messages
listlengths 1
1
| ground_truth
stringclasses 108
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "When randomly selecting 6 letters from the multiset {q: 2, f: 2, z: 3, m: 1, a: 4} to form a word, what is the expected number of matches of the pattern 'zq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.25
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {n: 3, c: 4, h: 3, z: 1, j: 1} 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"
}
] |
1.9
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {r: 4, o: 2, t: 1, f: 5} 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"
}
] |
0.39
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {q: 3, b: 4, l: 5}. 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"
}
] |
1.36
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {q: 3, y: 1, k: 4, c: 2, v: 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"
}
] |
1.36
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {c: 6, w: 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"
}
] |
3.41
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {j: 2, w: 6, s: 2, i: 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"
}
] |
0.23
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 4, s: 3, w: 2, m: 3}, what is the expected number of times the pattern 'm.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.02
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {m: 4, c: 8}. What is the expected number of occurrences of the pattern 'mc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.41
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 2, w: 3, e: 4, d: 1, v: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.23
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {c: 3, n: 2, e: 3, b: 4} to form a word, what is the expected number of matches of the pattern 'e*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.9
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {y: 2, r: 4, s: 2, b: 1, c: 3}, what is the expected number of times the pattern 'rs+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.33
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {n: 3, j: 5, k: 4}, what is the expected number of times the pattern 'kj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.07
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {y: 3, t: 3, p: 2, e: 1, z: 3}. What is the expected number of occurrences of the pattern 'zt+' 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": "When randomly selecting 6 letters from the multiset {v: 4, h: 4, j: 3, s: 1} to form a word, what is the expected number of matches of the pattern 's*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.15
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {a: 5, y: 5, l: 2} to form a word, what is the expected number of matches of the pattern 'a*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.84
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {m: 6, y: 6} 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"
}
] |
3.41
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {p: 2, h: 5, c: 5}. 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"
}
] |
2.27
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {i: 3, y: 3, z: 6}, what is the expected number of times the pattern 'zy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.8
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {g: 3, x: 4, r: 2, p: 3} to form a word, what is the expected number of matches of the pattern 'p+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.53
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {k: 4, w: 4, f: 4}, what is the expected number of times the pattern 'f*w' appears? Round 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 6 by randomly selecting letters from the multiset {a: 4, f: 1, w: 3, l: 4}, what is the expected number of times the pattern 'l.*f' appears? 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 6 by randomly selecting letters from the multiset {b: 1, x: 2, p: 4, l: 5}, 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"
}
] |
0.23
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {i: 6, n: 6}, 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"
}
] |
3.41
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {s: 5, c: 7}, 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"
}
] |
2.27
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {h: 3, m: 5, z: 4}. What is the expected number of occurrences of the pattern 'z+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.97
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {r: 3, g: 3, a: 2, u: 4} to form a word, what is the expected number of matches of the pattern 'ug*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.53
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {n: 4, p: 3, z: 5}. What is the expected number of occurrences of the pattern 'p.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.7
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {t: 3, j: 2, m: 4, y: 3}. What is the expected number of occurrences of the pattern 'y.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {a: 3, o: 3, b: 1, l: 5} 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"
}
] |
0.68
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {d: 1, n: 5, c: 4, q: 2}. What is the expected number of occurrences of the pattern 'q+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.41
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {c: 4, l: 3, x: 5} 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"
}
] |
1.36
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {n: 5, x: 4, v: 3}, what is the expected number of times the pattern 'x.*v' appears? 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 6 by randomly selecting letters from the multiset {q: 4, l: 8}, what is the expected number of times the pattern 'l.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.64
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {h: 3, a: 3, g: 1, v: 5} 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"
}
] |
2.3
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {k: 1, l: 3, w: 4, t: 4} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.36
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {y: 4, t: 2, m: 3, f: 2, u: 1}. 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"
}
] |
2.08
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {w: 2, x: 3, s: 3, u: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'u.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.68
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {o: 4, x: 5, r: 3}. What is the expected number of occurrences of the pattern 'x+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.8
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {j: 6, r: 1, x: 5} to form a word, what is the expected number of matches of the pattern 'rx*'? 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 6 letters from the multiset {i: 1, z: 2, a: 6, o: 1, u: 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"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {f: 1, m: 2, y: 5, d: 2, c: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {g: 7, o: 5}, what is the expected number of times the pattern 'g.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.98
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {y: 2, n: 2, f: 3, q: 2, t: 3}, what is the expected number of times the pattern 'q.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {e: 2, w: 2, x: 3, q: 2, y: 3} 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"
}
] |
0.68
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {c: 2, n: 5, z: 3, k: 1, t: 1}. 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"
}
] |
0.23
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {b: 6, q: 2, v: 3, x: 1}. What is the expected number of occurrences of the pattern 'q.*x' 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 6 letters from the multiset {w: 6, b: 2, g: 1, i: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'w.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {p: 3, t: 4, o: 5} 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"
}
] |
1.36
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {q: 3, w: 5, o: 4} to form a word, what is the expected number of matches of the pattern 'o.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.36
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {x: 6, y: 5, e: 1} to form a word, what is the expected number of matches of the pattern 'x.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.68
