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 {o: 4, k: 3, n: 5}. What is the expected number of occurrences of the pattern 'o*k' 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 {o: 4, h: 8} to form a word, what is the expected number of matches of the pattern 'oh+'? 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 {p: 4, h: 3, s: 3, u: 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"
}
] |
1.36
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 3, q: 4, k: 2, z: 3}, what is the expected number of times the pattern 'z+b' 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 6 by randomly selecting letters from the multiset {e: 2, s: 4, b: 1, g: 4, t: 1}, what is the expected number of times the pattern 'e.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.91
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 3, y: 4, t: 5}, 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"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {a: 8, h: 4} to form a word, what is the expected number of matches of the pattern 'a+h'? 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 {x: 2, a: 1, d: 3, m: 5, w: 1}, 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 {j: 6, a: 6}, what is the expected number of times the pattern 'a.*a' appears? 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 {y: 6, b: 6}. 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"
}
] |
3.41
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {z: 4, s: 7, m: 1} to form a word, what is the expected number of matches of the pattern 's+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.87
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 4, f: 3, l: 1, j: 2, e: 2}, what is the expected number of times the pattern 'f.*h' appears? 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 {q: 4, l: 4, p: 4}. What is the expected number of occurrences of the pattern 'l*q' 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 6 by randomly selecting letters from the multiset {h: 3, g: 3, l: 2, c: 4}, what is the expected number of times the pattern 'g*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.27
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {o: 5, k: 5, i: 2}. What is the expected number of occurrences of the pattern 'ik+' 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 6 by randomly selecting letters from the multiset {k: 7, f: 5}, 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"
}
] |
4.77
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {r: 3, n: 3, a: 3, e: 3}, what is the expected number of times the pattern 'ra+' appears? Round 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 {u: 5, c: 7} to form a word, what is the expected number of matches of the pattern 'cu+'? Round 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 {y: 3, v: 1, i: 5, x: 3} to form a word, what is the expected number of matches of the pattern 'v*y'? Round 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 {l: 4, r: 8}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6.36
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {z: 4, h: 1, c: 3, p: 1, l: 3}. What is the expected number of occurrences of the pattern 'hp+' 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 6 by randomly selecting letters from the multiset {a: 4, o: 8}, what is the expected number of times the pattern 'a+o' appears? 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 {o: 2, r: 5, s: 1, q: 2, g: 2}. What is the expected number of occurrences of the pattern 'r.*o' 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 6 letters from the multiset {x: 3, o: 3, q: 2, k: 3, c: 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"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {w: 6, d: 6} to form a word, what is the expected number of matches of the pattern 'dw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.14
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {t: 1, g: 6, w: 5}. What is the expected number of occurrences of the pattern 'g+w' 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": "Form a word by randomly choosing 6 letters from the multiset {j: 3, p: 3, b: 4, i: 2}. What is the expected number of occurrences of the pattern 'jp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.4
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {u: 2, v: 1, l: 4, z: 5}. 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"
}
] |
0.23
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {e: 4, d: 3, z: 3, m: 2} 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"
}
] |
0.68
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {s: 5, c: 4, a: 3}. What is the expected number of occurrences of the pattern 'cs+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.07
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {m: 5, g: 5, o: 2}, what is the expected number of times the pattern 'o*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.91
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {w: 1, o: 2, n: 4, z: 5} to form a word, what is the expected number of matches of the pattern 'n+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.19
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {n: 4, q: 5, w: 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"
}
] |
1.36
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 6, q: 6}, 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"
}
] |
3.41
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {l: 6, z: 1, u: 3, d: 2} to form a word, what is the expected number of matches of the pattern 'dl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.71
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {w: 7, u: 5} to form a word, what is the expected number of matches of the pattern 'u*w'? 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 {v: 4, e: 2, n: 6}. What is the expected number of occurrences of the pattern 'n.*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": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 3, i: 9}, 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"
}
] |
0.68
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {n: 3, h: 3, x: 4, e: 2}. 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"
}
] |
1.36
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {o: 2, v: 3, l: 2, u: 2, y: 3}. What is the expected number of occurrences of the pattern 'u.*v' 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 {p: 5, y: 7}. What is the expected number of occurrences of the pattern 'py*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.83
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 6, h: 6}, what is the expected number of times the pattern 'ph*' appears? 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 {e: 6, s: 6}, 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"
}
] |
3.41
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {i: 7, n: 5}. 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"
}
] |
2.27
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {c: 1, f: 1, y: 1, m: 7, d: 2} to form a word, what is the expected number of matches of the pattern 'fy+'? 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 6 letters from the multiset {i: 3, q: 4, t: 5}. 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"
}
] |
0.68
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 4, h: 1, u: 1, s: 4, v: 2}, what is the expected number of times the pattern 'jv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {b: 3, x: 3, u: 3, n: 1, t: 2}. What is the expected number of occurrences of the pattern 'nb*' 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": "If you form a word of length 6 by randomly selecting letters from the multiset {x: 9, c: 3}, what is the expected number of times the pattern 'cx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.82
