messages
listlengths 1
1
| ground_truth
stringclasses 108
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {e: 9, h: 3}. What is the expected number of occurrences of the pattern 'eh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.2
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {n: 4, b: 2, u: 3, h: 3}. What is the expected number of occurrences of the pattern 'u+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.53
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {p: 4, v: 2, o: 3, c: 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"
}
] |
1.36
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {z: 8, p: 2, c: 2}. What is the expected number of occurrences of the pattern 'z+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.21
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {a: 1, g: 1, q: 4, t: 3, k: 3}. What is the expected number of occurrences of the pattern 'k.*k' 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": "Form a word by randomly choosing 6 letters from the multiset {o: 3, f: 3, j: 2, e: 4}. What is the expected number of occurrences of the pattern 'e.*f' 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": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 2, s: 7, q: 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"
}
] |
0.23
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {s: 3, l: 3, c: 2, y: 2, q: 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"
}
] |
0.23
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {d: 9, s: 3}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8.18
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 1, t: 2, y: 3, l: 4, s: 2}, 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"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 4, b: 1, f: 4, z: 3}, 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"
}
] |
1.36
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {i: 6, f: 6} to form a word, what is the expected number of matches of the pattern 'if*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.14
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {l: 3, e: 2, d: 1, g: 4, u: 2}. What is the expected number of occurrences of the pattern 'd.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.23
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {i: 4, v: 8}, what is the expected number of times the pattern 'i+v' 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 {z: 1, m: 4, s: 1, b: 3, c: 3}, what is the expected number of times the pattern 'zm+' appears? 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 6 letters from the multiset {i: 2, o: 4, v: 4, m: 2}. What is the expected number of occurrences of the pattern 'o*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.39
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {e: 6, d: 6} to form a word, what is the expected number of matches of the pattern 'd*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.14
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 6, r: 2, m: 4}, what is the expected number of times the pattern 'm.*m' appears? 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 {n: 5, i: 2, g: 3, r: 2} to form a word, what is the expected number of matches of the pattern 'ri*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.16
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {m: 3, w: 2, e: 2, t: 5}. What is the expected number of occurrences of the pattern 'ew*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.16
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {s: 5, c: 4, 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"
}
] |
0.68
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 2, f: 1, l: 4, q: 5}, what is the expected number of times the pattern 'fq*' appears? 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 {c: 4, l: 5, a: 1, e: 2}. What is the expected number of occurrences of the pattern 'l+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.27
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {n: 3, y: 6, b: 3}. What is the expected number of occurrences of the pattern 'n*b' in each word? Round your answer 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 {d: 7, e: 5}, 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"
}
] |
4.77
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 2, s: 1, h: 3, g: 3, i: 3}, what is the expected number of times the pattern 'gs+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.11
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {p: 2, x: 5, w: 2, t: 3}. What is the expected number of occurrences of the pattern 't+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.27
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {z: 3, v: 4, d: 3, g: 2} to form a word, what is the expected number of matches of the pattern 'zd*'? 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 {x: 5, k: 4, g: 3}, what is the expected number of times the pattern 'k+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.97
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {w: 4, z: 2, y: 3, e: 3}, what is the expected number of times the pattern 'ye*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.9
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {i: 4, g: 5, t: 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"
}
] |
1.36
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {f: 5, l: 3, d: 4} to form a word, what is the expected number of matches of the pattern 'fl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.17
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {g: 5, p: 3, h: 2, t: 2} to form a word, what is the expected number of matches of the pattern 'h*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.91
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {e: 2, d: 1, a: 3, r: 4, z: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.68
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {i: 3, o: 4, y: 5}, what is the expected number of times the pattern 'oi+' appears? 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 {f: 2, d: 3, b: 5, y: 2}, what is the expected number of times the pattern 'y*d' 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 {v: 3, i: 5, l: 2, s: 2} to form a word, what is the expected number of matches of the pattern 'vs+'? 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 {a: 7, k: 5} to form a word, what is the expected number of matches of the pattern 'ak*'? 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 {i: 8, t: 4}, what is the expected number of times the pattern 'i+t' appears? Round 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 {o: 10, v: 2} to form a word, what is the expected number of matches of the pattern 'o+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.97
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {o: 3, j: 4, u: 3, y: 2}, what is the expected number of times the pattern 'y.*o' appears? 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 {v: 3, u: 2, y: 4, z: 3}. What is the expected number of occurrences of the pattern 'z*v' in each word? Round your answer 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 {i: 1, w: 1, x: 4, k: 4, z: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {c: 4, s: 3, y: 1, r: 4} to form a word, what is the expected number of matches of the pattern 'r*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.69
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {h: 4, w: 3, m: 5} to form a word, what is the expected number of matches of the pattern 'w.*h'? 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: 3, t: 2, y: 5, s: 1, v: 1}, what is the expected number of times the pattern 'y.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.57
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {p: 6, x: 6} 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"
}
] |
3.41
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {c: 3, s: 9}. What is the expected number of occurrences of the pattern 'c+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.2
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {w: 8, y: 4} to form a word, what is the expected number of matches of the pattern 'w*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.41
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {k: 6, m: 6} 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"
}
] |
3.41
