messages
listlengths 1
1
| ground_truth
stringclasses 65
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 5, j: 4}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.67
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {i: 3, 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"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {u: 1, j: 2, d: 2, z: 2, q: 2} to form a word, what is the expected number of matches of the pattern 'd*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.07
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {u: 1, s: 1, n: 4, y: 1, k: 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"
}
] |
0.17
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 2, k: 2, p: 1, f: 4}, what is the expected number of times the pattern 'k+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.09
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {l: 2, z: 2, t: 2, w: 3} 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"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {v: 1, m: 2, n: 3, o: 1, u: 2} 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"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {a: 4, y: 5} to form a word, what is the expected number of matches of the pattern 'y*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.01
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 4, f: 5}, what is the expected number of times the pattern 'd*f' appears? 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 4 by randomly selecting letters from the multiset {b: 2, g: 4, h: 3}, what is the expected number of times the pattern 'g.*h' 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 4 letters from the multiset {f: 5, e: 4} 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"
}
] |
1.67
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 6, o: 3}, what is the expected number of times the pattern 'h.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {q: 3, t: 3, a: 3} to form a word, what is the expected number of matches of the pattern 't.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.75
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {b: 3, l: 1, w: 2, n: 3}. What is the expected number of occurrences of the pattern 'lw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.09
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {b: 4, l: 3, q: 2} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {d: 3, o: 3, m: 1, g: 2} 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"
}
] |
0.5
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {q: 4, o: 5}. What is the expected number of occurrences of the pattern 'qo*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.01
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {t: 2, b: 2, r: 3, l: 2}. What is the expected number of occurrences of the pattern 't*b' 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 4 by randomly selecting letters from the multiset {t: 2, s: 3, g: 1, u: 2, r: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 4, h: 5}, what is the expected number of times the pattern 'h.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.67
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 4, a: 5}, what is the expected number of times the pattern 'a+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.23
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {u: 2, h: 3, j: 2, q: 2} 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"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {r: 1, i: 1, h: 3, c: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'ic*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.54
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {y: 1, s: 1, v: 3, i: 2, f: 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"
}
] |
0.08
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {r: 1, v: 2, i: 2, h: 4}. What is the expected number of occurrences of the pattern 'v.*h' 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 4 letters from the multiset {j: 3, i: 2, w: 1, c: 1, t: 2}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.17
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 4, k: 5}, what is the expected number of times the pattern 'k*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.01
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {c: 2, o: 3, u: 4}. What is the expected number of occurrences of the pattern 'uc*' 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 4 letters from the multiset {v: 1, n: 6, c: 2} to form a word, what is the expected number of matches of the pattern 'v*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.92
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 7, o: 2}, 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"
}
] |
0.17
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {b: 5, y: 4}. What is the expected number of occurrences of the pattern 'yy*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.38
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {g: 4, x: 2, t: 3}. What is the expected number of occurrences of the pattern 'gt+' 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 4 letters from the multiset {s: 4, y: 2, p: 3}. What is the expected number of occurrences of the pattern 'ys*' 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": "When randomly selecting 4 letters from the multiset {j: 2, o: 4, u: 3} 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"
}
] |
0.5
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 5, e: 4}, what is the expected number of times the pattern 'ue+' appears? 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 4 letters from the multiset {n: 5, y: 4}. 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"
}
] |
1.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {k: 1, f: 2, b: 2, e: 1, o: 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"
}
] |
0.5
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 2, x: 2, i: 3, y: 1, z: 1}, what is the expected number of times the pattern 'i*f' 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 4 by randomly selecting letters from the multiset {e: 3, n: 3, c: 3}, what is the expected number of times the pattern 'nc*' appears? Round 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 4 letters from the multiset {e: 5, b: 4}. What is the expected number of occurrences of the pattern 'ee+' in each word? Round your answer 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 4 letters from the multiset {i: 1, p: 4, n: 1, r: 1, d: 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"
}
] |
1.0
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 2, y: 2, m: 3, u: 2}, what is the expected number of times the pattern 'm.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {c: 3, p: 3, y: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'p.*y'? Round 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 4 letters from the multiset {n: 3, s: 5, u: 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"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {y: 2, x: 3, v: 3, a: 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"
}
] |
0.5
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 4, q: 5}, 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"
}
] |
1.0
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 2, i: 4, v: 2, e: 1}, what is the expected number of times the pattern 'r.*i' 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 4 letters from the multiset {k: 3, i: 1, e: 2, y: 2, u: 1}. What is the expected number of occurrences of the pattern 'u+e' 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 4 letters from the multiset {a: 4, u: 2, o: 3} to form a word, what is the expected number of matches of the pattern 'ua*'? 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 4 letters from the multiset {j: 2, p: 1, x: 3, m: 1, f: 2}. What is the expected number of occurrences of the pattern 'xm+' 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 4 by randomly selecting letters from the multiset {j: 1, t: 3, w: 5}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {s: 2, g: 5, o: 2} to form a word, what is the expected number of matches of the pattern 'gs+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.46
