messages list | ground_truth string | dataset string |
|---|---|---|
[
{
"content": "When randomly selecting 4 letters from the multiset {i: 1, x: 3, p: 5, r: 3} to form a word, what is the expected number of matches of the pattern 'ix+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 7, a: 4}, what is the expected number of times the pattern 'h+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.21 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 2, d: 1, w: 4, j: 3}, what is the expected number of times the pattern 'j*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.32 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {f: 3, h: 2, y: 5, r: 2}. What is the expected number of occurrences of the pattern 'yf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.61 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 2, e: 2, w: 2, l: 4}, what is the expected number of times the pattern 'r.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.53 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {x: 5, y: 5}. What is the expected number of occurrences of the pattern 'y*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.17 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {l: 6, g: 4, z: 1}. What is the expected number of occurrences of the pattern 'z+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.22 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {b: 3, w: 2, y: 2, z: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'y*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.42 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 6, k: 8}, what is the expected number of times the pattern 'ki+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.48 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {v: 2, a: 7, g: 3} to form a word, what is the expected number of matches of the pattern 'va*'? Round 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 {c: 4, d: 2, r: 3, h: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.18 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {t: 5, x: 5, d: 1, s: 2}. What is the expected number of occurrences of the pattern 'x+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.61 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {q: 6, f: 3, c: 4, d: 1}, what is the expected number of times the pattern 'q*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.63 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {k: 2, g: 2, h: 3, f: 2, v: 3} to form a word, what is the expected number of matches of the pattern 'v.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.68 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 1, k: 7, d: 2}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {f: 5, h: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'fr+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.64 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {d: 2, a: 3, x: 4, i: 3, v: 3} 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"
}
] | 0.26 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {v: 4, c: 6} 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"
}
] | 3.33 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {x: 4, o: 6} to form a word, what is the expected number of matches of the pattern 'ox*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.43 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {e: 3, o: 2, k: 4, w: 1}. What is the expected number of occurrences of the pattern 'w+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.07 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 5, q: 5, u: 4}, what is the expected number of times the pattern 'uq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.57 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {k: 4, g: 1, f: 1, x: 5}, what is the expected number of times the pattern 'x*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.71 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {q: 3, y: 8, p: 4} to form a word, what is the expected number of matches of the pattern 'qp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {g: 2, l: 2, t: 6, c: 2} to form a word, what is the expected number of matches of the pattern 'lt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.05 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {o: 3, m: 3, x: 2, z: 2, y: 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"
}
] | 0.18 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {u: 1, m: 3, f: 2, e: 3, g: 4}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.77 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {n: 4, p: 4, t: 5}. What is the expected number of occurrences of the pattern 'n+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.37 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 4, j: 3, k: 1, w: 3, r: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.23 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {j: 4, o: 1, u: 6} 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"
}
] | 2.73 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {i: 5, k: 4, f: 4} to form a word, what is the expected number of matches of the pattern 'ik+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.63 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 1, g: 4, a: 3, o: 1, d: 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"
}
] | 0.05 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {d: 3, b: 5, u: 4}. What is the expected number of occurrences of the pattern 'u+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.31 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {c: 3, p: 4, n: 6, k: 1}. What is the expected number of occurrences of the pattern 'kp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.36 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {f: 2, r: 9} to form a word, what is the expected number of matches of the pattern 'r*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.64 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {d: 5, m: 6}. What is the expected number of occurrences of the pattern 'md+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.11 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {x: 8, b: 6} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.99 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {h: 2, e: 5, i: 8}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.57 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {x: 2, s: 2, g: 4, o: 1, q: 4} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.46 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {u: 3, z: 2, r: 3, e: 7}. 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"
}
] | 0.09 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 5, t: 6}, what is the expected number of times the pattern 'wt*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.0 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {j: 1, c: 6, o: 4, w: 1} to form a word, what is the expected number of matches of the pattern 'j.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.05 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 11, d: 3}, what is the expected number of times the pattern 'a*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.83 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {q: 9, f: 6}. What is the expected number of occurrences of the pattern 'fq+' 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 {j: 4, p: 7, q: 4}. What is the expected number of occurrences of the pattern 'p+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.55 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {c: 6, f: 6}. What is the expected number of occurrences of the pattern 'c.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.64 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {a: 5, y: 1, s: 2, j: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {k: 3, o: 4, a: 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"
}
