messages list | ground_truth string | dataset string |
|---|---|---|
[
{
"content": "When randomly selecting 4 letters from the multiset {z: 6, 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"
}
] | 1.36 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 8, p: 5}, what is the expected number of times the pattern 'pb*' appears? 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 {k: 9, o: 3}, what is the expected number of times the pattern 'o.*k' appears? Round 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 {b: 2, o: 1, a: 1, p: 3, t: 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"
}
] | 0.33 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 4, u: 9}. 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"
}
] | 2.77 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {g: 5, z: 2, a: 3, q: 3, d: 1} 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"
}
] | 0.11 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 8, x: 3}, what is the expected number of times the pattern 'hx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.67 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 1, c: 5, f: 4, e: 4}, what is the expected number of times the pattern 'cf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.32 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {e: 2, q: 4, i: 3, g: 3}. What is the expected number of occurrences of the pattern 'q*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.14 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {t: 3, c: 2, o: 4, d: 4, x: 1}. 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"
}
] | 0.2 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {j: 5, r: 5} to form a word, what is the expected number of matches of the pattern 'jr*'? Round 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 4 letters from the multiset {w: 5, y: 1, d: 2, c: 2, f: 3}. What is the expected number of occurrences of the pattern 'c+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.04 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 4, i: 3, r: 7}, what is the expected number of times the pattern 'ti+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {z: 5, e: 4, a: 4, g: 2} 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"
}
] | 0.34 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 1, r: 2, u: 1, n: 3, k: 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"
}
] | 0.4 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 6, a: 1, q: 5, b: 1, h: 2}, what is the expected number of times the pattern 'hh*' 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 {k: 4, c: 4, q: 2, x: 1}, what is the expected number of times the pattern 'k*q' 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 4 by randomly selecting letters from the multiset {n: 6, q: 7}, what is the expected number of times the pattern 'n+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.1 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {h: 7, n: 3, b: 4} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {n: 3, h: 1, a: 2, l: 4}. What is the expected number of occurrences of the pattern 'lh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.18 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 2, s: 2, d: 3, v: 2, k: 1}, 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 3, t: 3, f: 2, g: 2}, 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"
}
] | 0.67 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 1, o: 4, v: 1, x: 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 2, t: 4, b: 1, m: 4, e: 4}, what is the expected number of times the pattern 'ed*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.49 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {g: 4, w: 4, i: 3, q: 2}. 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"
}
] | 0.38 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 5, u: 4, i: 6}, 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"
}
] | 0.86 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {i: 5, s: 8}. 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"
}
] | 3.59 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {u: 4, i: 3, y: 4}. What is the expected number of occurrences of the pattern 'iy*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.93 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {j: 10, f: 5} to form a word, what is the expected number of matches of the pattern 'f.*f'? 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: 3, x: 1, r: 3, v: 3, g: 3}. What is the expected number of occurrences of the pattern 'gr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.12 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 3, q: 7}, what is the expected number of times the pattern 'q+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.18 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {r: 2, k: 3, s: 4, x: 3, p: 2} 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"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 7, z: 7}, 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"
}
] | 1.63 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {b: 5, e: 10}. What is the expected number of occurrences of the pattern 'e+b' 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": "When randomly selecting 5 letters from the multiset {y: 5, o: 2, i: 3} to form a word, what is the expected number of matches of the pattern 'yo+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.49 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {m: 2, l: 1, v: 4, x: 4, u: 2} 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"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 5, u: 5, j: 5}, what is the expected number of times the pattern 'uj*' appears? 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 4 letters from the multiset {f: 4, s: 2, b: 4, a: 3, v: 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"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 5, h: 2, k: 3, n: 3, j: 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"
}
] | 0.1 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 5, d: 9}, what is the expected number of times the pattern 'di*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.5 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {x: 1, y: 4, k: 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 2, s: 4, a: 5}, what is the expected number of times the pattern 'vs+' appears? 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 5 by randomly selecting letters from the multiset {i: 4, r: 3, d: 1, t: 4, e: 2}, what is the expected number of times the pattern 'td+' appears? Round 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 {f: 2, e: 3, l: 2, h: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'l*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.79 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 5, q: 10}, what is the expected number of times the pattern 'a.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.43 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {w: 3, q: 3, u: 1, h: 3, c: 2}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.45 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 7, o: 3, s: 3}, what is the expected number of times the pattern 'c*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.51 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {v: 3, j: 4, y: 7}. What is the expected number of occurrences of the pattern 'vy+' in each word? Round your answer 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 4 by randomly selecting letters from the multiset {s: 1, m: 4, l: 1, y: 2, n: 3}, what is the expected number of times the pattern 'n*l' appears? 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 {g: 4, w: 3, u: 2, o: 2, d: 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"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {h: 5, s: 6}. What is the expected number of occurrences of the pattern 'h.