. What is the expected number of occurrences of the pattern 'pa+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, r: 3, v: 1}, what is the expected number of times the pattern 'r*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, h: 1, r: 3}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, z: 2, g: 2} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, y: 1, o: 1, u: 2, b: 1}. What is the expected number of occurrences of the pattern 'u*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, l: 1, n: 2, a: 1}. What is the expected number of occurrences of the pattern 'v*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, s: 4, k: 1} to form a word, what is the expected number of matches of the pattern 'ks*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, s: 1, r: 2, j: 1, h: 1}, what is the expected number of times the pattern 'as*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, x: 4} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, n: 3, r: 1, b: 1}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 4, c: 2}. What is the expected number of occurrences of the pattern 'e.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, o: 4} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, p: 2}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, m: 1, q: 2, h: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, q: 1, w: 3, f: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, c: 2, k: 1, s: 1, j: 1}, what is the expected number of times the pattern 'h*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, o: 2, v: 1, y: 1, c: 1}, what is the expected number of times the pattern 'om*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, y: 1, c: 1, a: 2}. What is the expected number of occurrences of the pattern 'ac+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 4, j: 2} to form a word, what is the expected number of matches of the pattern 'j*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, c: 1, z: 3}. What is the expected number of occurrences of the pattern 'z+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, o: 4, l: 1} to form a word, what is the expected number of matches of the pattern 'c.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, y: 2, i: 1, u: 1, z: 1}. What is the expected number of occurrences of the pattern 'zn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 4, w: 2} to form a word, what is the expected number of matches of the pattern 'wp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, c: 3, x: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'd.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, l: 1, e: 2, s: 1, v: 1}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 4, z: 2}, what is the expected number of times the pattern 'zj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, o: 1, v: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, o: 1, t: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'g.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, r: 1, f: 1, a: 1}. What is the expected number of occurrences of the pattern 'r*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 4, n: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'nb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, k: 2, r: 3}, what is the expected number of times the pattern 'k+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, o: 2, i: 3} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 4, k: 2}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, k: 1, o: 1, n: 1, i: 2}, what is the expected number of times the pattern 'i*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, t: 1, u: 1, y: 1, w: 1}, what is the expected number of times the pattern 'u+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, k: 1, b: 1, p: 1, s: 1}, what is the expected number of times the pattern 'k*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, t: 1, f: 2, v: 2}. What is the expected number of occurrences of the pattern 'p.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 3, s: 3}, what is the expected number of times the pattern 'ys+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, c: 4} to form a word, what is the expected number of matches of the pattern 'g*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, s: 3} to form a word, what is the expected number of matches of the pattern 's+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, d: 1, c: 3} to form a word, what is the expected number of matches of the pattern 'cd+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, c: 2, n: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'di+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, p: 1, i: 2, r: 2}. What is the expected number of occurrences of the pattern 'w.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, q: 3, t: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, t: 2, h: 1, f: 1, v: 1}, what is the expected number of times the pattern 'cf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, a: 2, d: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'ak*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, j: 1, z: 1, k: 2, h: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, d: 3, s: 2} to form a word, what is the expected number of matches of the pattern 'zs+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, j: 1, h: 2, i: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, t: 1, c: 1, y: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'ht*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 4, d: 2}, what is the expected number of times the pattern 'ds*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 4, l: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, e: 1, l: 1, s: 1, i: 1}. What is the expected number of occurrences of the pattern 'f+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, m: 1, l: 2, k: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'n.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, q: 3, y: 1}. What is the expected number of occurrences of the pattern 'v+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, m: 1, g: 1, n: 1, j: 2}, what is the expected number of times the pattern 'mj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, m: 1, q: 1, l: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'l*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, a: 2, l: 2, n: 1}. What is the expected number of occurrences of the pattern 'e+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, x: 2, g: 3} to form a word, what is the expected number of matches of the pattern 'gx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, r: 1, i: 1, g: 1, o: 2}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, z: 2, k: 2, n: 1}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, s: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, a: 1, o: 1, j: 1, u: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, m: 5} to form a word, what is the expected number of matches of the pattern 'm*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, q: 2, f: 2} to form a word, what is the expected number of matches of the pattern 'q.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, l: 1, n: 1, y: 2}, what is the expected number of times the pattern 'yx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, d: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'u.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, r: 1, x: 3}. What is the expected number of occurrences of the pattern 'i+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, g: 3}. What is the expected number of occurrences of the pattern 'qg*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, n: 1, y: 1, w: 2, x: 1}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, p: 3} to form a word, what is the expected number of matches of the pattern 't*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, g: 1, k: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'g*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, d: 2, b: 3}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, k: 1, h: 1, e: 2}, what is the expected number of times the pattern 'h*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, j: 2, b: 1, t: 2}, what is the expected number of times the pattern 'j+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, f: 1, m: 1, k: 1, i: 1}, what is the expected number of times the pattern 'km+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, h: 2, z: 2, s: 1}. What is the expected number of occurrences of the pattern 'sv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 5, q: 1}, what is the expected number of times the pattern 'p*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, w: 1, z: 1, h: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, i: 2, k: 2}, what is the expected number of times the pattern 'kq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, z: 1, y: 1, k: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'd*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, l: 1, i: 1, j: 2, n: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, z: 2, u: 1, t: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'z+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, e: 5}, what is the expected number of times the pattern 'fe+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, b: 3, r: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, y: 1, b: 1, c: 1, f: 1}. What is the expected number of occurrences of the pattern 'c*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, o: 2, x: 1}, what is the expected number of times the pattern 'e*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, i: 3, l: 2}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, o: 5}, what is the expected number of times the pattern 'mo+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, e: 5}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, q: 2, f: 1}. What is the expected number of occurrences of the pattern 'q+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, w: 2, x: 1, e: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, t: 1, m: 2, j: 1, z: 1} to form a word, what is the expected number of matches of the pattern 't*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, b: 1, v: 3}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, s: 1, n: 2}. What is the expected number of occurrences of the pattern 's.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, b: 1, w: 2, k: 2}. What is the expected number of occurrences of the pattern 'ww*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, f: 5} to form a word, what is the expected number of matches of the pattern 'fq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, x: 4} to form a word, what is the expected number of matches of the pattern 'xt+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, k: 2, r: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'kc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, m: 1, c: 1, j: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'm*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, k: 1, b: 1, f: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'k*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, h: 2, o: 2, a: 1}. What is the expected number of occurrences of the pattern 'io*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, d: 1, c: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, y: 3}. What is the expected number of occurrences of the pattern 'q.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, j: 1, n: 1, x: 1, i: 1}, what is the expected number of times the pattern 'z.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, d: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, e: 2, t: 1, h: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'ah*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, z: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'z.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, c: 2, p: 2}, what is the expected number of times the pattern 'p*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, b: 2, n: 1, q: 2}. What is the expected number of occurrences of the pattern 'n+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, s: 2, b: 1, j: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, q: 4}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, b: 1, a: 1, g: 1, r: 2}. What is the expected number of occurrences of the pattern 'r+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, v: 3, e: 2}. What is the expected number of occurrences of the pattern 'v*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, a: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'ae+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, h: 4} to form a word, what is the expected number of matches of the pattern 'nh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, f: 1, y: 1, o: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'f*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, f: 2, d: 1, v: 2}. What is the expected number of occurrences of the pattern 'f*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, s: 1, x: 2}, what is the expected number of times the pattern 'sp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 4, b: 2} to form a word, what is the expected number of matches of the pattern 'v+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, a: 4}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, k: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, u: 1, j: 1, l: 1, a: 1}, what is the expected number of times the pattern 'uj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, s: 1, b: 2, w: 1, g: 1}. What is the expected number of occurrences of the pattern 's*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, n: 1, m: 3}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 3, s: 1, y: 2}. What is the expected number of occurrences of the pattern 'y+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, g: 1, a: 3}. What is the expected number of occurrences of the pattern 'i+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, j: 3}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, z: 1, r: 1, u: 2}. What is the expected number of occurrences of the pattern 'a.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, x: 1, y: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'ml+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, e: 1, y: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'ye*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 4, d: 2}, what is the expected number of times the pattern 'du+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, q: 1, v: 1, b: 1, o: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, t: 1, g: 1, x: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, o: 4} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, n: 3}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, v: 1, j: 1, y: 2, f: 1}, what is the expected number of times the pattern 'f.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 5, j: 1} to form a word, what is the expected number of matches of the pattern 'jw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, a: 1, f: 2, s: 2}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, y: 1, w: 2, e: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, n: 1, k: 2}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, o: 1, u: 1, t: 3} to form a word, what is the expected number of matches of the pattern 'ot*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, d: 1, m: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'm.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, m: 1, z: 2, d: 1, x: 1}. What is the expected number of occurrences of the pattern 'x*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 4, q: 2}. What is the expected number of occurrences of the pattern 'q+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, t: 2, e: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'l.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, f: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'f+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, o: 2, p: 1, q: 1}, what is the expected number of times the pattern 'r+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, n: 2, l: 1, r: 2}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, m: 1, x: 1, t: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'a.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 4, r: 1, u: 1}. What is the expected number of occurrences of the pattern 'wu+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, h: 1, n: 1, m: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'n+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, c: 1, x: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'd+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, x: 3}. What is the expected number of occurrences of the pattern 'xk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, i: 1, c: 3}, what is the expected number of times the pattern 'i+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 4, x: 2}. What is the expected number of occurrences of the pattern 'xi*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, v: 3, l: 1} to form a word, what is the expected number of matches of the pattern 'l+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, j: 3} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, y: 3, e: 1, w: 1}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, z: 2, d: 1, p: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 4, u: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, g: 2, t: 1, l: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'lc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, l: 2, z: 2}, what is the expected number of times the pattern 'zl*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, w: 2, c: 1, m: 1, t: 1}. What is the expected number of occurrences of the pattern 'm*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, r: 1, b: 1, v: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, q: 1, x: 1, f: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'rb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, r: 3, k: 2} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, d: 2, r: 1, t: 1}. What is the expected number of occurrences of the pattern 'r.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, n: 4, g: 1}, what is the expected number of times the pattern 'g+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, z: 1, n: 3}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, c: 1, m: 2, e: 1, f: 1}, what is the expected number of times the pattern 'g+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, l: 4, h: 1}, what is the expected number of times the pattern 'lh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, n: 2, h: 2}, what is the expected number of times the pattern 'a*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, r: 1, n: 2, h: 1} to form a word, what is the expected number of matches of the pattern 'hh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 5, y: 1} to form a word, what is the expected number of matches of the pattern 'q+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, a: 1, v: 2, r: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 4, r: 2}. What is the expected number of occurrences of the pattern 're+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, e: 1, i: 1, n: 3}, what is the expected number of times the pattern 'ne*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 4, l: 2} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, u: 3}. What is the expected number of occurrences of the pattern 'u.