| {"messages": [{"content": "When randomly selecting 2 letters from the multiset {v: 1, r: 1, m: 1, b: 1, s: 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 {s: 1, i: 1, p: 1, q: 2, n: 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": "1.13", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, r: 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": "0.6", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 1, y: 5}, 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": "0.67", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, f: 1, j: 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": "0.33", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {o: 2, d: 1, b: 1, t: 1, 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": "0.37", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, k: 1, g: 1, u: 1, m: 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": "0.7", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {x: 1, i: 2, e: 1, c: 1, u: 1}, what is the expected number of times the pattern 'ci+' 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 2 letters from the multiset {q: 3, m: 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": "1.1", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, z: 2}. 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": "1.0", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 1, l: 5}, 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": "0.17", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {x: 1, t: 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": "Form a word by randomly choosing 3 letters from the multiset {e: 2, z: 1, a: 3}. 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": "0.25", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, k: 3, g: 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": "When randomly selecting 3 letters from the multiset {o: 2, x: 3} 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": "0.7", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {p: 1, u: 1, e: 1, l: 1, n: 1}, 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": "0.45", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 2 letters from the multiset {l: 1, v: 1, t: 3} 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": "0.45", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {u: 1, d: 2, c: 1, n: 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": "0.5", "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, y: 1}, what is the expected number of times the pattern 'v.*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": "Form a word by randomly choosing 3 letters from the multiset {i: 1, p: 3}. 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": "0.5", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, j: 1, e: 3, k: 1} to form a word, what is the expected number of matches of the pattern 'd.*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": "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 '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: 2, f: 1, g: 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 2 letters from the multiset {l: 1, g: 1, i: 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": "0.67", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, u: 1, r: 2} 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": "0.92", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, w: 4, b: 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: 2, k: 2}, 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": "0.83", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, q: 1, d: 3}, 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": "0.15", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {w: 1, g: 1, p: 1, l: 1, q: 2}. 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": "0.37", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, 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": "0.3", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {n: 2, v: 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": "0.1", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {b: 2, o: 1, 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": "0.08", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, d: 1, m: 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": "0.17", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {p: 1, n: 1, z: 1, j: 1, w: 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": "0.45", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {z: 2, e: 4}, 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": "1.6", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 1, f: 1, s: 1, b: 1}, 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": "0.58", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {w: 3, d: 1, g: 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 {n: 2, o: 2, a: 1, y: 1}, 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": "0.65", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 2 letters from the multiset {m: 1, x: 2, z: 3} 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": "0.2", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 2 letters from the multiset {h: 1, i: 1, c: 1, o: 1} 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": "0.08", "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+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": "When randomly selecting 4 letters from the multiset {q: 1, c: 2, f: 2, m: 1, w: 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": "0.29", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {o: 2, r: 1, t: 1, v: 2}. What is the expected number of occurrences of the pattern 'tr+' in 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: 2, a: 2, g: 3, y: 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": "0.11", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 4, q: 4}, 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": "1.2", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, a: 2, b: 2, f: 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": "1.07", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {o: 3, y: 1, w: 1, g: 1, n: 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": "0.21", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, g: 2, s: 1, f: 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": "0.14", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 2, d: 2, f: 2, j: 2}. What is the expected number of occurrences of the pattern 'jd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.24", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 4 letters from the multiset {c: 2, f: 4} 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": "3.6", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, s: 3, c: 1, y: 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": "0.14", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, u: 1, z: 1, e: 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 {j: 1, a: 2, z: 1, k: 1, b: 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": "0.05", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 5, b: 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": "When randomly selecting 4 letters from the multiset {o: 3, l: 2, w: 1, v: 1} 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": "1.93", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 4 letters from the multiset {g: 1, x: 2, v: 1, d: 1, p: 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": "0.2", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {y: 4, p: 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": "2.4", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, k: 3, z: 1, p: 1, 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": "0.13", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 4 letters from the multiset {x: 1, d: 2, c: 3, z: 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": "1.4", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 3, g: 3, q: 1}, 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": "0.28", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, p: 5}. 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": "2.77", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 1, j: 1, w: 1, c: 1, n: 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": "0.9", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 1, u: 4, s: 1, f: 2} 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": "0.12", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, g: 3, v: 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": "0.32", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 3, v: 3} 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": "1.8", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {y: 4, 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": "0.86", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, k: 4}. 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": "1.73", "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 'f.*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": "When randomly selecting 4 letters from the multiset {g: 1, h: 1, v: 2, p: 1, 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": "0.4", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, m: 1, z: 2, l: 1, x: 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": "0.1", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 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": "0.4", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 4 letters from the multiset {r: 3, i: 4, h: 1} 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": "0.21", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, z: 2, n: 2, r: 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": "0.2", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 1, c: 2, f: 3, o: 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": "0.21", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, s: 1, d: 1, b: 1, r: 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": "0.53", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 4 letters from the multiset {r: 2, o: 1, c: 1, h: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'sr*'? 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 4 letters from the multiset {m: 1, g: 1, i: 1, h: 2, o: 1}. What is the expected number of occurrences of the pattern 'ih*' in 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 {c: 2, j: 2, a: 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": "0.3", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, w: 4}, what is the expected number of times the pattern 'wd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.69", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {d: 1, n: 2, y: 1, q: 1, g: 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": "0.05", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, a: 2, p: 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": "0.15", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, e: 4, v: 3}, 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": "0.14", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 4 letters from the multiset {n: 1, b: 3, i: 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": "0.9", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, i: 4}. What is the expected number of occurrences of the pattern 'ih+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.69", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, y: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'nw*'? 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: 2, k: 2, t: 4}, what is the expected number of times the pattern 'o+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 {v: 1, a: 1, x: 1, d: 2, q: 2} 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": "0.1", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, d: 3, p: 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": "0.2", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, u: 2, d: 1, c: 2, 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": "0.11", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 1, e: 3, d: 2, q: 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": "0.64", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 2, o: 2, s: 3}, 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": "2.2", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 4, z: 4}. 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": "3.2", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, d: 1, s: 2, l: 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 4 by randomly selecting letters from the multiset {v: 1, k: 1, m: 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": "When randomly selecting 4 letters from the multiset {k: 1, m: 5} 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": "0.5", "dataset": "MATH"} | |
| {"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, m: 2, l: 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": "0.48", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, s: 1, m: 1, d: 1, 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": "0.0", "dataset": "MATH"} | |
| {"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 2, x: 1, a: 2, z: 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": "1.29", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 4 letters from the multiset {k: 2, g: 2, n: 1, b: 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": "1.53", "dataset": "MATH"} | |
| {"messages": [{"content": "When randomly selecting 4 letters from the multiset {q: 2, f: 2, w: 1, s: 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": "0.73", "dataset": "MATH"} | |