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {s: 1, i: 4, r: 4} to form a word, what is the expected number of matches of the pattern 'i+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.89
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {p: 3, y: 2, j: 2, v: 2}. What is the expected number of occurrences of the pattern 'v.*j' 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": "When randomly selecting 4 letters from the multiset {p: 4, v: 5} to form a word, what is the expected number of matches of the pattern 'v*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.01
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {b: 4, m: 5} to form a word, what is the expected number of matches of the pattern 'mb+'? 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 4 letters from the multiset {x: 5, e: 4}. What is the expected number of occurrences of the pattern 'x*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.01
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {p: 2, s: 2, f: 2, c: 3}. What is the expected number of occurrences of the pattern 's*p' 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 4 letters from the multiset {q: 4, o: 5} to form a word, what is the expected number of matches of the pattern 'q.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.67
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {x: 4, m: 5}. What is the expected number of occurrences of the pattern 'xm*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.01
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 2, j: 1, l: 4, r: 2}, what is the expected number of times the pattern 'dj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.08
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {b: 1, d: 3, z: 5} 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"
}
] |
3.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {q: 4, f: 5}. What is the expected number of occurrences of the pattern 'f+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.23
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {e: 5, q: 4}. 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"
}
] |
1.0
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {t: 5, e: 2, o: 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"
}
] |
0.46
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {v: 4, h: 5}. What is the expected number of occurrences of the pattern 'v*h' 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": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 2, n: 4, v: 1, g: 2}, what is the expected number of times the pattern 'v+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.08
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {p: 5, v: 4} to form a word, what is the expected number of matches of the pattern 'p.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.67
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 5, t: 2, j: 2}, what is the expected number of times the pattern 't+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.46
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {z: 6, v: 3} to form a word, what is the expected number of matches of the pattern 'z.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.5
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {d: 3, o: 2, i: 1, a: 2, v: 1}. 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"
}
] |
0.17
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {i: 1, l: 1, j: 1, k: 3, g: 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"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 2, o: 1, v: 4, j: 1, c: 1}, what is the expected number of times the pattern 'o.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.17
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 1, e: 1, t: 3, j: 2, m: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {c: 3, i: 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"
}
] |
0.5
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {s: 4, q: 4, y: 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"
}
] |
1.94
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 3, s: 3, t: 3}, 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"
}
] |
0.45
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 5, i: 4}, 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"
}
] |
1.67
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 2, l: 2, m: 3, s: 2}, what is the expected number of times the pattern 's.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.33
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {q: 4, d: 2, j: 3} to form a word, what is the expected number of matches of the pattern 'd.*j'? Round 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 4 letters from the multiset {a: 3, v: 2, g: 3, s: 1}. What is the expected number of occurrences of the pattern 'g*a' 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 4 letters from the multiset {p: 1, f: 8}. What is the expected number of occurrences of the pattern 'p*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.89
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {d: 2, q: 4, k: 1, n: 2}. 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"
}
] |
0.17
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {u: 3, m: 3, w: 3}. What is the expected number of occurrences of the pattern 'w*u' 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 4 letters from the multiset {y: 1, j: 2, z: 2, o: 3, d: 1} to form a word, what is the expected number of matches of the pattern 'dj+'? 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 4 by randomly selecting letters from the multiset {a: 2, t: 2, h: 5}, 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"
}
] |
0.17
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {f: 3, m: 1, t: 2, n: 3}. What is the expected number of occurrences of the pattern 'nm*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.46
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {g: 2, j: 1, s: 2, h: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'g+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.27
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 3, s: 2, i: 4}, what is the expected number of times the pattern 'js+' 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 4 letters from the multiset {d: 4, y: 1, l: 4}. What is the expected number of occurrences of the pattern 'y.*l' 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": "When randomly selecting 4 letters from the multiset {n: 1, f: 3, p: 1, g: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'n.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.17
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {q: 4, a: 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"
}
] |
1.0
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 3, g: 2, y: 4}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.17
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {f: 1, b: 2, n: 1, h: 2, v: 3} to form a word, what is the expected number of matches of the pattern 'vn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.46
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {l: 5, y: 4} 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"
}
] |
1.67
|
MATH
|
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {t: 4, a: 5}. What is the expected number of occurrences of the pattern 'a+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.23
|
MATH
|
[
{
"content": "When randomly selecting 4 letters from the multiset {v: 1, i: 3, z: 1, l: 3, p: 1} to form a word, what is the expected number of matches of the pattern 'l+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.15
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 2, l: 3, c: 1, x: 1, q: 2}, what is the expected number of times the pattern 's*l' appears? 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 4 letters from the multiset {x: 4, k: 5}. What is the expected number of occurrences of the pattern 'xk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.23
|
MATH
|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 3, c: 2, p: 2, v: 2}, what is the expected number of times the pattern 'c+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.27
|
MATH
|
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