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {v: 5, d: 1, t: 6}. 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"
}
] |
3.41
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {n: 7, u: 5}. 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"
}
] |
5.38
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 4, g: 3, z: 5}, what is the expected number of times the pattern 'gp+' 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 {i: 1, y: 4, l: 3, g: 2, d: 2}. What is the expected number of occurrences of the pattern 'gd*' 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": "Form a word by randomly choosing 6 letters from the multiset {w: 5, o: 7}. What is the expected number of occurrences of the pattern 'wo*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.83
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 6, d: 4, k: 2}, 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"
}
] |
1.36
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {a: 3, r: 5, b: 4} 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": "If you form a word of length 6 by randomly selecting letters from the multiset {m: 3, a: 1, q: 6, o: 2}, 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": "When randomly selecting 6 letters from the multiset {o: 2, h: 5, i: 3, e: 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"
}
] |
0.23
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {r: 3, u: 3, z: 6}. What is the expected number of occurrences of the pattern 'z+r' in each word? Round your answer 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 {c: 2, x: 1, p: 4, j: 3, m: 2} to form a word, what is the expected number of matches of the pattern 'cm*'? 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 {p: 4, v: 2, l: 3, r: 3}. What is the expected number of occurrences of the pattern 'lr*' 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": "Form a word by randomly choosing 6 letters from the multiset {s: 1, x: 4, p: 3, b: 3, q: 1}. What is the expected number of occurrences of the pattern 'ss*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {i: 5, l: 7}. What is the expected number of occurrences of the pattern 'i.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.98
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {d: 3, m: 4, r: 5}. What is the expected number of occurrences of the pattern 'r+d' 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 {w: 4, o: 3, y: 5} to form a word, what is the expected number of matches of the pattern 'ow+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.58
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {l: 5, u: 4, z: 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"
}
] |
1.36
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {g: 3, m: 5, q: 4}, 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"
}
] |
1.36
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {t: 8, x: 4} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.36
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {m: 3, q: 4, b: 2, d: 1, f: 2}. What is the expected number of occurrences of the pattern 'f+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 6 letters from the multiset {d: 5, v: 7}. 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"
}
] |
4.77
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 2, e: 2, h: 3, a: 4, d: 1}, what is the expected number of times the pattern 'a.*d' 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 {t: 7, q: 5}, 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"
}
] |
2.27
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {x: 2, n: 6, m: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'zx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.16
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {a: 5, p: 1, e: 6}, 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"
}
] |
2.69
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {c: 3, m: 4, f: 1, o: 4} to form a word, what is the expected number of matches of the pattern 'of*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.15
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {x: 3, g: 2, w: 3, m: 2, v: 2}. What is the expected number of occurrences of the pattern 'm.*w' 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 {z: 2, i: 2, a: 4, d: 2, f: 2}. What is the expected number of occurrences of the pattern 'di*' 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 {b: 1, u: 2, r: 5, p: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'ku+'? 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 {q: 3, s: 2, u: 1, m: 3, o: 3}, what is the expected number of times the pattern 's.*q' 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 {l: 4, k: 1, f: 2, a: 5}. What is the expected number of occurrences of the pattern 'f*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {r: 1, z: 4, x: 3, n: 4}. 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"
}
] |
0.63
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 3, g: 3, s: 5, i: 1}, what is the expected number of times the pattern 'is+' appears? Round 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 {i: 2, x: 2, f: 1, e: 3, z: 4}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.23
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {f: 1, y: 3, q: 1, o: 3, m: 4}. What is the expected number of occurrences of the pattern 'q+f' 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 {o: 7, r: 5} to form a word, what is the expected number of matches of the pattern 'o+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {o: 2, x: 6, v: 4}. 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"
}
] |
3.41
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {i: 4, o: 8}. 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": "Form a word by randomly choosing 6 letters from the multiset {l: 2, f: 4, s: 3, h: 3}. 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"
}
] |
1.36
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {n: 4, q: 3, o: 5}. What is the expected number of occurrences of the pattern 'no+' in each word? Round your answer 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 {j: 4, x: 3, p: 5} to form a word, what is the expected number of matches of the pattern 'x.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.7
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 2, n: 5, i: 3, f: 1, b: 1}, what is the expected number of times the pattern 'i.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.34
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {m: 1, n: 2, h: 3, a: 6} to form a word, what is the expected number of matches of the pattern 'am*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.23
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {d: 3, r: 4, j: 2, i: 2, k: 1}. What is the expected number of occurrences of the pattern 'ij*' 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 {p: 6, q: 6} to form a word, what is the expected number of matches of the pattern 'q*p'? 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 {d: 4, u: 1, y: 5, s: 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"
}
] |
0.97
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {z: 2, c: 2, f: 3, m: 3, s: 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"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {r: 3, s: 3, o: 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"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {v: 2, l: 5, p: 5} to form a word, what is the expected number of matches of the pattern 'v.*v'? 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 {l: 1, c: 6, u: 3, z: 2} 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"
}
] |
0.23
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {d: 3, f: 5, y: 4} to form a word, what is the expected number of matches of the pattern 'fy+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.97
|
MATH
|
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