messages listlengths 1 1 | ground_truth stringclasses 108 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "When randomly selecting 6 letters from the multiset {w: 3, t: 2, i: 1, m: 4, d: 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"
}
] | 1.75 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 3, f: 2, u: 2, l: 5}, 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"
}
] | 2.27 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 2, n: 7, v: 3}, 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"
}
] | 1.93 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {q: 2, y: 5, g: 3, a: 2}. 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"
}
] | 2.91 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {x: 2, p: 5, a: 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"
}
] | 2.27 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {f: 4, a: 4, t: 1, d: 3} 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"
}
] | 0.63 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {i: 7, 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"
}
] | 2.27 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {l: 2, x: 5, r: 5} 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"
}
] | 2.27 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {a: 3, c: 3, e: 3, s: 3}. 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"
}
] | 0.4 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 7, b: 1, f: 3, y: 1}, what is the expected number of times the pattern 'f.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.39 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {d: 3, o: 2, c: 3, w: 2, p: 2} 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"
}
] | 0.27 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {w: 5, c: 7}, 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"
}
] | 2.27 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {f: 3, t: 3, u: 3, k: 1, h: 2} 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"
}
] | 0.34 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {u: 5, x: 7} 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"
}
] | 2.27 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {d: 4, z: 6, i: 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"
}
] | 1.36 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {i: 4, k: 2, m: 4, o: 2}, 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"
}
] | 0.16 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 3, q: 2, t: 5, o: 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"
}
] | 2.3 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {o: 2, p: 3, l: 2, r: 3, 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"
}
] | 0.23 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {c: 5, h: 7} 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"
}
] | 2.33 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {f: 2, p: 2, j: 6, o: 1, u: 1} 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"
}
] | 0.04 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 2, b: 3, d: 7}, 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"
}
] | 1.75 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {v: 3, i: 2, n: 3, p: 3, j: 1} to form a word, what is the expected number of matches of the pattern 'vi+'? 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 6 letters from the multiset {z: 2, u: 1, p: 3, w: 2, j: 4}. 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"
}
] | 0.68 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {t: 4, g: 8}. 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"
}
] | 2.41 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {n: 1, g: 2, e: 3, i: 2, r: 4}. 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"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {o: 4, w: 8}. 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"
}
] | 6.36 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {s: 8, 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"
}
] | 1.36 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 3, r: 3, l: 2, g: 3, c: 1}, 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"
}
] | 0.13 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {q: 7, c: 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"
}
] | 4.77 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {j: 3, c: 3, u: 2, k: 4}. 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"
}
] | 0.58 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {q: 3, x: 3, v: 6} 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"
}
] | 2.05 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {u: 5, t: 7}. 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"
}
] | 3.98 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {g: 1, p: 3, s: 3, f: 5}. 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"
}
] | 0.27 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 3, q: 6, k: 3}, 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"
}
] | 3.8 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {t: 3, j: 5, 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"
}
] | 1.36 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {a: 2, v: 1, t: 6, r: 3}. 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"
}
] | 0.13 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {u: 3, r: 3, z: 4, t: 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"
}
] | 0.68 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 3, z: 3, r: 4, o: 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"
}
] | 0.27 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {l: 6, w: 6}. 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"
}
] | 4.09 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {f: 4, n: 2, w: 4, b: 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"
}
] | 1.08 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {l: 1, y: 4, b: 2, t: 2, m: 3} 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"
}
] | 1.16 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {v: 4, e: 3, n: 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"
}
] | 0.68 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 3, t: 4, l: 5}, 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"
}
] | 0.97 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {m: 3, b: 9} 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"
}
] | 0.68 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {k: 4, n: 3, j: 5}. 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"
}
] | 0.8 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {t: 4, h: 1, b: 2, l: 5} 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"
}
] | 1.36 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 3, n: 4, p: 1, r: 2, 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"
}
] | 1.36 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {k: 6, q: 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"
}
] | 0.68 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {q: 8, u: 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"
}
] | 6.36 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {g: 3, h: 3, k: 3, l: 2, p: 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"