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, y: 4} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 4, w: 2} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, r: 2, f: 2}. What is the expected number of occurrences of the pattern 'mr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, b: 1, q: 1, y: 1, p: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 5, d: 1}, what is the expected number of times the pattern 'dz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, t: 2, e: 1, n: 2}. What is the expected number of occurrences of the pattern 'a.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, o: 1, r: 1, x: 3}. What is the expected number of occurrences of the pattern 'o*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, w: 3}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, z: 1, i: 1, k: 1, c: 2}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, l: 1, p: 2, b: 1} to form a word, what is the expected number of matches of the pattern 'pe*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, m: 2, e: 2, p: 1}. What is the expected number of occurrences of the pattern 'i*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, s: 3}. What is the expected number of occurrences of the pattern 'l.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, w: 1, k: 1, a: 3}. What is the expected number of occurrences of the pattern 'kw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, t: 2, g: 1, v: 2} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, z: 1, t: 2}, what is the expected number of times the pattern 'it+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, t: 3, a: 2} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, y: 1, o: 1, s: 3}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, r: 1, u: 1, j: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'rk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, x: 1, z: 1, l: 2}, what is the expected number of times the pattern 'x+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, w: 2, y: 1, q: 2} to form a word, what is the expected number of matches of the pattern 'y.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, m: 1, n: 1, b: 3}. What is the expected number of occurrences of the pattern 'z+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'r*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, x: 1, n: 3, b: 1}. What is the expected number of occurrences of the pattern 'ax*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, l: 1, a: 3}, what is the expected number of times the pattern 'a*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, k: 1, z: 1, t: 1, q: 1}, what is the expected number of times the pattern 't.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, p: 4}. What is the expected number of occurrences of the pattern 'v.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, v: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'v*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, x: 1, c: 2, p: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, u: 1, i: 1, l: 1, p: 1}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'v*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, x: 2, y: 1, m: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, s: 5}, what is the expected number of times the pattern 'x+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, q: 2, b: 3} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, b: 2, i: 1, e: 1, u: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, g: 1, l: 1, w: 1, r: 2}, what is the expected number of times the pattern 'w.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, r: 3, c: 2}, what is the expected number of times the pattern 'cn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, j: 1, c: 1, t: 1, e: 1}. What is the expected number of occurrences of the pattern 'c+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, x: 2, q: 2} to form a word, what is the expected number of matches of the pattern 'x.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 4, y: 2}. What is the expected number of occurrences of the pattern 'g+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, l: 2, p: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, f: 1, e: 1, g: 2, w: 1}, what is the expected number of times the pattern 'w+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, v: 2, z: 2, r: 1}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, b: 1, a: 1, y: 2, f: 1}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, t: 2, j: 1, o: 1}, what is the expected number of times the pattern 'jt*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, y: 4}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, k: 1, e: 1, j: 1, a: 2}. What is the expected number of occurrences of the pattern 'k.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, v: 1, h: 2, d: 1, x: 1}, what is the expected number of times the pattern 'v+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, n: 1, f: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'i.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, z: 3}, what is the expected number of times the pattern 'z.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, t: 2, g: 1, u: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, p: 2, k: 2}, what is the expected number of times the pattern 'kp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, o: 1, j: 1, w: 2, m: 1}, what is the expected number of times the pattern 'd+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, b: 1, y: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'a+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, n: 2, g: 2}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, d: 1, y: 1, r: 2}. What is the expected number of occurrences of the pattern 'dd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, k: 1, p: 1, e: 1, v: 1}, what is the expected number of times the pattern 'ae+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, y: 1, k: 1, q: 1, g: 2}, what is the expected number of times the pattern 'a.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, a: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, o: 3}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, g: 3, p: 2}. What is the expected number of occurrences of the pattern 'op*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, m: 1, e: 1, p: 2, l: 1}, what is the expected number of times the pattern 'lf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, z: 1, e: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'zt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, l: 2, f: 2}. What is the expected number of occurrences of the pattern 'fl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, i: 3, r: 2}, what is the expected number of times the pattern 'rb+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, g: 2, f: 2, b: 1}. What is the expected number of occurrences of the pattern 'gn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, r: 1, h: 2, n: 1, z: 1}, what is the expected number of times the pattern 'h+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 4, w: 2} to form a word, what is the expected number of matches of the pattern 'wj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, x: 1, g: 1, c: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'xc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, k: 4}. What is the expected number of occurrences of the pattern 'z+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, k: 2, x: 1}. What is the expected number of occurrences of the pattern 'q.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, d: 2, a: 2}. What is the expected number of occurrences of the pattern 'd+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, y: 4} to form a word, what is the expected number of matches of the pattern 'ye+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 4, u: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, w: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'k+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, h: 3, z: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'zk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, y: 2, f: 1, v: 1, a: 1}. What is the expected number of occurrences of the pattern 'yv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, v: 2, l: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'uv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, i: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'ix+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 4, c: 2}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, v: 1, g: 1, k: 2, q: 1}, what is the expected number of times the pattern 'g*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, u: 1, o: 2, b: 1, f: 1}, what is the expected number of times the pattern 'fu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, c: 3, j: 1}. What is the expected number of occurrences of the pattern 'jj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 5, w: 1}. What is the expected number of occurrences of the pattern 'wt+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, d: 2, p: 1, v: 1}, what is the expected number of times the pattern 'd.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, f: 1, c: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, l: 1, h: 1, p: 3}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, s: 3, l: 2} to form a word, what is the expected number of matches of the pattern 'sl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, r: 1, o: 1, n: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, p: 2, t: 2, b: 1}, what is the expected number of times the pattern 't*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, c: 1, i: 2, y: 2}, what is the expected number of times the pattern 'v*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, d: 3, m: 2}, what is the expected number of times the pattern 'md*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, f: 3, p: 1}. What is the expected number of occurrences of the pattern 'g+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, f: 3}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, i: 4}, what is the expected number of times the pattern 'i*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 4, s: 2} to form a word, what is the expected number of matches of the pattern 'f*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, q: 2, d: 1, r: 1, f: 1}. What is the expected number of occurrences of the pattern 'cr+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, r: 3}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 3, p: 3}. What is the expected number of occurrences of the pattern 'p*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, h: 2, v: 1, s: 2}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, j: 4}, what is the expected number of times the pattern 'z+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, g: 1, i: 2}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, y: 1, j: 1, n: 1, i: 1}, what is the expected number of times the pattern 'ny+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, g: 2, s: 2}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, e: 1, q: 2, g: 1, v: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 4, u: 2}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 5, f: 1} to form a word, what is the expected number of matches of the pattern 'fx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, d: 1, z: 2, m: 1} to form a word, what is the expected number of matches of the pattern 'm.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, b: 2, o: 2}. What is the expected number of occurrences of the pattern 'i+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, a: 2, o: 3}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, c: 3, q: 1}. What is the expected number of occurrences of the pattern 'cq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, x: 3, y: 2}. What is the expected number of occurrences of the pattern 'y+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, p: 1, b: 3}, what is the expected number of times the pattern 'p+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, h: 1, c: 2, f: 1, s: 1}, what is the expected number of times the pattern 'hc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, n: 1, w: 1, p: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'e.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, i: 1, t: 2, u: 2}, what is the expected number of times the pattern 'z+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, g: 3}. What is the expected number of occurrences of the pattern 'l.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, o: 2, a: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'w.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, l: 4} to form a word, what is the expected number of matches of the pattern 'c+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, x: 1, k: 1, p: 1, o: 1}. What is the expected number of occurrences of the pattern 'o*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, y: 2, w: 3}. What is the expected number of occurrences of the pattern 'y*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, m: 3, y: 2}. What is the expected number of occurrences of the pattern 'z*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, e: 1, k: 2, d: 1, s: 1}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, l: 1, v: 2, w: 1}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, v: 1, b: 1, i: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, z: 1, w: 1, h: 1, u: 2}. What is the expected number of occurrences of the pattern 'u.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, l: 1, x: 1, c: 3}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, d: 1, q: 1, b: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'dm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 4, r: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, h: 3}, what is the expected number of times the pattern 'mh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 4, o: 2}. What is the expected number of occurrences of the pattern 'o*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, u: 2, a: 2, l: 1}, what is the expected number of times the pattern 'a*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, f: 2, k: 3} to form a word, what is the expected number of matches of the pattern 'fa*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, x: 1, u: 2, k: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, a: 1, v: 2, p: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'n*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, r: 2, z: 1, s: 2}, what is the expected number of times the pattern 'sz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, c: 1, w: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, b: 3, f: 2} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, h: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'jh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, r: 1, j: 2, n: 1}, what is the expected number of times the pattern 'jh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, f: 2, b: 1, u: 1, w: 1}, what is the expected number of times the pattern 't.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, n: 2, s: 2, p: 1}. What is the expected number of occurrences of the pattern 'on*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, p: 2, f: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, k: 2, l: 2, z: 1}. What is the expected number of occurrences of the pattern 'l+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, l: 1, i: 3}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, y: 1, o: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, z: 1, j: 3}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, a: 1, y: 3, x: 1}. What is the expected number of occurrences of the pattern 'x.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 4, w: 2} to form a word, what is the expected number of matches of the pattern 'wj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, j: 1, g: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'gj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, b: 3, m: 1}, what is the expected number of times the pattern 'gb+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, w: 1, d: 3} to form a word, what is the expected number of matches of the pattern 'w+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, x: 1, a: 1, o: 1, f: 2}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, t: 1, n: 2, y: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'tb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, q: 4, d: 1}, what is the expected number of times the pattern 'n+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, b: 4}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, m: 1, f: 3}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, s: 2, b: 2, m: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, j: 1, h: 1, c: 1, k: 2}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 4, x: 2}. What is the expected number of occurrences of the pattern 'q+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 3, y: 2, m: 1} to form a word, what is the expected number of matches of the pattern 'e+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, f: 1, t: 2, c: 1}. What is the expected number of occurrences of the pattern 'q+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, d: 4}, what is the expected number of times the pattern 'd.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, i: 1, b: 1, e: 2, d: 1}. What is the expected number of occurrences of the pattern 'fd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, n: 1, x: 1, i: 2}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, x: 1, i: 2, j: 1, c: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, l: 2, u: 2, x: 1}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, e: 2, k: 1, v: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 4, t: 2}, what is the expected number of times the pattern 'tg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, w: 3}, what is the expected number of times the pattern 'f+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, d: 2, o: 2}. What is the expected number of occurrences of the pattern 'd+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, s: 1, o: 1, x: 2, h: 1}. What is the expected number of occurrences of the pattern 'x.