messages
listlengths 1
1
| ground_truth
stringclasses 85
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {w: 6, d: 4}. What is the expected number of occurrences of the pattern 'd+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.43
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {t: 3, r: 1, b: 3, z: 1, d: 2}. 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"
}
] |
0.66
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {p: 4, r: 2, q: 4} to form a word, what is the expected number of matches of the pattern 'rp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.48
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {q: 3, x: 2, c: 4, b: 1} to form a word, what is the expected number of matches of the pattern 'q+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.32
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {d: 1, j: 5, x: 2, 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"
}
] |
0.1
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 6, w: 4}, what is the expected number of times the pattern 'wc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.8
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 3, i: 1, h: 1, d: 3, o: 2}, what is the expected number of times the pattern 'o.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 3, h: 2, r: 1, z: 4}, what is the expected number of times the pattern 'rh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.6
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {d: 1, f: 2, p: 2, h: 2, e: 3} to form a word, what is the expected number of matches of the pattern 'eh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.79
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 3, j: 4, h: 3}, what is the expected number of times the pattern 'hv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.98
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {f: 2, g: 2, h: 2, o: 4}. What is the expected number of occurrences of the pattern 'oh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.39
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {r: 1, x: 1, w: 2, s: 1, c: 5} to form a word, what is the expected number of matches of the pattern 'xr+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.04
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {x: 2, t: 3, m: 1, h: 4} to form a word, what is the expected number of matches of the pattern 't+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.16
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {g: 2, x: 3, v: 2, j: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'gf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.09
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {r: 4, a: 6} to form a word, what is the expected number of matches of the pattern 'a.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {l: 3, o: 4, j: 3} to form a word, what is the expected number of matches of the pattern 'j+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.48
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {a: 3, x: 4, m: 3} to form a word, what is the expected number of matches of the pattern 'a*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.98
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {u: 2, x: 3, p: 2, n: 2, o: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 2, v: 1, s: 2, t: 2, c: 3}, what is the expected number of times the pattern 't+s' appears? 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 5 by randomly selecting letters from the multiset {e: 2, b: 1, l: 2, m: 1, i: 4}, 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"
}
] |
0.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {x: 2, w: 4, z: 2, e: 1, i: 1}. What is the expected number of occurrences of the pattern 'w.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.89
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 5, r: 4, c: 1}, what is the expected number of times the pattern 'l*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.83
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 4, r: 3, j: 3}, what is the expected number of times the pattern 'e.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.33
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 3, s: 3, f: 4}, what is the expected number of times the pattern 'f.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {e: 2, j: 3, k: 2, p: 3}. What is the expected number of occurrences of the pattern 'j.*j' 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": "When randomly selecting 5 letters from the multiset {s: 2, z: 3, d: 3, o: 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"
}
] |
0.22
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {r: 1, y: 1, l: 2, v: 3, n: 3} to form a word, what is the expected number of matches of the pattern 'rv+'? 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 5 by randomly selecting letters from the multiset {b: 1, h: 3, t: 2, n: 2, i: 2}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {z: 1, y: 1, e: 2, u: 2, l: 4}, what is the expected number of times the pattern 'eu+' 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 5 letters from the multiset {l: 2, c: 2, z: 2, f: 3, x: 1}. What is the expected number of occurrences of the pattern 'fz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.29
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {v: 3, n: 3, e: 4} 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"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {p: 1, o: 5, h: 4} to form a word, what is the expected number of matches of the pattern 'p.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.44
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 1, y: 2, b: 2, d: 4, q: 1}, what is the expected number of times the pattern 'dd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.64
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {i: 4, t: 6} to form a word, what is the expected number of matches of the pattern 't+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.8
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 1, m: 2, j: 1, o: 5, g: 1}, 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"
}
] |
0.22
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {v: 4, f: 3, w: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'y+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.09
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {k: 5, m: 5}, what is the expected number of times the pattern 'k+m' 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 5 letters from the multiset {i: 2, e: 3, q: 1, f: 4} to form a word, what is the expected number of matches of the pattern 'q.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.44
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 4, i: 2, k: 2, l: 2}, what is the expected number of times the pattern 'k+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.39
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 5, o: 1, t: 3, w: 1}, what is the expected number of times the pattern 'te*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.5
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {e: 1, p: 4, o: 3, w: 2}. What is the expected number of occurrences of the pattern 'w+p' 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": "Form a word by randomly choosing 5 letters from the multiset {l: 4, j: 3, u: 3}. What is the expected number of occurrences of the pattern 'l*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.21
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {j: 3, h: 2, n: 2, b: 1, t: 2}. 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"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {q: 3, n: 2, g: 5}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {p: 6, i: 4}. What is the expected number of occurrences of the pattern 'ip*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.8
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {u: 5, s: 2, x: 3}, 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"
}
] |
0.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {e: 2, y: 3, v: 1, f: 2, t: 2}. What is the expected number of occurrences of the pattern 'f+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.19
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {o: 7, c: 3} 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"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {i: 6, m: 4} to form a word, what is the expected number of matches of the pattern 'mi+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.8
