messages
listlengths 1
1
| ground_truth
stringclasses 85
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 1, r: 2, h: 3, s: 4}, what is the expected number of times the pattern 'ro+' appears? Round 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 {c: 3, n: 1, t: 3, s: 2, q: 1}, what is the expected number of times the pattern 't.*q' appears? 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 {l: 5, r: 1, n: 1, u: 2, o: 1}. What is the expected number of occurrences of the pattern 'o*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.54
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 4, t: 2, q: 4}, what is the expected number of times the pattern 't*n' 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 5 by randomly selecting letters from the multiset {h: 1, x: 3, w: 1, t: 1, v: 4}, what is the expected number of times the pattern 'h+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.04
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {i: 1, v: 3, s: 1, e: 2, t: 3}. What is the expected number of occurrences of the pattern 't.*s' 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": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 2, o: 2, x: 1, s: 4, f: 1}, 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"
}
] |
0.6
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {e: 5, n: 3, c: 2} to form a word, what is the expected number of matches of the pattern 'e*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.5
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {p: 6, f: 4} to form a word, what is the expected number of matches of the pattern 'pf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.43
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {d: 3, b: 2, q: 2, k: 3} 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"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {m: 4, k: 6} to form a word, what is the expected number of matches of the pattern 'mk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.8
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 5, t: 5}, what is the expected number of times the pattern 'tp+' 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 {h: 2, o: 1, x: 1, z: 2, f: 4}, 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"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 6, m: 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"
}
] |
3.33
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {e: 3, c: 5, y: 2} 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"
}
] |
1.11
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {k: 6, d: 4}. What is the expected number of occurrences of the pattern 'd.*k' 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 5 letters from the multiset {e: 2, i: 2, x: 2, b: 3, u: 1} to form a word, what is the expected number of matches of the pattern 'e*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.19
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {o: 4, y: 6}. What is the expected number of occurrences of the pattern 'y*o' in each word? Round your answer 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 {j: 3, x: 3, w: 2, v: 2}. 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"
}
] |
1.79
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {x: 4, t: 1, y: 5} to form a word, what is the expected number of matches of the pattern 't*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.18
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {m: 6, o: 1, w: 2, k: 1}. 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 {w: 2, v: 2, u: 2, l: 4} to form a word, what is the expected number of matches of the pattern 'u.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.89
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {n: 3, v: 1, p: 2, x: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'n+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.32
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 7, b: 3}, what is the expected number of times the pattern 's+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.79
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {v: 2, s: 1, q: 4, z: 3} to form a word, what is the expected number of matches of the pattern 'zv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.29
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {b: 4, j: 6}. What is the expected number of occurrences of the pattern 'jb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.43
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 4, j: 4, m: 2}, what is the expected number of times the pattern 't.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.78
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {z: 3, u: 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"
}
] |
1.12
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {o: 4, a: 6} to form a word, what is the expected number of matches of the pattern 'a.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 2, v: 4, f: 2, r: 2}, what is the expected number of times the pattern 'c*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.19
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {n: 1, x: 2, q: 3, p: 4} to form a word, what is the expected number of matches of the pattern 'p*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.74
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {b: 3, d: 3, h: 2, c: 2}. What is the expected number of occurrences of the pattern 'd*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.32
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 5, a: 5}, 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"
}
] |
2.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {r: 3, a: 2, y: 2, l: 2, n: 1}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {g: 5, k: 1, s: 2, q: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {m: 5, g: 5} 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"
}
] |
2.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 1, g: 1, l: 1, w: 4, v: 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"
}
] |
0.04
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {m: 4, r: 3, a: 3} to form a word, what is the expected number of matches of the pattern 'r.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.33
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {k: 1, x: 3, i: 3, n: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'ki*'? 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 {x: 2, s: 3, g: 2, z: 1, t: 2}. What is the expected number of occurrences of the pattern 'z.*t' 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 5 letters from the multiset {e: 2, s: 2, q: 2, h: 3, k: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round 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 {k: 4, u: 2, e: 2, c: 2} 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"
}
] |
0.22
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {n: 1, j: 3, k: 1, a: 2, r: 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"
}
] |
0.22
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {s: 2, m: 3, w: 3, t: 2} 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"
}
] |
0.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {l: 3, c: 1, e: 2, w: 2, d: 2}. What is the expected number of occurrences of the pattern 'lc+' 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": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 3, j: 5, n: 2}, what is the expected number of times the pattern 'wj+' 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 5 letters from the multiset {q: 1, s: 4, k: 3, z: 2} to form a word, what is the expected number of matches of the pattern 'ks+'? Round 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 {p: 2, e: 3, s: 2, y: 3} 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"
}
] |
0.48
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 2, x: 2, r: 1, i: 3, n: 2}, what is the expected number of times the pattern 'sn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.19
