messages list | ground_truth string | dataset string |
|---|---|---|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 8, x: 7}, what is the expected number of times the pattern 'v.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.67 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {s: 2, d: 1, n: 1, p: 5, c: 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {s: 2, t: 4, e: 1, y: 5, b: 3} to form a word, what is the expected number of matches of the pattern 'ty+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.48 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {i: 4, s: 6, e: 5} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.95 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {z: 3, w: 4, x: 5, b: 3} to form a word, what is the expected number of matches of the pattern 'zb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.19 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {u: 7, g: 4}. What is the expected number of occurrences of the pattern 'g.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.55 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 4, g: 1, o: 2, d: 3, y: 2}, what is the expected number of times the pattern 'g.*g' 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 {w: 2, y: 3, f: 2, i: 3}, 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"
}
] | 1.98 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {s: 4, r: 1, x: 2, e: 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"
}
] | 0.44 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {e: 2, p: 4, o: 3, j: 3}. What is the expected number of occurrences of the pattern 'j.*e' 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": "When randomly selecting 4 letters from the multiset {s: 2, j: 5, q: 4} to form a word, what is the expected number of matches of the pattern 'qs*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.69 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {e: 3, s: 3, z: 3, r: 4} to form a word, what is the expected number of matches of the pattern 'e.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {p: 4, n: 3, d: 4} to form a word, what is the expected number of matches of the pattern 'dp+'? 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 {c: 8, v: 6}. 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"
}
] | 3.08 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {s: 4, v: 3, b: 5, q: 1}. What is the expected number of occurrences of the pattern 'q*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.23 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {z: 5, p: 2, h: 2, s: 3}. 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"
}
] | 0.09 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {h: 3, p: 7, d: 2, c: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'pi+'? 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 {z: 2, o: 4, u: 3, f: 5}, what is the expected number of times the pattern 'z.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {v: 8, z: 5, c: 2}. What is the expected number of occurrences of the pattern 'c*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.87 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {i: 7, o: 3} to form a word, what is the expected number of matches of the pattern 'i.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.33 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {g: 8, y: 3} to form a word, what is the expected number of matches of the pattern 'g+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.73 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {i: 2, g: 3, n: 1, l: 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"
}
] | 1.09 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {d: 7, p: 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"
}
] | 1.62 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 4, d: 4, z: 2, 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"
}
] | 0.23 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {t: 5, g: 2, m: 2, q: 3} to form a word, what is the expected number of matches of the pattern 't+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.45 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 2, e: 1, a: 2, c: 5, r: 4}, 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"
}
] | 0.73 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {m: 5, y: 5, p: 2, f: 2}. What is the expected number of occurrences of the pattern 'my+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.71 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {k: 1, z: 2, o: 2, t: 1, r: 4} to form a word, what is the expected number of matches of the pattern 'or*'? Round 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 4 letters from the multiset {f: 9, c: 6}. What is the expected number of occurrences of the pattern 'cf+' 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 {n: 2, j: 4, l: 3, c: 1, h: 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"
}
] | 0.4 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {m: 6, u: 4, r: 5}. What is the expected number of occurrences of the pattern 'r+u' 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 5 by randomly selecting letters from the multiset {a: 6, j: 6, n: 2}, what is the expected number of times the pattern 'n.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.66 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {i: 5, c: 7, x: 3} to form a word, what is the expected number of matches of the pattern 'i+x'? 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 5 by randomly selecting letters from the multiset {m: 2, s: 3, z: 4, p: 3}, what is the expected number of times the pattern 'ms+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.21 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {i: 4, v: 2, k: 5, u: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'm+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {a: 4, y: 1, e: 4, j: 1} to form a word, what is the expected number of matches of the pattern 'ey*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.73 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {k: 7, d: 3, f: 5}. What is the expected number of occurrences of the pattern 'd.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.71 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {z: 4, i: 2, f: 5, l: 3}. What is the expected number of occurrences of the pattern 'f*l' 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 4 by randomly selecting letters from the multiset {h: 2, x: 5, v: 2, g: 4}, what is the expected number of times the pattern 'vg+' appears? Round 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 4 by randomly selecting letters from the multiset {n: 7, r: 8}, what is the expected number of times the pattern 'n.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.6 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {f: 6, b: 2, k: 6}. What is the expected number of occurrences of the pattern 'kf+' in each word? Round your answer 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 {p: 5, s: 5, i: 3} to form a word, what is the expected number of matches of the pattern 's*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.15 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 4, m: 1, i: 4, w: 2}, what is the expected number of times the pattern 'm*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.96 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 6, o: 5, f: 2, m: 2}, 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"
}
] | 2.44 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {g: 3, j: 3, y: 1, p: 3, c: 3}. What is the expected number of occurrences of the pattern 'g*c' in each word? Round your answer 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 {l: 6, i: 4}, what is the expected number of times the pattern 'il*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.8 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {c: 6, r: 4, w: 2} to form a word, what is the expected number of matches of the pattern 'r*c'? 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 {l: 3, h: 5, j: 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"
}
] | 0.38 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {d: 5, q: 3, x: 2, a: 3}. What is the expected number of occurrences of the pattern 'x.*x' 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 {v: 6, l: 4, r: 3}. 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"