*s' 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 {f: 2, m: 3, d: 4, r: 1}, what is the expected number of times the pattern 'r*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.73 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 5, m: 2, x: 1, b: 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 2, v: 1, h: 4, s: 3}, what is the expected number of times the pattern 'v*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.87 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {y: 1, o: 3, s: 6, m: 2} to form a word, what is the expected number of matches of the pattern 'sm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.39 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {x: 2, v: 4, d: 2, s: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'd+q'? 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 5 by randomly selecting letters from the multiset {s: 8, t: 7}, what is the expected number of times the pattern 's+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.67 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 6, m: 4}, what is the expected number of times the pattern 'mx*' 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 {m: 1, i: 2, o: 3, l: 1, w: 3} to form a word, what is the expected number of matches of the pattern 'wl+'? 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 {x: 3, p: 3, w: 4, z: 3}, what is the expected number of times the pattern 'xp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.26 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {f: 4, u: 7}. 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"
}
] | 1.09 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {s: 2, e: 4, v: 4, g: 4} to form a word, what is the expected number of matches of the pattern 'g.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.88 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {p: 3, j: 5, c: 7} to form a word, what is the expected number of matches of the pattern 'j.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.71 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 2, z: 2, u: 4, y: 2}, what is the expected number of times the pattern 'w*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.94 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 5, t: 2, h: 3, u: 2, v: 2}. What is the expected number of occurrences of the pattern 't.*h' in each word? Round your answer 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 {s: 2, f: 4, d: 2, l: 5}, what is the expected number of times the pattern 'ld*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.2 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {q: 4, p: 1, s: 1, a: 3, g: 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"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {v: 3, i: 6, w: 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"
}
] | 2.27 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {e: 3, w: 2, m: 3, y: 3} to form a word, what is the expected number of matches of the pattern 'y.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.82 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {i: 2, h: 2, d: 3, e: 3} to form a word, what is the expected number of matches of the pattern 'i.*e'? 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 {z: 6, k: 4}. What is the expected number of occurrences of the pattern 'k.*z' in each word? Round your answer 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 {s: 3, n: 3, p: 3, v: 2}. What is the expected number of occurrences of the pattern 'n+v' 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 {w: 3, e: 3, o: 1, d: 5, i: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.66 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {i: 8, q: 4}. 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"
}
] | 4.24 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {z: 6, s: 6}, what is the expected number of times the pattern 'z.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.73 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {c: 3, r: 2, x: 6} to form a word, what is the expected number of matches of the pattern 'x.*r'? Round 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 4 by randomly selecting letters from the multiset {m: 2, z: 4, d: 2, n: 4}, what is the expected number of times the pattern 'z.*z' 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 {n: 1, a: 2, m: 2, y: 2, w: 4}. What is the expected number of occurrences of the pattern 'nw*' 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": "When randomly selecting 4 letters from the multiset {o: 2, y: 2, z: 4, l: 3} to form a word, what is the expected number of matches of the pattern 'oy+'? Round 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 {d: 3, x: 3, a: 4, l: 2, q: 3} to form a word, what is the expected number of matches of the pattern 'al*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.49 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 5, a: 5, x: 3}, what is the expected number of times the pattern 's*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.67 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 6, r: 6}, what is the expected number of times the pattern 'z.*r' appears? 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 {d: 4, r: 4, f: 2}. What is the expected number of occurrences of the pattern 'd*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.95 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {l: 4, a: 4, y: 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"
}
] | 1.09 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 4, v: 5, c: 3}, what is the expected number of times the pattern 'av+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.83 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {d: 4, g: 3, n: 1, p: 3} to form a word, what is the expected number of matches of the pattern 'gp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.28 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {a: 2, l: 4, n: 5} to form a word, what is the expected number of matches of the pattern 'ln*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.19 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 4, u: 5, t: 4}, what is the expected number of times the pattern 't+u' appears? 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 5 letters from the multiset {m: 5, x: 10}. 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"
}
] | 4.29 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {a: 2, r: 4, q: 3, v: 1, b: 2}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.15 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {o: 5, z: 2, n: 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"
}
] | 2.22 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {r: 3, e: 3, p: 3, l: 2, c: 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"
}
] | 0.13 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {f: 1, i: 3, v: 3, h: 4} to form a word, what is the expected number of matches of the pattern 'f.*v'? 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 5 by randomly selecting letters from the multiset {b: 2, h: 5, l: 4, j: 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"
}
] | 0.1 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {u: 1, b: 5, v: 2, z: 4}, 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"
}
] | 0.89 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 2, o: 5, b: 3, u: 2, y: 3}, what is the expected number of times the pattern 'sy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.79 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 2, v: 3, c: 1, u: 4}, 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"
}
] | 0.4 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 1, l: 1, z: 5, s: 2, b: 2}, 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 6, b: 4}, 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"
}
] | 2.0 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 4, u: 4, e: 1, f: 1, x: 3}, what is the expected number of times the pattern 'ea+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.09 | MATH |
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