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, n: 4} to form a word, what is the expected number of matches of the pattern 'n*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, x: 2, w: 1, s: 1, u: 1}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, q: 1, j: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, t: 2, j: 3}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 4, z: 2}, what is the expected number of times the pattern 'e.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, m: 1, o: 2, s: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, u: 1, m: 1, l: 1, h: 1}. What is the expected number of occurrences of the pattern 'm+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, d: 3, p: 2}, what is the expected number of times the pattern 'pd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, p: 2, h: 1, w: 1}, what is the expected number of times the pattern 'wp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'v*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, z: 1, b: 2, o: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, k: 1, y: 1, p: 2}, what is the expected number of times the pattern 'pk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, z: 1, f: 2, b: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'f+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, w: 2, p: 1, k: 1, g: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, e: 1, m: 2, o: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, c: 3, k: 2} to form a word, what is the expected number of matches of the pattern 'vk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, u: 2, e: 2}. What is the expected number of occurrences of the pattern 'k.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, y: 1, j: 2, l: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, j: 2, g: 3} to form a word, what is the expected number of matches of the pattern 'd*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, z: 1, c: 1, p: 1, g: 2}, what is the expected number of times the pattern 'tg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, d: 2, v: 3}, what is the expected number of times the pattern 'dv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, a: 1, p: 2}, what is the expected number of times the pattern 'a+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, m: 1, p: 1, o: 1, c: 2}. What is the expected number of occurrences of the pattern 'm*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, w: 5}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, j: 5} to form a word, what is the expected number of matches of the pattern 'ja+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, m: 2, t: 3}. What is the expected number of occurrences of the pattern 'd+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, l: 3, t: 1}. What is the expected number of occurrences of the pattern 't*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 4, r: 2}. What is the expected number of occurrences of the pattern 'rq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, o: 3, w: 2}, what is the expected number of times the pattern 'o*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, k: 1, x: 2, u: 1, l: 1}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, z: 2, k: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'gz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, m: 2, f: 1, b: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, e: 1, c: 1, l: 2, k: 1}. What is the expected number of occurrences of the pattern 't.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 5, c: 1}. What is the expected number of occurrences of the pattern 'c*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, z: 2, i: 1, j: 2} to form a word, what is the expected number of matches of the pattern 'j.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, g: 3, m: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, w: 2, d: 1, j: 2} to form a word, what is the expected number of matches of the pattern 'wd+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, f: 2, i: 1, p: 2}, what is the expected number of times the pattern 'if+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, b: 4, y: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, q: 1, l: 1, j: 2, z: 1}, what is the expected number of times the pattern 'jz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, q: 3, z: 2}, what is the expected number of times the pattern 'z+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, z: 3, v: 1} to form a word, what is the expected number of matches of the pattern 'r+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, m: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'k.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, n: 1, d: 3, k: 1} to form a word, what is the expected number of matches of the pattern 'dw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, w: 3} to form a word, what is the expected number of matches of the pattern 'tw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, t: 1, e: 1, s: 3}. What is the expected number of occurrences of the pattern 'i.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, t: 1, f: 2, j: 2}, what is the expected number of times the pattern 'i.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, w: 1, k: 2, x: 1} to form a word, what is the expected number of matches of the pattern 'x.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'h*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, o: 2, a: 1}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, y: 2, t: 1, p: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, e: 3}, what is the expected number of times the pattern 'k*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, v: 3}, what is the expected number of times the pattern 'z.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, q: 1, s: 1, z: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, v: 1, s: 1, r: 2, u: 1}. What is the expected number of occurrences of the pattern 'ur*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, a: 2, c: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, p: 3}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, o: 2, l: 1, k: 1, z: 1}, what is the expected number of times the pattern 'kz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, b: 1, j: 3}. What is the expected number of occurrences of the pattern 'cc+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, r: 1, h: 3} to form a word, what is the expected number of matches of the pattern 'r+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, m: 1, a: 1, l: 2}, what is the expected number of times the pattern 'l.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, m: 1, p: 1, i: 2}. What is the expected number of occurrences of the pattern 'm.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, j: 1, n: 1, l: 2}. What is the expected number of occurrences of the pattern 'nb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, w: 1, s: 2, d: 1, e: 1} to form a word, what is the expected number of matches of the pattern 's*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, h: 3, m: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, q: 1, x: 1, j: 1, s: 2}. What is the expected number of occurrences of the pattern 'z.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, i: 4}, what is the expected number of times the pattern 'r+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, y: 4} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, o: 1, p: 3}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, n: 1, r: 3, u: 1}, what is the expected number of times the pattern 'n*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, e: 1, w: 1, o: 2, y: 1}, what is the expected number of times the pattern 'ee+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, i: 2, v: 2, b: 1}. What is the expected number of occurrences of the pattern 'cb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, s: 4}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, g: 2, q: 3}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, j: 2, s: 2, v: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, w: 2, l: 3}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, q: 1, r: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'oq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, w: 2, i: 1, s: 1, r: 1}. What is the expected number of occurrences of the pattern 'si*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 4, s: 2} to form a word, what is the expected number of matches of the pattern 'w+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, d: 2, l: 2} to form a word, what is the expected number of matches of the pattern 'd+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, q: 1, i: 2, d: 1, w: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, w: 1, e: 2, b: 1, u: 1}, what is the expected number of times the pattern 'ww+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, d: 1, e: 1, l: 3} to form a word, what is the expected number of matches of the pattern 'e*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, h: 1, i: 1, n: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'z*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, i: 3}. What is the expected number of occurrences of the pattern 'im+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, j: 2, b: 1, a: 1, r: 1}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, a: 4} to form a word, what is the expected number of matches of the pattern 'a.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, x: 2, i: 1, r: 1, y: 1}, what is the expected number of times the pattern 'xy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, q: 1, c: 1, p: 1, i: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, e: 1, l: 1, j: 2, b: 1} to form a word, what is the expected number of matches of the pattern 'ob+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, r: 1, q: 2, i: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, y: 1, q: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, z: 1, f: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, u: 2, t: 1, q: 1}. What is the expected number of occurrences of the pattern 'u.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, p: 3}, what is the expected number of times the pattern 'pi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, q: 1, e: 1, s: 2, l: 1}, what is the expected number of times the pattern 'g*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, i: 1, k: 2, e: 1}. What is the expected number of occurrences of the pattern 'u+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, w: 3} to form a word, what is the expected number of matches of the pattern 'w*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, v: 1, n: 1, b: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'n+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, x: 1, o: 2, e: 2}, what is the expected number of times the pattern 'x*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, a: 1, e: 1, i: 3} to form a word, what is the expected number of matches of the pattern 'ey+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, j: 1, l: 3}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, e: 4}. What is the expected number of occurrences of the pattern 'ej*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, o: 1, r: 2}, what is the expected number of times the pattern 'o*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, g: 1, u: 2, z: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'eg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, q: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'rq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, e: 2, d: 1, n: 1, y: 1}. What is the expected number of occurrences of the pattern 'ye+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, n: 1, k: 2, z: 1, f: 1}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, u: 1, m: 2, k: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'm+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, t: 2, n: 2}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, f: 1, u: 1, x: 2}. What is the expected number of occurrences of the pattern 'f*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, r: 1, z: 3}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, i: 2, m: 1, j: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, y: 3}, what is the expected number of times the pattern 'y.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, y: 1, j: 1, n: 2}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, r: 1, e: 1, l: 2}. What is the expected number of occurrences of the pattern 'r.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, x: 2, j: 2} to form a word, what is the expected number of matches of the pattern 'qj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 4, e: 2} to form a word, what is the expected number of matches of the pattern 'je+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, p: 1, y: 1, s: 3}, what is the expected number of times the pattern 'pz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, o: 2, w: 2, a: 1}, what is the expected number of times the pattern 'k.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, r: 1, w: 1, k: 1, e: 2}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, c: 2, l: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'l.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, e: 3, x: 2}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, b: 1, y: 3}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, j: 2, k: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, i: 1, x: 3, n: 1}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, y: 3} to form a word, what is the expected number of matches of the pattern 'a.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, g: 1, w: 1, t: 2} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, i: 3}, what is the expected number of times the pattern 'i.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, z: 1, s: 1, f: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, i: 1, d: 2, p: 2}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, w: 1, i: 1, d: 3} to form a word, what is the expected number of matches of the pattern 'di+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, a: 3, f: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'a.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, f: 3, a: 2} to form a word, what is the expected number of matches of the pattern 'u.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, t: 1, e: 2}, what is the expected number of times the pattern 'w.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, s: 1, l: 1, z: 1, g: 1}. What is the expected number of occurrences of the pattern 'g*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, i: 4}. What is the expected number of occurrences of the pattern 'oi*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 4, a: 2} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 5, c: 1} to form a word, what is the expected number of matches of the pattern 'r+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, t: 2, d: 1, p: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, e: 2, y: 1, w: 1}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, w: 1, s: 3}. What is the expected number of occurrences of the pattern 'w*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, d: 1, j: 3, c: 1}, what is the expected number of times the pattern 'f*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, j: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'mq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, d: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'dz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, f: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, d: 3, h: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, y: 3, m: 2}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, t: 1, p: 1, r: 1, y: 1}, what is the expected number of times the pattern 'r.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, g: 1, e: 2, n: 2}, what is the expected number of times the pattern 'eg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, q: 1, v: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, i: 3, o: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, i: 3, e: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, k: 4} to form a word, what is the expected number of matches of the pattern 'yk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, s: 2, k: 1}, what is the expected number of times the pattern 's*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, m: 2, l: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'l*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, z: 1, a: 4} to form a word, what is the expected number of matches of the pattern 'a+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, t: 3, b: 1}. What is the expected number of occurrences of the pattern 't+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 4, l: 2}, what is the expected number of times the pattern 'il*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, g: 1, l: 1, e: 1, p: 1}, what is the expected number of times the pattern 'l+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, n: 3, x: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'n.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, l: 1, o: 1, x: 1, m: 1}. What is the expected number of occurrences of the pattern 'm.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, l: 1, k: 1, h: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'q*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 5, s: 1} to form a word, what is the expected number of matches of the pattern 'j*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, u: 2, l: 2}. What is the expected number of occurrences of the pattern 'u.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, m: 1, b: 2, t: 1, e: 1}. What is the expected number of occurrences of the pattern 't+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 4, o: 2}, what is the expected number of times the pattern 'jo*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, p: 3, i: 1}, what is the expected number of times the pattern 'p.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, z: 1, h: 1, k: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'hk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 4, w: 2} to form a word, what is the expected number of matches of the pattern 'uw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, f: 2, d: 1, m: 2}, what is the expected number of times the pattern 'md*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, x: 2, s: 2}. What is the expected number of occurrences of the pattern 'se*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, n: 1, y: 2}, what is the expected number of times the pattern 'yn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, i: 1, y: 1, u: 1, a: 2}, what is the expected number of times the pattern 'a.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, t: 4}, what is the expected number of times the pattern 't.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, n: 2, w: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 4, m: 2}, what is the expected number of times the pattern 'm.