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {v: 2, k: 2, w: 4, g: 2, t: 2}. What is the expected number of occurrences of the pattern 'vw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.39
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {z: 1, f: 3, c: 3, h: 3, x: 2} to form a word, what is the expected number of matches of the pattern 'f+h'? 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 6 letters from the multiset {w: 3, l: 4, t: 2, n: 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"
}
] |
1.36
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {g: 3, z: 7, f: 2}. What is the expected number of occurrences of the pattern 'f.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.59
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {k: 3, z: 1, j: 4, w: 3, g: 1}. What is the expected number of occurrences of the pattern 'g+z' 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": "When randomly selecting 6 letters from the multiset {i: 6, h: 6} to form a word, what is the expected number of matches of the pattern 'i.*i'? 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 {x: 2, y: 1, z: 3, h: 4, c: 2} to form a word, what is the expected number of matches of the pattern 'y.*x'? 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 {v: 3, o: 3, g: 6}, what is the expected number of times the pattern 'og+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.07
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {b: 3, g: 2, j: 6, v: 1} to form a word, what is the expected number of matches of the pattern 'g+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.25
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 1, j: 2, z: 3, b: 1, r: 5}, 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 6 by randomly selecting letters from the multiset {v: 3, s: 4, w: 2, r: 1, b: 2}, 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"
}
] |
0.23
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {o: 3, a: 1, c: 3, i: 5}, 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"
}
] |
0.68
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {u: 8, m: 4}, 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"
}
] |
6.36
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {p: 5, h: 7} 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"
}
] |
3.98
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {b: 7, q: 3, t: 2} to form a word, what is the expected number of matches of the pattern 'qb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.4
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {o: 3, n: 4, d: 3, e: 2} to form a word, what is the expected number of matches of the pattern 'ne+'? 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 {l: 6, r: 4, w: 2}, what is the expected number of times the pattern 'lr+' appears? Round 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 6 by randomly selecting letters from the multiset {w: 1, f: 2, j: 4, d: 2, v: 3}, what is the expected number of times the pattern 'df*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.16
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {c: 1, z: 4, i: 4, s: 3}. What is the expected number of occurrences of the pattern 's*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.63
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {x: 4, y: 2, e: 6}. What is the expected number of occurrences of the pattern 'y.*e' 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": "Form a word by randomly choosing 6 letters from the multiset {a: 2, j: 2, t: 4, n: 4}. What is the expected number of occurrences of the pattern 'j+a' 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 6 letters from the multiset {h: 3, f: 2, y: 1, e: 2, z: 4} 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"
}
] |
0.23
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {m: 3, a: 2, q: 4, p: 3}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.68
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 2, t: 1, v: 4, q: 2, f: 3}, what is the expected number of times the pattern 'ft+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.11
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {h: 3, d: 9}. 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"
}
] |
0.68
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {k: 2, g: 4, e: 2, x: 4}. What is the expected number of occurrences of the pattern 'x.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.82
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {m: 4, t: 3, s: 2, l: 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"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {z: 5, b: 5, q: 2} to form a word, what is the expected number of matches of the pattern 'qz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.54
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {e: 3, b: 1, y: 2, u: 3, s: 3}. 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"
}
] |
0.23
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {n: 2, j: 3, z: 4, q: 3} 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"
}
] |
0.23
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {z: 8, l: 4}. 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"
}
] |
1.36
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {m: 2, k: 4, s: 1, l: 1, g: 4} to form a word, what is the expected number of matches of the pattern 'sk+'? 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 6 letters from the multiset {d: 2, y: 3, q: 2, s: 1, v: 4}. What is the expected number of occurrences of the pattern 'sy+' 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": "When randomly selecting 6 letters from the multiset {d: 4, g: 4, x: 1, o: 3} to form a word, what is the expected number of matches of the pattern 'do+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.53
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {o: 2, d: 3, i: 2, c: 2, f: 3}. What is the expected number of occurrences of the pattern 'o+d' in each word? Round your answer 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 {a: 2, r: 3, p: 2, v: 2, n: 3} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.68
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {l: 5, t: 7}, 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"
}
] |
2.27
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {f: 4, l: 2, n: 2, m: 3, z: 1}. 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"
}
] |
1.61
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {m: 7, l: 5}. What is the expected number of occurrences of the pattern 'ml+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.88
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {h: 2, e: 1, v: 2, x: 4, r: 3} to form a word, what is the expected number of matches of the pattern 'ev+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.08
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {y: 4, p: 4, u: 1, s: 1, w: 2}. 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"
}
] |
1.36
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {k: 5, m: 1, v: 3, n: 1, i: 2}, 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"
}
] |
0.23
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {q: 2, e: 4, z: 6}, what is the expected number of times the pattern 'e.*e' 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 {o: 3, p: 3, y: 2, h: 1, x: 3}, what is the expected number of times the pattern 'yx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.27
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {k: 2, z: 3, a: 2, t: 3, c: 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"
}
] |
0.23
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {n: 2, v: 5, q: 3, y: 2} to form a word, what is the expected number of matches of the pattern 'y.*n'? 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 6 letters from the multiset {n: 7, h: 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": "When randomly selecting 6 letters from the multiset {v: 2, m: 3, w: 3, g: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'mn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.25
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 2, u: 7, z: 3}, what is the expected number of times the pattern 'h.*z' 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 {q: 7, z: 5} to form a word, what is the expected number of matches of the pattern 'q.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.98
|
MATH
|
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