messages list | ground_truth string | dataset string |
|---|---|---|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 5, v: 3, f: 3, n: 3}, what is the expected number of times the pattern 'fn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.22 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 7, n: 4, 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"
}
] | 1.2 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {y: 6, b: 2, k: 4} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.91 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {q: 3, x: 4, b: 7}. What is the expected number of occurrences of the pattern 'qq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.96 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {o: 7, d: 5}. What is the expected number of occurrences of the pattern 'o+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.76 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {h: 4, p: 8, l: 3} to form a word, what is the expected number of matches of the pattern 'hl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.26 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 4, z: 1, m: 5, l: 2}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.91 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {k: 3, u: 2, w: 1, r: 3, s: 2}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.18 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {a: 6, f: 5, m: 3}. What is the expected number of occurrences of the pattern 'f.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.82 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {w: 1, x: 5, a: 2, u: 2, s: 2}. What is the expected number of occurrences of the pattern 'sx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.25 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {d: 5, m: 2, l: 7} to form a word, what is the expected number of matches of the pattern 'ml*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.9 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 3, d: 3, g: 3, p: 1}, what is the expected number of times the pattern 'p*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.63 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {d: 6, k: 2, j: 4}. What is the expected number of occurrences of the pattern 'd+j' 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 5 by randomly selecting letters from the multiset {b: 3, c: 5, z: 2, m: 4}, what is the expected number of times the pattern 'z.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 6, d: 9}, what is the expected number of times the pattern 'q+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.0 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {j: 3, m: 2, e: 4, t: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'j*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.64 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {z: 1, f: 3, l: 3, h: 3, y: 2}. What is the expected number of occurrences of the pattern 'f.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.45 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {c: 3, n: 7, h: 3}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.69 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {g: 3, m: 1, k: 3, e: 3, p: 1}, what is the expected number of times the pattern 'me+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 5, m: 3, p: 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"
}
] | 1.38 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {o: 1, z: 2, w: 5, r: 5} to form a word, what is the expected number of matches of the pattern 'z.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.38 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 8, p: 7}, what is the expected number of times the pattern 'lp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.23 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {r: 6, l: 5} to form a word, what is the expected number of matches of the pattern 'l.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.64 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {k: 5, p: 7}. What is the expected number of occurrences of the pattern 'k+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.04 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 3, b: 2, t: 5}, 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"
}
] | 2.22 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {d: 7, z: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'i.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.47 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 1, h: 2, o: 1, t: 2, q: 5}, 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"
}
] | 0.11 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 7, t: 6}, what is the expected number of times the pattern 't*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.26 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 6, n: 3, s: 2}, what is the expected number of times the pattern 's*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.27 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 7, h: 6}, what is the expected number of times the pattern 'h+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.1 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {h: 2, n: 2, c: 5, u: 2}. What is the expected number of occurrences of the pattern 'n.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.22 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {a: 9, g: 6}. What is the expected number of occurrences of the pattern 'a.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.54 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {v: 1, w: 4, o: 2, q: 2, r: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 2, t: 5, y: 5}, what is the expected number of times the pattern 'tl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.24 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {f: 4, g: 3, x: 2, h: 4, t: 2}. What is the expected number of occurrences of the pattern 'tg+' 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 5 letters from the multiset {u: 4, g: 9, f: 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"
}
] | 0.57 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 6, f: 6}, what is the expected number of times the pattern 'w.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.64 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 4, t: 7, d: 4}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.2 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {p: 6, l: 9}. What is the expected number of occurrences of the pattern 'lp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.4 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, v: 5, f: 3}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {w: 9, q: 6}. What is the expected number of occurrences of the pattern 'w+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.18 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {c: 2, q: 2, e: 2, t: 7}. What is the expected number of occurrences of the pattern 'e*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.44 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {f: 1, x: 4, g: 3, i: 2} to form a word, what is the expected number of matches of the pattern 'x+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {w: 2, u: 2, o: 3, q: 3, f: 2}. What is the expected number of occurrences of the pattern 'qw*' 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 {o: 3, d: 2, t: 1, e: 6}. What is the expected number of occurrences of the pattern 'oe+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.82 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {e: 3, g: 4, q: 1, t: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'to+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 2, k: 4, w: 3, j: 4}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.77 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 5, d: 3, x: 7}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.95 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {a: 4, k: 6, t: 3}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.46 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {e: 5, k: 3, w: 5, c: 2} to form a word, what is the expected number of matches of the pattern 'c+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.15 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 3, m: 1, k: 1, h: 2, p: 4}, what is the expected number of times the pattern 'm+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {r: 3, t: 5, a: 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"
