messages list | ground_truth string | dataset string |
|---|---|---|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, a: 3, b: 4, c: 1, o: 2}, 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"
}
] | 0.14 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {j: 1, w: 5, z: 2, g: 1, d: 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 3, g: 2, s: 1, q: 2, o: 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"
}
] | 0.4 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {x: 3, p: 4, 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"
}
] | 0.27 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, m: 2, h: 3, c: 5}. 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"
}
] | 0.04 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {z: 3, a: 2, o: 3, v: 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 2, i: 6}, 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"
}
] | 3.71 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {m: 4, b: 4, 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"
}
] | 1.27 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, y: 4, g: 1, q: 3, p: 2}. 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"
}
] | 0.58 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {s: 4, o: 3, h: 3} 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"
}
] | 0.3 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, y: 9}. 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"
}
] | 0.35 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, x: 2, a: 4, h: 4}, 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"
}
] | 0.14 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, s: 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"
}
] | 0.32 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, w: 3, q: 2, l: 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"
}
] | 0.82 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {h: 4, w: 6} 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"
}
] | 3.43 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, l: 4, s: 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"
}
] | 0.16 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {f: 4, i: 5, x: 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"
}
] | 0.22 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {z: 4, m: 2, b: 5}. 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"
}
] | 1.83 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, v: 3, c: 1, p: 3, s: 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"
}
] | 0.16 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {a: 4, d: 2, t: 2} 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"
}
] | 0.6 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {l: 5, e: 3} 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"
}
] | 1.27 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, m: 3, u: 4}, 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"
}
] | 0.3 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {c: 2, m: 2, q: 2, d: 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {p: 2, g: 4, l: 2, i: 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"
}
] | 0.07 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {t: 7, r: 5}. 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"
}
] | 0.69 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 4, 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"
}
] | 2.21 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, q: 8}, 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"
}
] | 0.51 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, u: 2, s: 1, g: 3, i: 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"
}
] | 0.07 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {p: 3, v: 4, z: 2, b: 2} 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"
}
] | 0.15 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {p: 5, g: 4, 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"
}
] | 1.02 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {u: 2, c: 2, f: 2, o: 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"
}
] | 0.04 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 3, h: 3, f: 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"
}
] | 0.64 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {e: 7, w: 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"
}
] | 1.17 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 4, f: 7}, 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"
}
] | 0.65 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {e: 5, w: 4} 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"
}
] | 0.83 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, j: 4, a: 2, h: 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"
}
] | 0.79 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {u: 2, f: 2, n: 3, c: 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"
}
] | 0.18 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {t: 3, x: 1, y: 4, r: 2} 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"
}
] | 1.89 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {p: 4, u: 3, l: 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"
}
] | 0.25 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {x: 1, f: 2, u: 1, e: 3, r: 2}. What is the expected number of occurrences of the pattern 'e*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.19 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {j: 4, r: 4, z: 6} 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"
}
] | 1.45 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {u: 1, p: 5, l: 8}, 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"
}
] | 3.22 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {f: 3, p: 3, 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"
}
] | 0.29 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {c: 3, r: 7}. 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"
}
] | 3.29 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {p: 3, y: 2, b: 3, h: 7} 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"
}
] | 2.65 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {h: 4, q: 3, k: 3, z: 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"
}
] | 0.23 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {y: 2, v: 2, l: 4, k: 2, h: 3} 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"
}
] | 0.11 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 7, i: 4, b: 3}, 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"
}
] | 0.3 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 7, z: 2, p: 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"
}
] | 1.06 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 4, n: 3, g: 3}, 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"
}
] | 2.64 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {h: 4, c: 2, o: 5, a: 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"
}
] | 0.57 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {h: 1, l: 5, n: 3, x: 3, y: 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"
}
] | 0.45 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {d: 4, h: 5, t: 5}. 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"
}
] | 1.1 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 6, h: 7}, 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"
}
] | 1.62 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {i: 5, x: 10}. 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"
}
] | 1.15 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {b: 3, s: 3, l: 3, k: 3, 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"
}
] | 0.11 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 3, o: 5, u: 5}, what is the expected number of times the pattern 'o.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.6 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 5, h: 5, o: 5}, 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"
}
] | 0.71 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {x: 3, m: 7} 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"
}
] | 2.38 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {g: 6, l: 6}. 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"
}
] | 1.36 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {d: 2, w: 1, o: 2, z: 3, e: 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"
}
] | 0.4 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {e: 9, l: 4} 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"
}
] | 1.15 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {d: 4, i: 4, n: 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"
}
] | 1.33 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {x: 6, y: 6} 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"
}
] | 3.15 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {f: 5, w: 5} 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"
}
] | 1.67 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 7, g: 3}, 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"
}
] | 1.4 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 7, m: 3}, 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"
}
] | 1.79 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {c: 5, i: 6, h: 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"
}
] | 1.15 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 3, t: 4, m: 1, z: 1, p: 3}, 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"
}
] | 1.57 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 2, j: 8}, 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"
}
] | 0.98 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {r: 5, a: 5}. What is the expected number of occurrences of the pattern 'ar+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.17 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 9, d: 6}, what is the expected number of times the pattern 'dc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.74 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {d: 4, m: 4, y: 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"
}
] | 0.87 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 3, j: 5, p: 1, s: 1, 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"
}
] | 0.82 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 3, z: 9, 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"
}
] | 2.77 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 6, p: 3, q: 3}, 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"
}
] | 0.32 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 6, k: 6}, what is the expected number of times the pattern 'hk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.64 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 1, i: 5, h: 2, r: 3, x: 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"
}
] | 0.53 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 4, u: 3, r: 2, 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"
}
] | 0.21 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 8, r: 5}, 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"
}
] | 1.28 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 5, p: 6}, 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"
}
] | 4.29 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 6, b: 1, u: 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"
}
] | 2.73 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {i: 10, r: 3} to form a word, what is the expected number of matches of the pattern 'ir*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.73 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 3, w: 6, l: 4}, 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"
}
] | 0.55 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {s: 3, m: 3, k: 3, t: 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"
}
] | 0.32 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {q: 1, s: 1, o: 3, p: 3, 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"
}
] | 0.22 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {h: 6, n: 5} 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"
}
] | 2.73 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {d: 6, o: 5} 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"
}
] | 1.09 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, o: 3, q: 3, r: 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"
}
] | 0.4 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {c: 7, r: 3}. 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"
}
] | 3.62 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 6, k: 4}, 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"
}
] | 1.03 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {k: 4, c: 6}, what is the expected number of times the pattern 'kc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.8 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {i: 3, f: 2, w: 10} 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"
}
] | 0.29 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {x: 5, z: 5}. 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"
}
] | 1.33 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 4, k: 2, l: 3, t: 4}, what is the expected number of times the pattern 'rt+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.37 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {c: 8, 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"
}
] | 0.77 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {m: 3, t: 4, v: 1, c: 3, b: 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"
}
] | 0.57 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {y: 4, u: 4, j: 4} 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"
}
] | 2.28 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {w: 3, f: 3, y: 3, s: 2, r: 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"
}
] | 0.32 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {j: 6, c: 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"
}
] | 1.64 | MATH |
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