}
] | 0.38 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {h: 2, l: 3, b: 3, d: 2, w: 1}. What is the expected number of occurrences of the pattern 'w+l' 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": "If you form a word of length 5 by randomly selecting letters from the multiset {u: 10, z: 3}, what is the expected number of times the pattern 'z+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.88 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 5, q: 1, x: 2, o: 2, m: 3}, what is the expected number of times the pattern 'xq*' 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 5 letters from the multiset {z: 2, n: 5, c: 2, g: 2}. What is the expected number of occurrences of the pattern 'c+g' 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": "When randomly selecting 5 letters from the multiset {q: 3, v: 3, z: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'mv+'? Round 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 {d: 1, o: 4, i: 2, j: 3} to form a word, what is the expected number of matches of the pattern 'jd+'? 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 {w: 3, n: 1, k: 1, q: 1, i: 4}, what is the expected number of times the pattern 'n.*w' 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 4 by randomly selecting letters from the multiset {p: 3, d: 2, w: 2, f: 3, x: 1}, what is the expected number of times the pattern 'px*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.17 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {h: 3, g: 2, b: 4, o: 2} 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"
}
] | 0.11 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {w: 3, t: 7} 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"
}
] | 1.18 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {q: 3, o: 1, l: 1, n: 3, c: 3}. 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"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {o: 1, p: 3, w: 1, c: 2, b: 3}. 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {x: 5, c: 3, o: 3, s: 2} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {b: 5, y: 4, l: 4} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round 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 5 letters from the multiset {t: 8, u: 7}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.67 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {u: 6, f: 5} to form a word, what is the expected number of matches of the pattern 'fu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.02 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {f: 3, d: 2, b: 2, z: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'z+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.07 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 5, q: 3, j: 2, d: 2}, what is the expected number of times the pattern 'qw+' appears? Round 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 4 letters from the multiset {l: 5, u: 7, g: 3}. What is the expected number of occurrences of the pattern 'lg+' 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": "When randomly selecting 5 letters from the multiset {g: 3, l: 2, h: 3, m: 2} to form a word, what is the expected number of matches of the pattern 'g*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.98 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {e: 6, j: 9}. What is the expected number of occurrences of the pattern 'j*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.74 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {f: 4, m: 2, x: 4} 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"
}
] | 0.8 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 3, s: 7}, what is the expected number of times the pattern 'q+s' appears? 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 4 by randomly selecting letters from the multiset {r: 5, g: 1, n: 3, m: 4}, what is the expected number of times the pattern 'r*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.29 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 4, y: 2, a: 5}, what is the expected number of times the pattern 'd.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.73 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {u: 4, d: 3, x: 2, f: 2, l: 3} 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"
}
] | 0.2 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {x: 4, i: 2, e: 2, q: 3, h: 2}. What is the expected number of occurrences of the pattern 'h*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.88 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 3, l: 1, k: 2, b: 4}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {i: 4, g: 10} to form a word, what is the expected number of matches of the pattern 'ig+'? 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 {y: 5, u: 1, t: 2, z: 2}, what is the expected number of times the pattern 'tu*' 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 {b: 5, u: 2, q: 4}. What is the expected number of occurrences of the pattern 'uu+' 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 4 by randomly selecting letters from the multiset {d: 3, i: 3, w: 3, c: 4, u: 1}, what is the expected number of times the pattern 'iw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 7, l: 4, n: 3}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 3, x: 4, v: 6, c: 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"
}
] | 0.57 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 6, i: 4}, what is the expected number of times the pattern 'it*' 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 5 letters from the multiset {e: 1, j: 1, c: 3, h: 3, n: 2}. What is the expected number of occurrences of the pattern 'c.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.67 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {j: 2, z: 4, l: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'jh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.21 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {r: 3, d: 4, z: 4, y: 3} to form a word, what is the expected number of matches of the pattern 'yz*'? 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 {v: 4, j: 3, p: 2, w: 2}. 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"
}
] | 1.09 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {d: 2, b: 3, e: 3, t: 5} to form a word, what is the expected number of matches of the pattern 'dd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.82 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {f: 2, g: 3, c: 6}, what is the expected number of times the pattern 'f.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.55 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 2, h: 3, g: 6}, 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"
}
] | 0.18 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 3, z: 3, c: 2, e: 3}, what is the expected number of times the pattern 'q+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.28 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {f: 1, k: 3, m: 3, a: 4, t: 2}. What is the expected number of occurrences of the pattern 'km*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.42 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {z: 7, t: 6}. 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"
}
] | 2.69 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 4, q: 3, h: 8}, what is the expected number of times the pattern 'q.*y' 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 {i: 2, r: 5, l: 3, x: 3}. What is the expected number of occurrences of the pattern 'r.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.38 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {h: 8, n: 5} to form a word, what is the expected number of matches of the pattern 'h+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.77 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 6, a: 3, c: 4, e: 1}, what is the expected number of times the pattern 'c+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 5 letters from the multiset {c: 6, t: 5} to form a word, what is the expected number of matches of the pattern 't*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.29 | MATH |
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