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 5, e: 1}, what is the expected number of times the pattern 'e.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, w: 4} to form a word, what is the expected number of matches of the pattern 'c+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, s: 1, i: 1, j: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'r.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, y: 3}, what is the expected number of times the pattern 'y.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, q: 1, a: 1, i: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, l: 2, b: 1, p: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'l*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, c: 1, r: 1, l: 2, j: 1}. What is the expected number of occurrences of the pattern 'cr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, i: 3}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, l: 1, w: 1, j: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'j.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, k: 1, c: 2, v: 1}. What is the expected number of occurrences of the pattern 'o+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, m: 1, p: 1, a: 3}. What is the expected number of occurrences of the pattern 'am+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 4, x: 2}, what is the expected number of times the pattern 'o.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, e: 1, m: 1, b: 3}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, y: 1, c: 1, f: 1, o: 1}, what is the expected number of times the pattern 'y+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, h: 2, m: 1, y: 1, j: 1}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, m: 2, b: 3} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, v: 1, k: 1, g: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, u: 2, n: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'wn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, p: 1, c: 2, g: 2} to form a word, what is the expected number of matches of the pattern 'cg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, t: 2, q: 1, w: 1}. What is the expected number of occurrences of the pattern 'w.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, z: 1, o: 1, l: 1, f: 1}, what is the expected number of times the pattern 'lk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, z: 1, c: 3, v: 1}, what is the expected number of times the pattern 'w+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 4, k: 2}, what is the expected number of times the pattern 'k.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, d: 1, t: 2, a: 1, z: 1} to form a word, what is the expected number of matches of the pattern 't*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, n: 3} to form a word, what is the expected number of matches of the pattern 'ng*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, e: 1, w: 1, q: 2, x: 1}. What is the expected number of occurrences of the pattern 'f.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, m: 2, x: 1, a: 1, v: 1}, what is the expected number of times the pattern 'c+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 4, b: 2} to form a word, what is the expected number of matches of the pattern 'cc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 4, g: 2}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, f: 3, c: 2}. What is the expected number of occurrences of the pattern 'c.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, p: 1, g: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'i+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, z: 1, s: 1, m: 1, i: 1}, what is the expected number of times the pattern 'm+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, v: 2, o: 1, l: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, u: 1, h: 1, a: 1, x: 1}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, x: 3, r: 2} to form a word, what is the expected number of matches of the pattern 'x+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, k: 1, i: 2, p: 1, b: 1}, what is the expected number of times the pattern 'ip*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, q: 1, u: 1, f: 3} to form a word, what is the expected number of matches of the pattern 'q.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, q: 1, f: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, s: 1, i: 1, r: 2, p: 1}. What is the expected number of occurrences of the pattern 'n*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, q: 1, e: 1, x: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'x+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 4, k: 2}. What is the expected number of occurrences of the pattern 'm*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, m: 3, f: 2}, what is the expected number of times the pattern 'gf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, r: 2, b: 2, v: 1}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, r: 1, w: 2, b: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, f: 2, o: 3}, what is the expected number of times the pattern 'f+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, k: 3} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, g: 1, j: 2, f: 1, v: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, u: 2, l: 1, n: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, b: 4}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 3, m: 3} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, s: 2, n: 1, i: 1, d: 1}. What is the expected number of occurrences of the pattern 'df+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, b: 2, l: 1}, what is the expected number of times the pattern 'lb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, m: 2, n: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'n*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, l: 3}, what is the expected number of times the pattern 'r*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, o: 5} to form a word, what is the expected number of matches of the pattern 'o*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, t: 1, f: 1, s: 1, z: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, i: 2, a: 2, h: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, b: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'u+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, r: 2, c: 2, n: 1}, what is the expected number of times the pattern 'un+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, b: 4}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, m: 2, y: 1, v: 2}, what is the expected number of times the pattern 'y*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, s: 1, k: 2, d: 2}. What is the expected number of occurrences of the pattern 'sw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, j: 1, q: 1, e: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'eq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, s: 3, c: 1}, what is the expected number of times the pattern 'sb+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, p: 2, v: 1, z: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, b: 4}. What is the expected number of occurrences of the pattern 'u*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 4, c: 2} to form a word, what is the expected number of matches of the pattern 'j+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, e: 1, y: 1, h: 3}. What is the expected number of occurrences of the pattern 'z*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, n: 1, t: 1, c: 1, v: 2}. What is the expected number of occurrences of the pattern 'n.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, o: 2, k: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, b: 2, v: 3}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, h: 1, q: 1, m: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, l: 1, h: 1, b: 2, i: 1}. What is the expected number of occurrences of the pattern 'l.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, t: 2, q: 2, z: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, f: 1, a: 3}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, t: 1, w: 2, l: 2} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, a: 3, u: 1} to form a word, what is the expected number of matches of the pattern 'a+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, o: 1, w: 1, c: 3} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, a: 1, f: 1, t: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'f.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, r: 1, f: 2, a: 1}. What is the expected number of occurrences of the pattern 'fe*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, n: 4} to form a word, what is the expected number of matches of the pattern 't+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, c: 3, n: 1, e: 1}. What is the expected number of occurrences of the pattern 'me+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, w: 2, u: 3} to form a word, what is the expected number of matches of the pattern 'a*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, h: 1, t: 1, j: 1, r: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, x: 3}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, o: 1, d: 2, y: 1, u: 1}. What is the expected number of occurrences of the pattern 'o*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, f: 3, g: 2}. What is the expected number of occurrences of the pattern 'g.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, e: 1, m: 3, p: 1}. What is the expected number of occurrences of the pattern 'p+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 4, r: 2} to form a word, what is the expected number of matches of the pattern 'rq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, k: 3} to form a word, what is the expected number of matches of the pattern 'k+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, r: 1, p: 3}. What is the expected number of occurrences of the pattern 'rp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, x: 3}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, e: 2, c: 1, d: 1, r: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, y: 2, m: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, a: 1, z: 1, m: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'r*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, u: 1, c: 2, q: 2}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, a: 3, e: 1, c: 1}, what is the expected number of times the pattern 'e*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, x: 1, m: 3}, what is the expected number of times the pattern 'x.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, y: 1, p: 1, t: 2, u: 1}. What is the expected number of occurrences of the pattern 'p+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, u: 2, p: 1, t: 1}. What is the expected number of occurrences of the pattern 'u.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, i: 1, j: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'n+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, z: 2, y: 1, l: 1, d: 1}, what is the expected number of times the pattern 'ly*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 4, y: 2} to form a word, what is the expected number of matches of the pattern 'c.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, k: 3, l: 1}. What is the expected number of occurrences of the pattern 'qk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, p: 1, j: 2, i: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, p: 1, w: 1, h: 2, n: 1}. What is the expected number of occurrences of the pattern 'nw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, s: 3, v: 1, f: 1}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, g: 1, h: 1, l: 2}. What is the expected number of occurrences of the pattern 'g*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, z: 1, j: 1, k: 1, r: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, a: 2, j: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, x: 1, c: 2}, what is the expected number of times the pattern 'q*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, q: 4}, what is the expected number of times the pattern 'r*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, c: 2, s: 1, z: 1} to form a word, what is the expected number of matches of the pattern 's*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, o: 1, s: 2}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, b: 1, a: 2, q: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, u: 2, b: 1} to form a word, what is the expected number of matches of the pattern 'uu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, o: 3, v: 1}. What is the expected number of occurrences of the pattern 'vx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, c: 1, a: 1, p: 1}, what is the expected number of times the pattern 'c+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, a: 2, o: 2}. What is the expected number of occurrences of the pattern 'jo+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, u: 1, a: 1, r: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'ur+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, n: 2, x: 1, t: 1, f: 1}. What is the expected number of occurrences of the pattern 'n+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, n: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'n.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, m: 2, e: 2} to form a word, what is the expected number of matches of the pattern 'e+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, i: 3, f: 1}. What is the expected number of occurrences of the pattern 'f.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, x: 4}, what is the expected number of times the pattern 'n+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, o: 1, h: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'h.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, l: 2, b: 1, s: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, h: 2, f: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'z*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, v: 2, l: 1, r: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, j: 1, p: 2, e: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'pe*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 5, t: 1}, what is the expected number of times the pattern 't.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, b: 1, t: 1, z: 1, q: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, u: 1, w: 3} to form a word, what is the expected number of matches of the pattern 'uw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, q: 3}. What is the expected number of occurrences of the pattern 'q+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 4, p: 2}. What is the expected number of occurrences of the pattern 'lp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 4, x: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, a: 2, o: 3} to form a word, what is the expected number of matches of the pattern 'o.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, r: 1, l: 1, i: 1, u: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, h: 2, u: 3}. What is the expected number of occurrences of the pattern 'v+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, q: 1, j: 3} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, c: 3, b: 1} to form a word, what is the expected number of matches of the pattern 'c+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, o: 1, k: 2, v: 2}. What is the expected number of occurrences of the pattern 'o*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, s: 2, g: 1, m: 1} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, b: 1, e: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'eb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, w: 1, z: 2, t: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, s: 3}, what is the expected number of times the pattern 'se+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, v: 2, z: 2, h: 1}, what is the expected number of times the pattern 'h*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, q: 2, k: 1, a: 1, p: 1}. What is the expected number of occurrences of the pattern 'kq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, n: 2, a: 2}, what is the expected number of times the pattern 'v*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, d: 2, j: 1, i: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'u+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, d: 1, s: 3, c: 1}. What is the expected number of occurrences of the pattern 'n*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 4, y: 2} to form a word, what is the expected number of matches of the pattern 'j.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, n: 1, d: 1, j: 3}. What is the expected number of occurrences of the pattern 'v+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, j: 1, p: 1, e: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'p.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, a: 3, w: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, q: 1, x: 2, m: 2}, what is the expected number of times the pattern 'xq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, h: 1, l: 1, p: 2}. What is the expected number of occurrences of the pattern 'l.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, e: 1, x: 1, d: 2, p: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, i: 3, b: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, w: 1, g: 3, m: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 4, a: 2}, what is the expected number of times the pattern 'la+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 3, n: 2, m: 1}, what is the expected number of times the pattern 'n.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, x: 1, q: 2, e: 1, f: 1}, what is the expected number of times the pattern 'q*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, v: 5} to form a word, what is the expected number of matches of the pattern 's.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, z: 1, p: 1, g: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'z.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, u: 3, z: 2}, what is the expected number of times the pattern 'xu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, a: 2, o: 1, i: 1, w: 1}, what is the expected number of times the pattern 'o+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, n: 1, a: 2, y: 1}. What is the expected number of occurrences of the pattern 'a.