}
] | 0.68 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {k: 4, q: 2, u: 4, o: 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"
}
] | 1.82 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {r: 5, i: 4, e: 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"
}
] | 1.36 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {z: 2, a: 4, t: 3, o: 2, w: 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"
}
] | 1.61 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {p: 4, n: 3, q: 5}. 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"
}
] | 2.3 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {e: 4, n: 3, v: 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"
}
] | 2.27 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {x: 1, y: 3, o: 4, k: 3, e: 1}, what is the expected number of times the pattern 'ye*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.61 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {f: 5, g: 4, 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 3, o: 2, k: 2, t: 2, q: 3}, 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"
}
] | 0.25 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 3, d: 3, y: 4, g: 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"
}
] | 0.68 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {f: 3, k: 5, c: 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"
}
] | 0.8 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 3, u: 4, g: 3, s: 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"
}
] | 0.4 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {m: 3, o: 2, c: 5, b: 2}, 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"
}
] | 3.47 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {c: 5, o: 1, i: 3, y: 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"
}
] | 0.4 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {d: 7, c: 5} 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"
}
] | 1.88 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {p: 2, m: 4, f: 1, w: 2, i: 3}. 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"
}
] | 0.45 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {z: 2, a: 4, e: 4, x: 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"
}
] | 2.78 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {s: 5, j: 2, i: 2, r: 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"
}
] | 0.23 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {k: 3, p: 3, s: 3, h: 3}. 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"
}
] | 0.4 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 4, u: 4, a: 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"
}
] | 1.36 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {q: 5, d: 3, n: 4}. What is the expected number of occurrences of the pattern 'nd+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.53 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {w: 5, z: 3, p: 3, n: 1} 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"
}
] | 0.13 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {n: 4, t: 4, a: 1, h: 2, f: 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 4, p: 1, i: 7}, 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"
}
] | 0.19 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {l: 5, a: 7}, 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"
}
] | 4.83 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {o: 6, j: 6} 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"
}
] | 5.14 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 4, t: 4, 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"
}
] | 2.78 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {k: 4, u: 3, 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"
}
] | 1.75 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {l: 4, j: 2, z: 2, h: 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"
}
] | 1.16 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {k: 2, p: 3, m: 2, r: 2, a: 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"
}
] | 0.23 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {l: 6, i: 6}. 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"
}
] | 2.14 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 3, n: 4, y: 1, e: 2, l: 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"
}
] | 0.39 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {q: 6, b: 6}, 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"
}
] | 3.41 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {q: 1, k: 6, u: 1, b: 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {x: 3, s: 4, k: 2, c: 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"
}
] | 0.68 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {c: 6, d: 3, y: 3}. What is the expected number of occurrences of the pattern 'y+d' 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": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 5, c: 1, f: 1, o: 5}, 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"
}
] | 1.34 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {e: 3, f: 2, r: 4, n: 3} 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"
}
] | 0.68 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {j: 5, y: 7} 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"
}
] | 2.27 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {a: 1, j: 7, u: 3, l: 1}, 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"
}
] | 0.97 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {p: 5, c: 3, h: 4} 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"
}
] | 0.67 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 3, q: 3, w: 2, c: 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"
}
] | 0.68 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 5, o: 7}, 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"
}
] | 4.83 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {j: 6, i: 6}. What is the expected number of occurrences of the pattern 'i*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5.14 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {c: 2, t: 5, x: 2, h: 3} 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"
}
] | 0.54 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 3, t: 3, r: 4, s: 1, h: 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"
}
] | 2.53 | MATH |
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {u: 3, d: 4, j: 4, v: 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"
}
] | 2.53 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {l: 5, z: 7} 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"
}
] | 4.77 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {i: 4, u: 5, p: 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"
}
] | 1.36 | MATH |
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {s: 5, d: 3, y: 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"
}
] | 0.68 | MATH |
[
{
"content": "When randomly selecting 6 letters from the multiset {y: 2, b: 6, z: 4} 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"
}
] | 0.53 | MATH |
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