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {j: 4, s: 8}. What is the expected number of occurrences of the pattern 'j.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.64
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {w: 3, n: 2, d: 3, e: 1, h: 3} 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"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {x: 3, t: 6, e: 3} to form a word, what is the expected number of matches of the pattern 'xt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.57
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 4, a: 8}, what is the expected number of times the pattern 'p+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.56
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 1, i: 3, y: 4, q: 2, e: 2}, what is the expected number of times the pattern 'q*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.75
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {g: 1, t: 2, z: 3, f: 5, s: 1} to form a word, what is the expected number of matches of the pattern 'z.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.34
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {t: 5, c: 4, x: 3}. What is the expected number of occurrences of the pattern 'tx+' 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": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 7, n: 5}, what is the expected number of times the pattern 'dn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.38
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {t: 4, o: 8}. What is the expected number of occurrences of the pattern 't.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.64
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {c: 3, o: 2, g: 1, q: 3, k: 3}. What is the expected number of occurrences of the pattern 'ok*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.27
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {w: 2, i: 2, j: 4, e: 1, q: 3} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.36
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {s: 4, p: 8} 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"
}
] |
1.56
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {b: 4, u: 3, q: 5}. 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"
}
] |
2.27
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 6, s: 6}, 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"
}
] |
3.41
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {q: 4, x: 2, s: 6} 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"
}
] |
3.41
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {q: 7, m: 5}, what is the expected number of times the pattern 'qm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.38
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 2, q: 3, l: 1, c: 6}, 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": "If you form a word of length 6 by randomly selecting letters from the multiset {c: 2, o: 3, t: 5, p: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.23
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {i: 5, g: 7} 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"
}
] |
4.83
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {k: 2, v: 3, t: 1, r: 2, p: 4}. What is the expected number of occurrences of the pattern 't+v' in each word? Round your answer 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 6 by randomly selecting letters from the multiset {n: 6, j: 6}, what is the expected number of times the pattern 'j.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.09
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {i: 7, w: 5} to form a word, what is the expected number of matches of the pattern 'w*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.38
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {r: 2, k: 1, x: 3, u: 2, h: 4}. What is the expected number of occurrences of the pattern 'h+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.39
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {s: 5, l: 1, p: 3, u: 3} to form a word, what is the expected number of matches of the pattern 's*l'? 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 6 letters from the multiset {q: 3, x: 2, j: 5, p: 2}. 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"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {w: 8, p: 4} to form a word, what is the expected number of matches of the pattern 'p+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.56
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {x: 8, k: 4}. What is the expected number of occurrences of the pattern 'x+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.41
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {a: 3, t: 1, y: 4, k: 4} to form a word, what is the expected number of matches of the pattern 'ya+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.53
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 2, z: 5, x: 3, b: 2}, what is the expected number of times the pattern 'xx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.75
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {o: 6, p: 6} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.41
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {p: 8, k: 4} to form a word, what is the expected number of matches of the pattern 'p+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.41
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 5, c: 7}, what is the expected number of times the pattern 'ch*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.37
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {g: 3, n: 2, i: 1, r: 2, u: 4}. What is the expected number of occurrences of the pattern 'n*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.33
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 4, a: 2, h: 3, r: 2, i: 1}, what is the expected number of times the pattern 'r*p' 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 6 by randomly selecting letters from the multiset {s: 3, w: 4, k: 2, y: 1, q: 2}, 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"
}
] |
1.61
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {r: 3, u: 2, v: 3, d: 1, h: 3}, what is the expected number of times the pattern 'u.*u' 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 6 letters from the multiset {e: 3, p: 3, t: 2, r: 2, g: 2} 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"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {l: 4, d: 4, w: 4} to form a word, what is the expected number of matches of the pattern 'l*w'? Round 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 6 by randomly selecting letters from the multiset {d: 4, p: 4, c: 4}, what is the expected number of times the pattern 'c+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.78
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {f: 5, d: 5, 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"
}
] |
0.23
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {c: 3, u: 2, h: 1, m: 3, d: 3}, what is the expected number of times the pattern 'hu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.58
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {n: 2, z: 5, o: 4, a: 1}. What is the expected number of occurrences of the pattern 'a+n' 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": "When randomly selecting 6 letters from the multiset {k: 2, l: 2, u: 3, m: 1, n: 4} to form a word, what is the expected number of matches of the pattern 'u.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.68
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {m: 3, i: 2, o: 5, e: 2}. What is the expected number of occurrences of the pattern 'm*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.17
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {g: 6, c: 6}. What is the expected number of occurrences of the pattern 'cg+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.14
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {y: 4, b: 2, i: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'hb+'? 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 6 by randomly selecting letters from the multiset {b: 2, g: 2, z: 1, k: 2, m: 5}, what is the expected number of times the pattern 'k+b' appears? Round 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 6 letters from the multiset {k: 2, o: 4, e: 3, p: 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"
}
] |
1.36
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {t: 4, p: 2, z: 2, d: 3, n: 1} 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"
}
] |
1.36
|
MATH
|
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