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, z: 4}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, f: 2, d: 1, a: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, e: 4} to form a word, what is the expected number of matches of the pattern 'e*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, f: 1, v: 2, m: 1} to form a word, what is the expected number of matches of the pattern 'm+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, e: 1, z: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'r+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, l: 1, v: 3, j: 1} to form a word, what is the expected number of matches of the pattern 'l+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, h: 2, z: 1, x: 1, y: 1}. What is the expected number of occurrences of the pattern 'hz*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, k: 1, q: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'qk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, u: 4} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 4, b: 2} to form a word, what is the expected number of matches of the pattern 'p*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, o: 3} to form a word, what is the expected number of matches of the pattern 'jo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, a: 1, o: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'a*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, y: 1, v: 1, h: 1, c: 1}, what is the expected number of times the pattern 'y*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, f: 2, m: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, n: 4}, what is the expected number of times the pattern 'n+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, w: 3}, what is the expected number of times the pattern 'w.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 4, b: 1, y: 1}. What is the expected number of occurrences of the pattern 'yy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, a: 1, f: 4}. What is the expected number of occurrences of the pattern 'a+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, x: 2}. What is the expected number of occurrences of the pattern 't+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, w: 2, a: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, n: 2, m: 1, s: 1, t: 1}, what is the expected number of times the pattern 's*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, d: 3, f: 2} to form a word, what is the expected number of matches of the pattern 'fd+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, y: 1, l: 1, c: 1}. What is the expected number of occurrences of the pattern 'c*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, u: 1, v: 1, o: 1, x: 2}. What is the expected number of occurrences of the pattern 't+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, t: 3, h: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, z: 2, h: 2}. What is the expected number of occurrences of the pattern 'hs*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, g: 1, f: 1, h: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'l+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, c: 1, v: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'qc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, y: 3}, what is the expected number of times the pattern 'ty*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, c: 1, i: 1, d: 1, o: 1}. What is the expected number of occurrences of the pattern 'yd+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, s: 1, r: 1, y: 2, b: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, g: 2, f: 1, q: 1, e: 1}, what is the expected number of times the pattern 'g+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, b: 1, r: 3, s: 1}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, v: 2, a: 1}. What is the expected number of occurrences of the pattern 'a+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, w: 1, h: 1, i: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'p.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, f: 1, o: 1, y: 1, v: 2}, what is the expected number of times the pattern 'fw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, e: 3, f: 2} to form a word, what is the expected number of matches of the pattern 'fo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, o: 3, q: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'd*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, v: 4}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, k: 1, n: 2, r: 1, g: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, q: 2, u: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'qt+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, c: 1, l: 1, q: 1, z: 2}, what is the expected number of times the pattern 'w+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, s: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'r*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, m: 3, s: 1} to form a word, what is the expected number of matches of the pattern 'r*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, d: 1, y: 1, c: 1, o: 2}, what is the expected number of times the pattern 'c+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, j: 1, h: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, p: 2, x: 3}. What is the expected number of occurrences of the pattern 'x.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, r: 1, f: 2, n: 2}, what is the expected number of times the pattern 'nr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, o: 2, y: 1, f: 1, m: 1}, what is the expected number of times the pattern 'o*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, f: 1, l: 2, t: 2}, what is the expected number of times the pattern 'ft*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, s: 1, d: 1, o: 1, l: 1}, what is the expected number of times the pattern 'd.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, l: 3, h: 2}. What is the expected number of occurrences of the pattern 'l+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, y: 3}, what is the expected number of times the pattern 'y+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, i: 1, u: 1, w: 3}. What is the expected number of occurrences of the pattern 'u*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, d: 1, j: 1, u: 1, w: 2}, what is the expected number of times the pattern 'dw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, k: 1, q: 2, j: 1, v: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, f: 1, c: 1, u: 2, m: 1}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 4, x: 1, b: 1}, what is the expected number of times the pattern 'x+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, a: 1, w: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, z: 3, l: 1, g: 1}, what is the expected number of times the pattern 'fz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, a: 1, r: 1, e: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, c: 4, x: 1}, what is the expected number of times the pattern 'ac*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, w: 1, m: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'i*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, y: 4}, what is the expected number of times the pattern 'y.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 5, y: 1}. What is the expected number of occurrences of the pattern 'm.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, g: 1, i: 4}. What is the expected number of occurrences of the pattern 'w.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, w: 2, r: 2} to form a word, what is the expected number of matches of the pattern 't*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, t: 3, x: 1}, what is the expected number of times the pattern 'tx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, p: 1, k: 1, h: 1, d: 1}, what is the expected number of times the pattern 'm+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, v: 2, t: 2}. What is the expected number of occurrences of the pattern 'z+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, m: 4}. What is the expected number of occurrences of the pattern 'mp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, g: 2, l: 1}. What is the expected number of occurrences of the pattern 'g.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, u: 1, s: 1, z: 2, m: 1} to form a word, what is the expected number of matches of the pattern 's.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, p: 1, b: 2, d: 1, s: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, c: 1, i: 2, g: 2}, what is the expected number of times the pattern 'i+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 4, t: 2} to form a word, what is the expected number of matches of the pattern 't.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, l: 2, p: 2, u: 1}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, e: 3, w: 1} to form a word, what is the expected number of matches of the pattern 'e*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, m: 2, u: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'm+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 5, y: 1}, what is the expected number of times the pattern 'y+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, j: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'n*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, w: 2, e: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, q: 3} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, t: 1, n: 1, m: 1, v: 1}. What is the expected number of occurrences of the pattern 'n+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, y: 1, e: 2, g: 1}, what is the expected number of times the pattern 'z+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, i: 4} to form a word, what is the expected number of matches of the pattern 'i*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, f: 2, k: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'f*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, u: 1, k: 2, h: 2}. What is the expected number of occurrences of the pattern 'ik*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, g: 4}, what is the expected number of times the pattern 'lg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 3, d: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, t: 4}, what is the expected number of times the pattern 'p*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, s: 1, x: 2}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, k: 3} to form a word, what is the expected number of matches of the pattern 'k+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, x: 1, v: 2, h: 1} to form a word, what is the expected number of matches of the pattern 'lv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, g: 1, j: 2, z: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, p: 1, w: 2, j: 1, v: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, h: 2, q: 1, r: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'q.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, v: 1, k: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, m: 4}. What is the expected number of occurrences of the pattern 'w.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, y: 1, h: 2, l: 1, n: 1}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, p: 3}, what is the expected number of times the pattern 'pp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, j: 1, h: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'h+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, s: 4}, what is the expected number of times the pattern 'm+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, v: 1, i: 1, j: 2}, what is the expected number of times the pattern 'iv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, l: 2, b: 1, t: 1}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, v: 3}. What is the expected number of occurrences of the pattern 'v*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, p: 1, i: 2, f: 1, a: 1}, what is the expected number of times the pattern 'i.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, m: 2, r: 1, s: 2}. What is the expected number of occurrences of the pattern 'm+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, j: 1, x: 1, z: 1, q: 2}, what is the expected number of times the pattern 'vq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, d: 1, z: 1, e: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'd.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, k: 1, e: 1, v: 1}. What is the expected number of occurrences of the pattern 'v*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, z: 1, h: 1, b: 2}, what is the expected number of times the pattern 'hz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, h: 3}, what is the expected number of times the pattern 'h*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, c: 1, y: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'c+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, w: 2, b: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'jv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, i: 3, y: 1} to form a word, what is the expected number of matches of the pattern 'iy+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, a: 1, n: 2, r: 2}. What is the expected number of occurrences of the pattern 'a+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 4, d: 2} to form a word, what is the expected number of matches of the pattern 'qd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, p: 3, m: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, f: 2, e: 2}, what is the expected number of times the pattern 'f.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, d: 1, q: 1, s: 1, n: 2}, what is the expected number of times the pattern 'n+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, r: 1, i: 1, u: 2, x: 1}. What is the expected number of occurrences of the pattern 'x+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, o: 1, g: 1, v: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, u: 2, c: 1, y: 2}, what is the expected number of times the pattern 'c.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, w: 2, n: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'fc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, b: 1, h: 1, r: 1, a: 1}, what is the expected number of times the pattern 'rh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 4, e: 2}. What is the expected number of occurrences of the pattern 'ex*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, w: 1, m: 2}. What is the expected number of occurrences of the pattern 'xm*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, f: 1, d: 1, g: 1, j: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, u: 3, b: 2}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, t: 2, u: 2, c: 1}. What is the expected number of occurrences of the pattern 'cu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, g: 4} to form a word, what is the expected number of matches of the pattern 'q+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, c: 3, x: 1}. What is the expected number of occurrences of the pattern 'c.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, k: 2, y: 1, i: 2}. What is the expected number of occurrences of the pattern 'y*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, k: 1, d: 1, e: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, a: 1, n: 2, v: 1, c: 1}, what is the expected number of times the pattern 'n*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, z: 2, n: 1, a: 1, l: 1}, what is the expected number of times the pattern 'an*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, q: 1, z: 1, x: 1, h: 1}. What is the expected number of occurrences of the pattern 'z.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, m: 1, y: 1, c: 1, a: 2}, what is the expected number of times the pattern 'm*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, s: 1, w: 3}. What is the expected number of occurrences of the pattern 'qs*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 4, g: 2}. What is the expected number of occurrences of the pattern 'g.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 5, d: 1}. What is the expected number of occurrences of the pattern 'i+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, l: 3, c: 1}, what is the expected number of times the pattern 'c+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, v: 1, x: 2, z: 2}. What is the expected number of occurrences of the pattern 'h.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, n: 3} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, v: 4, i: 1}. What is the expected number of occurrences of the pattern 'li*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 4, j: 2}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 4, n: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'n*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 4, m: 2}, what is the expected number of times the pattern 'h*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, e: 3}. What is the expected number of occurrences of the pattern 'ed+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, p: 2, q: 1, z: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'dx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, x: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, d: 2, s: 1, f: 1}. What is the expected number of occurrences of the pattern 'd+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, n: 2, v: 1, c: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'z.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, p: 3}, what is the expected number of times the pattern 'p*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, i: 2, r: 3}. What is the expected number of occurrences of the pattern 'rh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, g: 3, i: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, w: 2, c: 2} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, m: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 4, s: 2}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, l: 2, h: 2}, what is the expected number of times the pattern 'w.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, i: 1, c: 1, l: 1, s: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, i: 1, e: 1, k: 1, f: 1}, what is the expected number of times the pattern 'q*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, p: 3}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, a: 1, z: 1, x: 1, k: 1}, what is the expected number of times the pattern 'k+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, j: 1, a: 3, w: 1}. What is the expected number of occurrences of the pattern 'w+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, l: 1, z: 1, m: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'ql*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, r: 2, f: 2, a: 1}. What is the expected number of occurrences of the pattern 'a+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, h: 3}. What is the expected number of occurrences of the pattern 'x*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, q: 3}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 4, o: 2}. What is the expected number of occurrences of the pattern 'jo+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, y: 1, c: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'c+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, g: 1, d: 1, l: 2, u: 1}, what is the expected number of times the pattern 'gu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, w: 1, n: 1, h: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'n.