] | 0.33 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 3, l: 3, p: 4, t: 2, b: 3}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.57 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {e: 3, p: 2, o: 4, m: 5} to form a word, what is the expected number of matches of the pattern 'eo+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.32 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {u: 3, y: 5, h: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'e.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.23 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {n: 4, l: 3, j: 3, u: 2}. What is the expected number of occurrences of the pattern 'u+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.19 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {x: 3, a: 2, m: 5} 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"
}
] | 0.4 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {k: 7, i: 8}. What is the expected number of occurrences of the pattern 'i*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.03 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {d: 9, m: 6}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.43 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {p: 4, c: 3, x: 1, d: 4, b: 2}. What is the expected number of occurrences of the pattern 'cb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.21 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 2, j: 1, g: 2, f: 3, s: 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"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 4, c: 2, j: 2, y: 3, q: 3}, what is the expected number of times the pattern 'lj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.62 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 5, d: 5}, what is the expected number of times the pattern 'd*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.17 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 4, m: 4, f: 2}, what is the expected number of times the pattern 'f*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.39 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 3, k: 1, p: 3, g: 4, l: 1}, what is the expected number of times the pattern 'pl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.07 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {c: 4, i: 5, y: 3} to form a word, what is the expected number of matches of the pattern 'y.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.55 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {e: 7, u: 1, a: 4, f: 3} to form a word, what is the expected number of matches of the pattern 'eu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 6, l: 5, y: 3}, what is the expected number of times the pattern 'ly*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.7 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {z: 6, p: 1, a: 4, s: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 3, i: 4, j: 3, k: 2}, what is the expected number of times the pattern 'ki+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.31 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {n: 2, o: 4, b: 2, u: 2, d: 3}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.23 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 1, u: 2, n: 2, e: 1, w: 4}, what is the expected number of times the pattern 'e.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 7, b: 4}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.09 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {z: 6, k: 8}. What is the expected number of occurrences of the pattern 'z+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.48 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {x: 2, u: 8, v: 4}. What is the expected number of occurrences of the pattern 'uv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.71 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 4, l: 3, w: 4}, what is the expected number of times the pattern 'gw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.0 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {r: 2, d: 4, a: 3, y: 2}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.18 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 5, z: 5, w: 1}, what is the expected number of times the pattern 'z*w' 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 {i: 5, z: 4, h: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'z.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.36 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 4, y: 6, j: 2, p: 1}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {g: 5, n: 4, t: 6} to form a word, what is the expected number of matches of the pattern 'gn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.12 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 4, q: 1, n: 6, c: 3}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {r: 3, t: 7} to form a word, what is the expected number of matches of the pattern 'tr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.62 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {q: 3, s: 3, j: 2, p: 3, i: 4}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 3, w: 4, u: 3, p: 2}, what is the expected number of times the pattern 'u*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.09 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 5, v: 6}, what is the expected number of times the pattern 'v+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.2 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {i: 5, f: 3, x: 2, y: 1, w: 2}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {g: 2, f: 8, t: 1, o: 1, e: 2}. What is the expected number of occurrences of the pattern 'f*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.64 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {y: 2, h: 3, o: 2, k: 2, s: 2}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.18 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {q: 2, n: 2, x: 5, k: 3, r: 1}. What is the expected number of occurrences of the pattern 'q+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.16 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {h: 6, u: 6, x: 3}. What is the expected number of occurrences of the pattern 'u*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.47 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {d: 3, k: 2, b: 3, t: 1, s: 2}. What is the expected number of occurrences of the pattern 's+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.24 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 4, g: 2, v: 4, k: 4}, what is the expected number of times the pattern 'a.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.88 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {y: 1, p: 5, g: 6} to form a word, what is the expected number of matches of the pattern 'py*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.78 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {s: 1, c: 6, o: 4, x: 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"
}
] | 1.65 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {h: 6, q: 4, k: 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"
}
] | 0.66 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 5, i: 5}, what is the expected number of times the pattern 'p+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.67 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {j: 3, z: 3, r: 3, a: 4}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.23 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {l: 4, v: 2, j: 6} to form a word, what is the expected number of matches of the pattern 'l*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.42 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {j: 4, r: 2, q: 5, b: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.91 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {q: 3, f: 5, v: 2, d: 5}, what is the expected number of times the pattern 'df+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.61 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 7, x: 2, b: 2}, what is the expected number of times the pattern 'yx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.73 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {i: 3, p: 3, t: 1, l: 4} to form a word, what is the expected number of matches of the pattern 't+i'? 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 {p: 1, x: 1, q: 1, h: 4, z: 3}. What is the expected number of occurrences of the pattern 'x+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.18 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {y: 3, w: 4, a: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.23 | MATH |
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