}
] | 2.5 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {q: 5, a: 7, h: 3}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.95 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 2, n: 3, b: 1, p: 6}, what is the expected number of times the pattern 'p.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.55 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {e: 3, t: 2, p: 1, k: 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {l: 4, h: 2, i: 1, c: 4} to form a word, what is the expected number of matches of the pattern 'i.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.11 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 4, c: 1, j: 5, e: 1, b: 3}, what is the expected number of times the pattern 'j+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 7, w: 6}, what is the expected number of times the pattern 'ww*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.58 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {s: 1, c: 3, p: 8} to form a word, what is the expected number of matches of the pattern 'ps+'? 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 {n: 3, r: 4, s: 2, y: 4} 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"
}
] | 0.37 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {h: 4, b: 5, r: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {n: 3, l: 4, z: 2, d: 2, h: 1}. What is the expected number of occurrences of the pattern 'zd+' 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 5 letters from the multiset {t: 3, k: 2, x: 3, v: 3}. What is the expected number of occurrences of the pattern 'xv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.39 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 3, c: 2, s: 5}, what is the expected number of times the pattern 'es+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.7 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 7, w: 4, k: 4}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.57 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 4, t: 7, p: 4}. What is the expected number of occurrences of the pattern 'p*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.33 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {a: 4, c: 4, w: 2, o: 5}. What is the expected number of occurrences of the pattern 'c.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.76 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {e: 7, f: 4}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.65 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {d: 3, n: 4, l: 4} to form a word, what is the expected number of matches of the pattern 'l*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.5 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {k: 8, f: 6}, 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"
}
] | 3.08 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {l: 3, m: 3, c: 5}. What is the expected number of occurrences of the pattern 'c*m' 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 5 by randomly selecting letters from the multiset {q: 6, h: 5, s: 4}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.95 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {q: 5, u: 6}. What is the expected number of occurrences of the pattern 'u.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.64 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 5, f: 4, t: 6}, what is the expected number of times the pattern 'tw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.53 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {r: 1, v: 4, n: 2, m: 4}. What is the expected number of occurrences of the pattern 'v.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.44 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {f: 4, q: 6}, what is the expected number of times the pattern 'f*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.43 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {k: 6, l: 3, d: 2}. What is the expected number of occurrences of the pattern 'k.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.65 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {u: 4, s: 4, g: 4}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.91 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 2, u: 4, h: 2, p: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.22 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {h: 1, a: 2, q: 1, k: 2, x: 4}. What is the expected number of occurrences of the pattern 'hq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.43 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {d: 2, m: 3, l: 5, v: 2}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.91 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {s: 3, x: 6, f: 5}. What is the expected number of occurrences of the pattern 'x.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.59 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {i: 5, n: 6, s: 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"
}
] | 3.33 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 2, q: 3, b: 3, u: 4}, what is the expected number of times the pattern 'ub+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.42 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {t: 6, o: 6}. What is the expected number of occurrences of the pattern 'ot*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.14 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 4, a: 1, f: 3, n: 3}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.09 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 4, z: 2, m: 4}, what is the expected number of times the pattern 'zt*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.14 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 3, y: 2, l: 4, h: 3, e: 1}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.77 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 4, b: 7, k: 1}, what is the expected number of times the pattern 'k+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.12 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 7, m: 8}, 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"
}
] | 3.23 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {b: 6, l: 6}. What is the expected number of occurrences of the pattern 'l.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.73 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {i: 6, c: 3, x: 2, j: 3, m: 1}. What is the expected number of occurrences of the pattern 'x+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.12 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {l: 6, c: 5} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.73 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 6, i: 6}, 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"
}
] | 1.15 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {x: 3, p: 6, j: 2} to form a word, what is the expected number of matches of the pattern 'j*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.6 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 2, v: 3, x: 2, b: 2, p: 3}, what is the expected number of times the pattern 'zp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.16 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {x: 3, j: 4, r: 3, w: 1, b: 3} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {n: 1, t: 2, v: 3, z: 2, p: 3} to form a word, what is the expected number of matches of the pattern 'z.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.55 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {f: 2, a: 2, r: 3, s: 3}. What is the expected number of occurrences of the pattern 'r+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.35 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {t: 9, q: 2, y: 3} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.37 | MATH |
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