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, u: 1, b: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'z.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, w: 1, x: 1, l: 1, o: 1}, what is the expected number of times the pattern 'x+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, z: 2, c: 2, e: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, b: 3, x: 1}. What is the expected number of occurrences of the pattern 'xb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, y: 4} to form a word, what is the expected number of matches of the pattern 'yu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, i: 2, x: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'x*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, i: 1, l: 3} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, e: 1, g: 2, t: 1, u: 1}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, o: 4}, what is the expected number of times the pattern 'e*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, w: 2, t: 2}, what is the expected number of times the pattern 'tp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, n: 1, o: 1, t: 2, u: 1}, what is the expected number of times the pattern 'f.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, n: 1, m: 1, a: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'n+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, j: 2, i: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'i*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, u: 1, v: 1, z: 1}. What is the expected number of occurrences of the pattern 'v.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, d: 1, u: 3, l: 1}, what is the expected number of times the pattern 'f.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, m: 1, h: 1, l: 2, w: 1}. What is the expected number of occurrences of the pattern 'hm+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, a: 2, m: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, e: 2, q: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'qv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 4, u: 2}, what is the expected number of times the pattern 'ue+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, q: 1, w: 2, o: 1, x: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, k: 2, j: 1, d: 1, w: 1}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, c: 2, n: 1, s: 2}, what is the expected number of times the pattern 'n*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, e: 3} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 4, c: 2} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, b: 4}. What is the expected number of occurrences of the pattern 'uu+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, c: 2, d: 2}, what is the expected number of times the pattern 'uc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, a: 2, t: 3}, what is the expected number of times the pattern 'ap+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, c: 5} to form a word, what is the expected number of matches of the pattern 'u+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 4, h: 2}, what is the expected number of times the pattern 'n+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, x: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'x*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, b: 1, x: 1, t: 1, a: 2}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, q: 1, j: 3, a: 1}, what is the expected number of times the pattern 'a+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, m: 2, f: 3} to form a word, what is the expected number of matches of the pattern 'm.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, z: 3, x: 1} to form a word, what is the expected number of matches of the pattern 'zx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, g: 2, x: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, j: 2, o: 1, h: 1, q: 1}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, t: 3}, what is the expected number of times the pattern 't*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, h: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'h*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, p: 2, q: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, e: 1, v: 1, q: 1, j: 2} to form a word, what is the expected number of matches of the pattern 'd.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, t: 1, r: 1, w: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 4, r: 1, t: 1} to form a word, what is the expected number of matches of the pattern 't+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, x: 1, b: 1, k: 1, d: 1}. What is the expected number of occurrences of the pattern 'x+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, c: 1, h: 3}. What is the expected number of occurrences of the pattern 'hc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, h: 3, r: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, y: 2, z: 1, s: 2}, what is the expected number of times the pattern 'z.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, d: 3, o: 1}, what is the expected number of times the pattern 'd.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, q: 1, k: 1, v: 2}. What is the expected number of occurrences of the pattern 'v*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, e: 1, y: 2, m: 1, r: 1}. What is the expected number of occurrences of the pattern 'r*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, o: 2, u: 2}, what is the expected number of times the pattern 'u.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, j: 1, s: 3} to form a word, what is the expected number of matches of the pattern 'sy*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, r: 1, e: 2, b: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, s: 1, x: 1, i: 2, v: 1}, what is the expected number of times the pattern 'x*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, z: 2, c: 1}. What is the expected number of occurrences of the pattern 'c.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, w: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'w.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, l: 1, r: 2, o: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'r.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, u: 2, t: 1, c: 1, v: 1}, what is the expected number of times the pattern 'tn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, u: 1, m: 2}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, c: 1, y: 3}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, j: 2, v: 1, b: 2} to form a word, what is the expected number of matches of the pattern 's+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, v: 1, p: 2, o: 1}, what is the expected number of times the pattern 'm.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 4, m: 2}, what is the expected number of times the pattern 'v.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, o: 1, v: 2, u: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, j: 2, e: 1, l: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'h+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, w: 2, s: 3}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, r: 1, b: 2, z: 1}. What is the expected number of occurrences of the pattern 'z.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, y: 3} to form a word, what is the expected number of matches of the pattern 'y.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, d: 3}. What is the expected number of occurrences of the pattern 'd.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, n: 1, a: 2, j: 2}. What is the expected number of occurrences of the pattern 'n.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, o: 4}. What is the expected number of occurrences of the pattern 'o*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, z: 1, q: 2, a: 1, b: 1}, what is the expected number of times the pattern 'zq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, k: 2, a: 1, q: 1, l: 1}, what is the expected number of times the pattern 'k*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, z: 1, o: 1, a: 1, d: 2}, what is the expected number of times the pattern 'di+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, m: 1, v: 2, j: 2}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, s: 2, f: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, o: 1, g: 2, j: 1}, what is the expected number of times the pattern 'jo*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, c: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'x.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, g: 4, f: 1} to form a word, what is the expected number of matches of the pattern 'fc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, m: 3} to form a word, what is the expected number of matches of the pattern 'h*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 4, z: 2}, what is the expected number of times the pattern 'c*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, o: 1, j: 1, r: 3}. What is the expected number of occurrences of the pattern 'n.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 5, d: 1}. What is the expected number of occurrences of the pattern 'd+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, l: 1, b: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, n: 4}. What is the expected number of occurrences of the pattern 'w*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, k: 1, f: 2, q: 2}, what is the expected number of times the pattern 'l.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, s: 2, a: 3}, what is the expected number of times the pattern 'fa*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, f: 4}, what is the expected number of times the pattern 'f*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, x: 1, r: 2, b: 2}, what is the expected number of times the pattern 'x*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, t: 4}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, k: 1, x: 3, q: 1}. What is the expected number of occurrences of the pattern 'kq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, v: 1, l: 1, b: 1}, what is the expected number of times the pattern 'pl*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 4, o: 1, b: 1}, what is the expected number of times the pattern 'x*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 3, u: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, b: 2, w: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'yb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, m: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, y: 2, j: 3} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, h: 1, w: 1, i: 2, e: 1}, what is the expected number of times the pattern 'o+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, g: 1, e: 2, x: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'g+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, z: 3} to form a word, what is the expected number of matches of the pattern 'z.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, s: 2, d: 2}. What is the expected number of occurrences of the pattern 'se*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, x: 2, b: 1, f: 2}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 3, p: 3} to form a word, what is the expected number of matches of the pattern 'p.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, g: 3} to form a word, what is the expected number of matches of the pattern 'gh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, k: 2, o: 3}. What is the expected number of occurrences of the pattern 'k*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, i: 3, a: 2} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, q: 1, f: 3} to form a word, what is the expected number of matches of the pattern 'ef*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'xb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, q: 4} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, i: 1, o: 4}, what is the expected number of times the pattern 'oo*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, c: 2, a: 2, p: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, h: 1, t: 1, l: 2, k: 1}, what is the expected number of times the pattern 'k+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, u: 1, l: 1, s: 3}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, o: 1, u: 2, m: 1}. What is the expected number of occurrences of the pattern 'g.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, w: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'w.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, v: 1, c: 1, e: 3} to form a word, what is the expected number of matches of the pattern 'cv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 4, o: 2} to form a word, what is the expected number of matches of the pattern 'o*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, k: 1, z: 1, o: 2}, what is the expected number of times the pattern 'so+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, b: 2, s: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 3, k: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, r: 2, v: 1, n: 1}, what is the expected number of times the pattern 'tn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, h: 2, b: 3} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, z: 3, n: 2}. What is the expected number of occurrences of the pattern 'zn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 5, x: 1}. What is the expected number of occurrences of the pattern 'f+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, a: 2, c: 1, n: 1}. What is the expected number of occurrences of the pattern 'a.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 4, d: 2}, what is the expected number of times the pattern 'd+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, b: 1, y: 3, i: 1} to form a word, what is the expected number of matches of the pattern 'h*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, f: 1, t: 2, k: 1, a: 1}, what is the expected number of times the pattern 't.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 4, k: 2} to form a word, what is the expected number of matches of the pattern 'i.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, t: 2, k: 1, f: 2}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, l: 1, h: 2}, what is the expected number of times the pattern 'g+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, t: 3, h: 1} to form a word, what is the expected number of matches of the pattern 'ht+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, k: 1, o: 2, r: 1, d: 1}. What is the expected number of occurrences of the pattern 'ro*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, e: 1, v: 1, d: 1, l: 1}, what is the expected number of times the pattern 'v*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, k: 1, y: 1, x: 1, b: 1}. What is the expected number of occurrences of the pattern 'c+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, c: 1, d: 2, p: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, c: 2, k: 2}, what is the expected number of times the pattern 'uk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, v: 1, c: 1, f: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, n: 2, s: 1}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, v: 1, u: 2, g: 1, y: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, w: 5}. What is the expected number of occurrences of the pattern 'zw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, h: 1, p: 3}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, b: 2, a: 2, x: 1} to form a word, what is the expected number of matches of the pattern 'ab+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, z: 1, b: 2, f: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'zw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, d: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'ez+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 4, p: 2}. What is the expected number of occurrences of the pattern 'p*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, r: 1, i: 4}, what is the expected number of times the pattern 'xr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, k: 3}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, h: 1, v: 1, a: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, e: 1, j: 2}. What is the expected number of occurrences of the pattern 'e+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, a: 3}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, b: 2, z: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'ab+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, v: 1, d: 2, h: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'h+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, l: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'za+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, n: 5}. What is the expected number of occurrences of the pattern 'nv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, z: 1, t: 2, q: 1, c: 1}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, f: 4}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, b: 3, y: 1}, what is the expected number of times the pattern 'k+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, r: 1, y: 2, e: 1, b: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, l: 5}, what is the expected number of times the pattern 'l.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, p: 1, x: 3}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, t: 2, e: 2, b: 1}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, q: 1, d: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'r*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, j: 2, q: 3}, what is the expected number of times the pattern 'j*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, d: 3}, what is the expected number of times the pattern 'dk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, a: 1, i: 1, q: 2, c: 1}. What is the expected number of occurrences of the pattern 'qj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, y: 3, e: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, k: 3, l: 1}. What is the expected number of occurrences of the pattern 'e*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, x: 5}. What is the expected number of occurrences of the pattern 'x+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, v: 1, l: 1, j: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'v+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, d: 3, g: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, e: 1, c: 1, z: 1, v: 2}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, b: 1, i: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'j*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, s: 4} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, z: 1, t: 2, x: 2} to form a word, what is the expected number of matches of the pattern 't*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, x: 2, o: 1, t: 1} to form a word, what is the expected number of matches of the pattern 't.