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {a: 1, i: 3, e: 2, s: 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"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {k: 3, c: 7}. What is the expected number of occurrences of the pattern 'c+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.79
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {n: 3, e: 2, l: 2, u: 1, b: 2} 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"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {f: 3, t: 3, p: 1, i: 1, o: 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"
}
] |
0.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {p: 5, n: 5}. What is the expected number of occurrences of the pattern 'p.*n' 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": "When randomly selecting 5 letters from the multiset {e: 2, s: 1, i: 2, u: 4, y: 1} to form a word, what is the expected number of matches of the pattern 'y*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.54
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {m: 5, o: 2, b: 2, c: 1}. What is the expected number of occurrences of the pattern 'ob*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.19
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {q: 1, r: 3, g: 1, t: 1, v: 4}. What is the expected number of occurrences of the pattern 'g.*q' 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": "Form a word by randomly choosing 5 letters from the multiset {y: 1, n: 2, c: 1, a: 1, h: 5}. What is the expected number of occurrences of the pattern 'n.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.22
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {l: 5, y: 3, b: 2} to form a word, what is the expected number of matches of the pattern 'yl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.5
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {z: 2, c: 2, w: 2, s: 1, r: 3}. 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"
}
] |
0.67
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {a: 2, n: 4, t: 2, x: 2}. What is the expected number of occurrences of the pattern 'x+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.19
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {o: 2, l: 8} to form a word, what is the expected number of matches of the pattern 'l+o'? 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 5 letters from the multiset {y: 2, t: 2, n: 3, e: 2, p: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {v: 1, t: 3, k: 2, o: 1, b: 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"
}
] |
1.09
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 2, u: 1, o: 1, q: 2, y: 4}, what is the expected number of times the pattern 'q.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 1, j: 3, w: 2, b: 3, d: 1}, what is the expected number of times the pattern 'w*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.09
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {e: 5, b: 3, u: 2}. What is the expected number of occurrences of the pattern 'e+u' 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 5 by randomly selecting letters from the multiset {o: 3, b: 3, y: 4}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {i: 3, x: 6, c: 1}. What is the expected number of occurrences of the pattern 'i*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.96
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 2, b: 2, o: 3, x: 3}, what is the expected number of times the pattern 'co*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.32
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 4, g: 2, m: 2, k: 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"
}
] |
0.22
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {l: 6, m: 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"
}
] |
3.33
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 2, z: 1, s: 1, q: 3, g: 3}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 6, x: 4}, what is the expected number of times the pattern 'x.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {b: 3, q: 2, f: 2, u: 3} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {m: 2, h: 3, x: 3, c: 2}, 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"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {i: 2, h: 3, u: 1, p: 4} to form a word, what is the expected number of matches of the pattern 'i*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.39
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 4, g: 2, o: 2, n: 2}, what is the expected number of times the pattern 'g+n' appears? 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 5 by randomly selecting letters from the multiset {i: 2, w: 1, q: 3, j: 4}, what is the expected number of times the pattern 'jw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.18
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {h: 1, g: 4, i: 5}. What is the expected number of occurrences of the pattern 'i+g' 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 5 letters from the multiset {j: 5, s: 3, z: 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"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {c: 2, z: 3, e: 2, s: 3} to form a word, what is the expected number of matches of the pattern 'es*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.32
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {m: 3, k: 3, v: 4}, what is the expected number of times the pattern 'm*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.98
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 1, g: 1, q: 3, w: 4, e: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {k: 3, z: 3, i: 4} to form a word, what is the expected number of matches of the pattern 'k.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.0
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {u: 7, w: 3} to form a word, what is the expected number of matches of the pattern 'w.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.33
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {c: 2, s: 3, d: 5} 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"
}
] |
0.67
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {q: 4, s: 1, k: 3, e: 2}. What is the expected number of occurrences of the pattern 's*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.18
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 2, l: 3, p: 2, g: 3}, what is the expected number of times the pattern 'lg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.48
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {n: 5, a: 4, k: 1}. What is the expected number of occurrences of the pattern 'n*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.33
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {d: 1, j: 9} to form a word, what is the expected number of matches of the pattern 'j*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.5
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 5, i: 5}, what is the expected number of times the pattern 'it*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.17
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {z: 2, k: 1, c: 1, d: 4, i: 2} to form a word, what is the expected number of matches of the pattern 'zk+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.09
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {u: 2, j: 1, a: 3, x: 2, m: 2}. What is the expected number of occurrences of the pattern 'u.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.44
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 4, j: 1, l: 3, v: 1, d: 1}, what is the expected number of times the pattern 'lj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.63
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {m: 4, d: 6} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.33
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 2, z: 1, v: 1, p: 4, a: 2}, what is the expected number of times the pattern 'sa*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.19
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 3, w: 1, s: 1, g: 3, b: 2}, 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"
}
] |
1.63
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {f: 2, h: 3, n: 5} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {f: 3, q: 1, i: 4, d: 2} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
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