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 3, q: 2, k: 2, p: 3}, what is the expected number of times the pattern 'q+k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.19
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {l: 2, z: 2, d: 2, g: 2, q: 2} to form a word, what is the expected number of matches of the pattern 'gz+'? 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 {f: 4, z: 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"
}
] |
3.33
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {o: 2, c: 2, t: 4, i: 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"
}
] |
0.39
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {y: 2, x: 5, o: 3}. What is the expected number of occurrences of the pattern 'x*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {d: 5, p: 5} 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"
}
] |
2.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {j: 3, u: 2, f: 5}. What is the expected number of occurrences of the pattern 'uf+' 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": "Form a word by randomly choosing 5 letters from the multiset {s: 4, d: 4, y: 2}. What is the expected number of occurrences of the pattern 's+d' in each word? Round your answer 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 {p: 2, q: 1, w: 1, h: 4, y: 2} to form a word, what is the expected number of matches of the pattern 'h.*p'? 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 {n: 7, h: 3}, what is the expected number of times the pattern 'h.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.33
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 4, c: 6}, what is the expected number of times the pattern 'n*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.43
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {a: 2, t: 8} 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"
}
] |
6.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {g: 3, r: 2, x: 1, d: 4}. What is the expected number of occurrences of the pattern 'xg*' 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": "When randomly selecting 5 letters from the multiset {l: 2, u: 2, j: 2, f: 2, g: 2} 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"
}
] |
0.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 4, y: 4, n: 2}, 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"
}
] |
2.95
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 2, q: 3, x: 2, u: 1, b: 2}, 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"
}
] |
0.29
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 2, k: 3, v: 5}, what is the expected number of times the pattern 'wv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {y: 3, m: 1, s: 3, x: 3}. What is the expected number of occurrences of the pattern 'y*m' 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": "When randomly selecting 5 letters from the multiset {b: 3, t: 2, l: 3, d: 2} to form a word, what is the expected number of matches of the pattern 'd.*b'? Round 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 {k: 2, x: 3, g: 2, r: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'r*g'? Round 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 {b: 3, x: 7} to form a word, what is the expected number of matches of the pattern 'xb+'? Round 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 5 by randomly selecting letters from the multiset {o: 3, n: 1, l: 3, k: 3}, what is the expected number of times the pattern 'no+' 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 5 letters from the multiset {q: 2, h: 2, b: 2, n: 3, o: 1} to form a word, what is the expected number of matches of the pattern 'h+h'? 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 {j: 4, f: 2, e: 3, p: 1} to form a word, what is the expected number of matches of the pattern 'ep*'? 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 {p: 2, s: 3, q: 1, r: 3, x: 1} 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": "Form a word by randomly choosing 5 letters from the multiset {u: 3, z: 2, g: 3, c: 2}. What is the expected number of occurrences of the pattern 'gu*' in each word? Round your answer 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 {c: 4, l: 3, u: 3}. What is the expected number of occurrences of the pattern 'lu+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.48
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 3, z: 2, m: 1, j: 4}, what is the expected number of times the pattern 'z+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {m: 4, i: 2, l: 4}. What is the expected number of occurrences of the pattern 'im+' in each word? Round your answer 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 {z: 4, y: 6} to form a word, what is the expected number of matches of the pattern 'zy*'? 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 {p: 7, g: 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"
}
] |
1.79
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {q: 3, z: 4, u: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'q.*u'? Round 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 {u: 3, a: 3, z: 4} to form a word, what is the expected number of matches of the pattern 'z.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.33
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 3, b: 4, e: 3}, 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"
}
] |
1.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {t: 2, i: 1, r: 3, y: 3, w: 1}. 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"
}
] |
0.67
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {s: 2, t: 1, y: 3, h: 3, a: 1}. What is the expected number of occurrences of the pattern 'y*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.32
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {b: 1, i: 1, a: 4, h: 2, x: 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"
}
] |
1.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {i: 6, d: 4}. What is the expected number of occurrences of the pattern 'd+i' in each word? Round your answer 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 {v: 1, h: 3, x: 3, d: 1, o: 2}. What is the expected number of occurrences of the pattern 'o*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.6
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {v: 4, w: 1, q: 2, e: 2, n: 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"
}
] |
1.33
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {g: 2, x: 5, 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"
}
] |
0.67
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {h: 3, o: 3, s: 1, u: 2, c: 1}. 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": "If you form a word of length 5 by randomly selecting letters from the multiset {u: 4, i: 3, w: 3}, what is the expected number of times the pattern 'i*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.98
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {t: 3, p: 6, f: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? 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 {d: 3, u: 4, a: 3}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {h: 6, u: 4} 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"
}
] |
1.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {x: 5, p: 5}. What is the expected number of occurrences of the pattern 'x.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.78
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 1, b: 2, j: 1, y: 3, k: 3}, what is the expected number of times the pattern 'y.*y' 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 {k: 1, d: 4, j: 4, w: 1}, what is the expected number of times the pattern 'd+j' appears? 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 {t: 7, w: 3} to form a word, what is the expected number of matches of the pattern 'tw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.63
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {q: 3, n: 3, e: 1, j: 2, t: 1}, what is the expected number of times the pattern 'tn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.16
|
MATH
|
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