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, k: 3, l: 2}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, f: 2, p: 3}. What is the expected number of occurrences of the pattern 'p.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, j: 1, d: 3, b: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'ax*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, e: 1, o: 3} to form a word, what is the expected number of matches of the pattern 'o.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 4, z: 2}, what is the expected number of times the pattern 'jz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, i: 1, q: 4} to form a word, what is the expected number of matches of the pattern 'i*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, v: 3}. What is the expected number of occurrences of the pattern 'v.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, w: 2, u: 3} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, u: 3, o: 2}. What is the expected number of occurrences of the pattern 'oz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, b: 1, u: 3}. What is the expected number of occurrences of the pattern 'u+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, j: 3, s: 1} to form a word, what is the expected number of matches of the pattern 's.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, j: 1, u: 1, m: 1, g: 2}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, k: 1, q: 2, t: 1, j: 1}. What is the expected number of occurrences of the pattern 'gq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, w: 2, x: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, e: 1, v: 2} to form a word, what is the expected number of matches of the pattern 've*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, n: 1, g: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 4, o: 2} to form a word, what is the expected number of matches of the pattern 'oh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, x: 2, r: 1}. What is the expected number of occurrences of the pattern 'yx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, m: 3} to form a word, what is the expected number of matches of the pattern 't+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 4, q: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 4, w: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, a: 3, l: 2}, what is the expected number of times the pattern 'l*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, v: 3, o: 2} to form a word, what is the expected number of matches of the pattern 'vo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, w: 1, g: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'w+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 5, l: 1}. What is the expected number of occurrences of the pattern 'z+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, j: 2, k: 2}. What is the expected number of occurrences of the pattern 'kj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, g: 1, p: 1, z: 2, b: 1}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, y: 2, e: 1}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, t: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'gk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, o: 1, b: 1, h: 1, d: 2}, what is the expected number of times the pattern 'd+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, o: 1, b: 3} to form a word, what is the expected number of matches of the pattern 'i+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, n: 2, j: 2}. What is the expected number of occurrences of the pattern 'ju+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, v: 3, e: 1, z: 1}, what is the expected number of times the pattern 'w.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, k: 3}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, b: 2, s: 2}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, i: 3}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, m: 1, z: 2, t: 2}, what is the expected number of times the pattern 'i+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, c: 2, e: 1}, what is the expected number of times the pattern 'c+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, w: 4, y: 1} to form a word, what is the expected number of matches of the pattern 'w*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, r: 3, h: 1}, what is the expected number of times the pattern 'h*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, b: 2, m: 2, t: 1}, what is the expected number of times the pattern 'm+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, t: 3, a: 2} to form a word, what is the expected number of matches of the pattern 'ta+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, z: 2, j: 3} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, r: 2, a: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, o: 2, e: 2} to form a word, what is the expected number of matches of the pattern 'oe*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, t: 3, u: 1}, what is the expected number of times the pattern 'yu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, q: 2, f: 3}. What is the expected number of occurrences of the pattern 'q*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, k: 4}, what is the expected number of times the pattern 'gk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, x: 1, i: 1, j: 1, k: 2}. What is the expected number of occurrences of the pattern 'je*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'tb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, k: 1, d: 2, t: 1}, what is the expected number of times the pattern 'td*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, m: 2, p: 1, o: 2}. What is the expected number of occurrences of the pattern 'm*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, x: 1, s: 2, t: 1, y: 1} to form a word, what is the expected number of matches of the pattern 's.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, x: 1, e: 1, w: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, e: 1, b: 1, d: 1, r: 2}, what is the expected number of times the pattern 'i*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, b: 1, i: 1, l: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'z*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 5, j: 1} to form a word, what is the expected number of matches of the pattern 'o*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, s: 4, q: 1}, what is the expected number of times the pattern 'sq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, m: 2, h: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'm*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, b: 2, s: 1, m: 1, a: 1}. What is the expected number of occurrences of the pattern 'm*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, u: 1, d: 2, r: 2} to form a word, what is the expected number of matches of the pattern 'qr+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, g: 1, p: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'p+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 4, x: 2}, what is the expected number of times the pattern 'r+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, u: 2, h: 1, k: 1}. What is the expected number of occurrences of the pattern 'yh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, u: 2, x: 3} to form a word, what is the expected number of matches of the pattern 'ux*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 4, c: 2} to form a word, what is the expected number of matches of the pattern 'z*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, b: 2, r: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, g: 5}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, g: 1, b: 2, d: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'kg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, k: 1, o: 2, t: 1}, what is the expected number of times the pattern 'g*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, p: 1, y: 2, o: 1, l: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, j: 3}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, r: 4, j: 1}, what is the expected number of times the pattern 'v+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, f: 1, b: 1, m: 2}. What is the expected number of occurrences of the pattern 'fb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, u: 1, s: 3} to form a word, what is the expected number of matches of the pattern 's*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, u: 1, c: 2, b: 1}, what is the expected number of times the pattern 'u.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, i: 2, s: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, r: 4}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, j: 2, a: 1, u: 1, m: 1}. What is the expected number of occurrences of the pattern 'ju*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, f: 3, m: 2}. What is the expected number of occurrences of the pattern 'fi+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, l: 1, x: 1, y: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, t: 3}. What is the expected number of occurrences of the pattern 'm.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, o: 1, e: 1, k: 2, j: 1}. What is the expected number of occurrences of the pattern 'le*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 5, v: 1}, what is the expected number of times the pattern 'p+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, e: 1, q: 1, v: 1, h: 1}, what is the expected number of times the pattern 'e+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, t: 3, p: 2}, what is the expected number of times the pattern 'j+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, m: 1, d: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, b: 1, y: 3}, what is the expected number of times the pattern 'kb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 4, k: 2} to form a word, what is the expected number of matches of the pattern 'x*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, e: 1, s: 1, t: 1, l: 1}, what is the expected number of times the pattern 'm.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, w: 1, f: 1, j: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'fm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, e: 3}. What is the expected number of occurrences of the pattern 'ue+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, e: 1, m: 2, y: 2}. What is the expected number of occurrences of the pattern 'h.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, l: 1, x: 2}. What is the expected number of occurrences of the pattern 'x.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, j: 1, g: 2, q: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 4, j: 2}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, u: 1, t: 2, p: 1}. What is the expected number of occurrences of the pattern 'e+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, g: 3} to form a word, what is the expected number of matches of the pattern 'x*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 4, q: 2}, what is the expected number of times the pattern 'q+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, c: 1, k: 1, p: 1, g: 1}, what is the expected number of times the pattern 'ap+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, b: 1, w: 1, z: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, s: 1, y: 2}. What is the expected number of occurrences of the pattern 'c+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, z: 3}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, h: 3}, what is the expected number of times the pattern 'h+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 4, m: 2}. What is the expected number of occurrences of the pattern 'j+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, l: 1, a: 3}. What is the expected number of occurrences of the pattern 'y+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, z: 1, d: 1, u: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, o: 2, u: 2}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, o: 2, k: 1}, what is the expected number of times the pattern 'v+k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, p: 3, h: 2}, what is the expected number of times the pattern 'ph+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, y: 4}. What is the expected number of occurrences of the pattern 'yb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, y: 1, s: 1, e: 3}, what is the expected number of times the pattern 's.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 4, y: 2} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, i: 2, l: 2} to form a word, what is the expected number of matches of the pattern 'i.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, v: 1, r: 2, e: 1}. What is the expected number of occurrences of the pattern 'nv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, j: 2, n: 2}. What is the expected number of occurrences of the pattern 'j.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, p: 1, u: 1, b: 1, k: 1}, what is the expected number of times the pattern 'uu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, q: 3, v: 2}. What is the expected number of occurrences of the pattern 'q.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 5, u: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, b: 4}. What is the expected number of occurrences of the pattern 'ab+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, a: 3}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, q: 1, o: 2, i: 1, n: 1}, what is the expected number of times the pattern 'o*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, k: 1, s: 2, v: 1}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, z: 1, u: 1, j: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'j.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, i: 1, b: 2, n: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'n+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, u: 4}. What is the expected number of occurrences of the pattern 'g.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, u: 1, z: 1, v: 2, n: 1}, what is the expected number of times the pattern 'v*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, b: 1, p: 3, j: 1}. What is the expected number of occurrences of the pattern 'j*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, j: 1, c: 1, m: 2}. What is the expected number of occurrences of the pattern 'o+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, a: 4}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, t: 3}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, l: 1, h: 1, q: 1, b: 2}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, f: 2, c: 2} to form a word, what is the expected number of matches of the pattern 'mc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, y: 1, i: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, o: 1, e: 3, j: 1}, what is the expected number of times the pattern 'n.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, b: 3, v: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, l: 4}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, j: 3, y: 1} to form a word, what is the expected number of matches of the pattern 'j.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, l: 2, z: 1, q: 1, w: 1}, what is the expected number of times the pattern 'zw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, n: 2, b: 2}, what is the expected number of times the pattern 'mb+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, i: 1, d: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'p*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, y: 1, f: 2, g: 2}, what is the expected number of times the pattern 't*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, i: 2, f: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'f+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, b: 3, g: 1}. What is the expected number of occurrences of the pattern 's*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, b: 2, w: 2, y: 1}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, e: 2, r: 1, x: 1, d: 1}, what is the expected number of times the pattern 'x+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, h: 3, y: 1}. What is the expected number of occurrences of the pattern 'h+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, e: 1, o: 2, p: 1, s: 1}, what is the expected number of times the pattern 's*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 3, d: 3}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, r: 2, j: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, n: 1, h: 2, g: 2}. What is the expected number of occurrences of the pattern 'gn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, f: 1, l: 1, v: 2}, what is the expected number of times the pattern 'f+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, v: 2, z: 2}, what is the expected number of times the pattern 'nv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, u: 1, p: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'pl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, r: 1, b: 1, c: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'cp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, h: 2, o: 1, x: 2} to form a word, what is the expected number of matches of the pattern 't+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, s: 1, k: 1, x: 1, e: 1}. What is the expected number of occurrences of the pattern 's*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 3, c: 3}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, e: 3, h: 1} to form a word, what is the expected number of matches of the pattern 'e.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, j: 1, g: 1, c: 3}, what is the expected number of times the pattern 'ck*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, y: 4, v: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, e: 1, i: 2, y: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'i+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, a: 2, o: 1}, what is the expected number of times the pattern 'ow+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, s: 1, j: 1, d: 2}. What is the expected number of occurrences of the pattern 'j+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, a: 1, u: 1, i: 1, j: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, r: 2, d: 1, n: 1, o: 1}. What is the expected number of occurrences of the pattern 'rn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, w: 3, l: 1}. What is the expected number of occurrences of the pattern 'l*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 4, r: 2}, what is the expected number of times the pattern 'm*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 4, o: 2}, what is the expected number of times the pattern 'o*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 3, f: 3}, what is the expected number of times the pattern 'f+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, x: 1, j: 2, m: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 4, v: 2} to form a word, what is the expected number of matches of the pattern 's.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, m: 1, x: 2}, what is the expected number of times the pattern 'm*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, q: 1, b: 3, m: 1} to form a word, what is the expected number of matches of the pattern 'q*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, l: 1, u: 1, z: 1, m: 1}, what is the expected number of times the pattern 'lm+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, n: 2, l: 2, k: 1}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, h: 1, n: 3}, what is the expected number of times the pattern 'h+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, r: 2, s: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'u*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, h: 1, k: 1, o: 2, d: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 4, c: 1, q: 1}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 5, e: 1}. What is the expected number of occurrences of the pattern 'e*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, s: 2, v: 2}, what is the expected number of times the pattern 'xs+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 4, j: 2} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, o: 1, j: 1, p: 2}. What is the expected number of occurrences of the pattern 'op+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, t: 3}. What is the expected number of occurrences of the pattern 't+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, r: 3}, what is the expected number of times the pattern 'qr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, t: 2, i: 1, u: 1, a: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, y: 4}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, v: 1, i: 3}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, r: 1, g: 1, y: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 4, d: 2}, what is the expected number of times the pattern 'u+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, f: 2, l: 3}. What is the expected number of occurrences of the pattern 'n+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, d: 2, i: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, h: 3, i: 2} to form a word, what is the expected number of matches of the pattern 'h*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 4, j: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'o.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, l: 1, g: 3, j: 1} to form a word, what is the expected number of matches of the pattern 'jg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, d: 4, a: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, x: 4} to form a word, what is the expected number of matches of the pattern 'x*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, q: 3}, what is the expected number of times the pattern 'h.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, o: 1, u: 2, m: 1, h: 1}, what is the expected number of times the pattern 'mu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, r: 2, i: 2, n: 1}. What is the expected number of occurrences of the pattern 'nr+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, w: 3} to form a word, what is the expected number of matches of the pattern 'w*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, i: 1, y: 1, z: 1}. What is the expected number of occurrences of the pattern 'ez*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, h: 3, g: 1, i: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, o: 2, m: 1} to form a word, what is the expected number of matches of the pattern 'mi+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, y: 2, e: 2, i: 1}, what is the expected number of times the pattern 'e.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 4, e: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, u: 5}, what is the expected number of times the pattern 'um+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, j: 1, g: 3}, what is the expected number of times the pattern 'g.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'm.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, x: 2, h: 1, y: 1}. What is the expected number of occurrences of the pattern 'h+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, v: 1, u: 4}, what is the expected number of times the pattern 'u.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, r: 1, f: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'i+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, l: 1, i: 1, s: 1, e: 2}. What is the expected number of occurrences of the pattern 'nl+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, h: 1, l: 1, c: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'c+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, q: 1, f: 3}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 4, l: 2}, what is the expected number of times the pattern 'l+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, q: 4}, what is the expected number of times the pattern 'q*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, w: 3, z: 1}. What is the expected number of occurrences of the pattern 'z+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, z: 3, w: 1}, what is the expected number of times the pattern 'w.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, x: 4} to form a word, what is the expected number of matches of the pattern 'xj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, d: 3}, what is the expected number of times the pattern 'dj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, p: 2, k: 1, e: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'kw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, t: 1, m: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'yk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, s: 1, o: 1, y: 1}. What is the expected number of occurrences of the pattern 's.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 3, q: 3}, what is the expected number of times the pattern 'lq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, s: 1, k: 1, i: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'is*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, w: 1, a: 1, g: 2, t: 1} to form a word, what is the expected number of matches of the pattern 'g+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, k: 2, g: 1, e: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, l: 1, f: 1, e: 2, q: 1}. What is the expected number of occurrences of the pattern 'q*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, m: 3}, what is the expected number of times the pattern 'k+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, a: 2, f: 1, v: 1, c: 1}. What is the expected number of occurrences of the pattern 'af*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, i: 3}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, n: 2, j: 1}. What is the expected number of occurrences of the pattern 'nj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, m: 1, j: 1, o: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'dj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, z: 2, x: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, n: 2, e: 2, g: 1}, what is the expected number of times the pattern 'i+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, o: 2, u: 1, c: 1, f: 1}, what is the expected number of times the pattern 'fv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 4, f: 2}, what is the expected number of times the pattern 'e+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, p: 1, t: 1, m: 1, h: 1}, what is the expected number of times the pattern 'p+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, d: 1, e: 1, v: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'sv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, w: 1, d: 1, k: 2}. What is the expected number of occurrences of the pattern 'we*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, r: 2, i: 1, y: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, k: 2, q: 3}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, o: 2, n: 1, h: 1, q: 1}, what is the expected number of times the pattern 'qn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 4, e: 2}, what is the expected number of times the pattern 'te+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, r: 1, d: 1, s: 1, f: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, i: 1, o: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, n: 2, a: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'c.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, e: 1, f: 1, m: 1, c: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, x: 1, d: 1, w: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 4, a: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, r: 2, t: 2}, what is the expected number of times the pattern 'r.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, w: 2, m: 2, x: 1}. What is the expected number of occurrences of the pattern 'we+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, s: 3}, what is the expected number of times the pattern 'ws+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, r: 1, n: 1, z: 2, i: 1}. What is the expected number of occurrences of the pattern 'li+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, n: 1, h: 1, q: 2} to form a word, what is the expected number of matches of the pattern 'q.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, q: 2, l: 1, b: 1, n: 1}, what is the expected number of times the pattern 'l*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, e: 2, u: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'k.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, k: 2, d: 1, a: 1, u: 1}, what is the expected number of times the pattern 'd.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, z: 2, d: 1}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, t: 3} to form a word, what is the expected number of matches of the pattern 'at+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, f: 2, m: 1, l: 1, j: 1}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, k: 1, j: 1, n: 1, z: 1}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, a: 2, r: 1, w: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'w*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, t: 3} to form a word, what is the expected number of matches of the pattern 'ct+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, z: 3}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, c: 4} to form a word, what is the expected number of matches of the pattern 'c+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, q: 3, d: 1}. What is the expected number of occurrences of the pattern 'd+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, z: 1, d: 1, x: 2, k: 1}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, v: 1, u: 2, e: 1, z: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, h: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'u.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 4, w: 2}. What is the expected number of occurrences of the pattern 'wr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, e: 1, i: 1, k: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'f.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, v: 3, f: 1} to form a word, what is the expected number of matches of the pattern 'fl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, t: 3, a: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, t: 1, s: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, y: 4, s: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, s: 2, r: 1}, what is the expected number of times the pattern 'fs+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, u: 1, t: 1, j: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, b: 2, m: 3}. What is the expected number of occurrences of the pattern 'ub+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, z: 3}, what is the expected number of times the pattern 'zp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, b: 3, l: 2} to form a word, what is the expected number of matches of the pattern 'w.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, z: 3}, what is the expected number of times the pattern 'rz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, m: 1, k: 1, t: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, k: 2, j: 1, n: 2}. What is the expected number of occurrences of the pattern 'j+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, k: 1, a: 2, g: 1}, what is the expected number of times the pattern 'gk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, g: 1, z: 1, a: 2, h: 1}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, o: 1, k: 2, b: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, o: 1, y: 2, r: 2}, what is the expected number of times the pattern 'yx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, z: 2, j: 1}, what is the expected number of times the pattern 'j*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 4, n: 2}. What is the expected number of occurrences of the pattern 'n*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, f: 2, t: 1, r: 2}, what is the expected number of times the pattern 'f.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, u: 1, l: 3} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, b: 1, n: 2, j: 1, k: 1}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, l: 3, m: 1}. What is the expected number of occurrences of the pattern 'y.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, w: 2, y: 2}. What is the expected number of occurrences of the pattern 'w.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, t: 2, r: 1}, what is the expected number of times the pattern 'r*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, h: 2, r: 1, l: 1}, what is the expected number of times the pattern 'lr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, h: 4}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, q: 4} to form a word, what is the expected number of matches of the pattern 'p*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, m: 2, x: 3}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, q: 3, t: 1, x: 1}. What is the expected number of occurrences of the pattern 'qa*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, q: 1, z: 3, c: 1} to form a word, what is the expected number of matches of the pattern 'c*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, r: 1, e: 4} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, k: 1, z: 1, n: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, q: 1, o: 1, x: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'q.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, h: 1, r: 3} to form a word, what is the expected number of matches of the pattern 'rh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, w: 1, m: 2, p: 1, i: 1}, what is the expected number of times the pattern 'r+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, n: 1, e: 1, s: 1, h: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, g: 4} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 4, d: 2}, what is the expected number of times the pattern 'du+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, v: 4, q: 1} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, h: 1, s: 1, i: 2, e: 1}. What is the expected number of occurrences of the pattern 'e+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, r: 1, s: 3}, what is the expected number of times the pattern 's*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 4, d: 2}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, w: 3}. What is the expected number of occurrences of the pattern 'j+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, h: 2, b: 1, p: 1, k: 1}. What is the expected number of occurrences of the pattern 'p*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, y: 1, g: 2, v: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'g+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, j: 3, f: 2} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, m: 1, b: 2, o: 1, f: 1}. What is the expected number of occurrences of the pattern 'm*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, o: 3, b: 1, g: 1}, what is the expected number of times the pattern 'go+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, h: 2, u: 1, q: 2} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, t: 3, e: 1}. What is the expected number of occurrences of the pattern 'et+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, g: 2, t: 3}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'u.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 4, x: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, m: 1, h: 1, e: 3}. What is the expected number of occurrences of the pattern 'th+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, p: 4}, what is the expected number of times the pattern 'x.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, j: 1, h: 2, x: 1} to form a word, what is the expected number of matches of the pattern 'uh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, j: 2, k: 2}, what is the expected number of times the pattern 'x+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, y: 2, v: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, l: 4} to form a word, what is the expected number of matches of the pattern 'yl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, u: 1, c: 3}, what is the expected number of times the pattern 'un+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, g: 2, x: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'xg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, d: 1, q: 1, l: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 5, k: 1} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, r: 2, s: 1, k: 2}. What is the expected number of occurrences of the pattern 's.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, m: 2, d: 1, b: 1, n: 1}. What is the expected number of occurrences of the pattern 'd*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, r: 1, n: 1, i: 1, c: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, g: 3} to form a word, what is the expected number of matches of the pattern 'g+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, e: 1, o: 1, t: 2}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, l: 3}, what is the expected number of times the pattern 'v.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, m: 3}, what is the expected number of times the pattern 'm*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 4, u: 2}, what is the expected number of times the pattern 'z.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 3, g: 3}, what is the expected number of times the pattern 'wg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, z: 4}, what is the expected number of times the pattern 'zn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, f: 1, p: 1, r: 1, o: 1}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, e: 2, u: 1}. What is the expected number of occurrences of the pattern 'u+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}