messages
listlengths 1
1
| ground_truth
stringclasses 85
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "When randomly selecting 5 letters from the multiset {y: 2, n: 1, g: 3, e: 4} to form a word, what is the expected number of matches of the pattern 'g*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.64
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {m: 3, y: 3, c: 4}. What is the expected number of occurrences of the pattern 'm.*c' 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": "Form a word by randomly choosing 5 letters from the multiset {z: 5, r: 5}. What is the expected number of occurrences of the pattern 'zr*' in each word? Round your answer 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 {v: 3, d: 3, u: 1, p: 2, s: 1} 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"
}
] |
0.29
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {z: 3, m: 4, e: 3} to form a word, what is the expected number of matches of the pattern 'e*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.98
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {z: 3, p: 4, t: 3} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {j: 2, h: 2, l: 6} to form a word, what is the expected number of matches of the pattern 'j*h'? Round 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 {g: 4, r: 3, o: 3}. What is the expected number of occurrences of the pattern 'o.*r' 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 5 letters from the multiset {d: 4, l: 6} to form a word, what is the expected number of matches of the pattern 'ld*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.43
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {r: 4, s: 2, c: 2, q: 2}, what is the expected number of times the pattern 'q*r' appears? 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 {i: 1, y: 2, j: 3, w: 2, m: 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"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {m: 2, o: 3, a: 2, y: 3} to form a word, what is the expected number of matches of the pattern 'a+o'? Round 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 {n: 5, a: 5} to form a word, what is the expected number of matches of the pattern 'a*n'? 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 {k: 4, f: 1, h: 2, g: 3} to form a word, what is the expected number of matches of the pattern 'hg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.32
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {x: 1, b: 5, r: 4}. What is the expected number of occurrences of the pattern 'xb*' in each word? Round your answer 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 {c: 3, d: 2, t: 3, o: 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"
}
] |
0.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {k: 3, i: 1, s: 2, w: 2, o: 2}. What is the expected number of occurrences of the pattern 'k.*s' 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 {k: 4, w: 6}. What is the expected number of occurrences of the pattern 'k+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": "When randomly selecting 5 letters from the multiset {j: 2, o: 1, d: 3, l: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'v.*d'? 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 {u: 7, o: 3}. What is the expected number of occurrences of the pattern 'ou+' 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 {y: 3, d: 2, v: 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"
}
] |
2.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {g: 8, r: 2}. What is the expected number of occurrences of the pattern 'g+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.56
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {w: 3, m: 2, p: 3, l: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'm*w'? Round 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 {o: 1, c: 3, p: 3, b: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'fc+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.16
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {d: 6, a: 4}. 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"
}
] |
3.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {b: 3, g: 3, n: 4}. 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"
}
] |
1.33
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {w: 4, x: 3, d: 3} to form a word, what is the expected number of matches of the pattern 'xw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.21
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 2, d: 2, j: 1, q: 4, i: 1}, what is the expected number of times the pattern 'i*h' 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 {c: 6, b: 4}. What is the expected number of occurrences of the pattern 'c*b' 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": "Form a word by randomly choosing 5 letters from the multiset {k: 3, e: 2, d: 2, t: 3}. What is the expected number of occurrences of the pattern 'k*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.32
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {s: 2, y: 5, r: 2, b: 1}. What is the expected number of occurrences of the pattern 'r*s' 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 {e: 2, f: 2, c: 4, i: 2}. What is the expected number of occurrences of the pattern 'ce*' 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": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 6, f: 1, y: 3}, what is the expected number of times the pattern 'yf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.63
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {j: 4, g: 2, h: 2, l: 2}. 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"
}
] |
1.33
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {p: 1, h: 3, w: 4, y: 2} 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"
}
] |
0.48
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {v: 7, c: 3}. What is the expected number of occurrences of the pattern 'v*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.29
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {m: 3, r: 1, h: 2, l: 4} to form a word, what is the expected number of matches of the pattern 'l*h'? 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 {w: 1, r: 3, u: 3, m: 1, v: 2} 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"
}
] |
0.29
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {x: 4, y: 3, p: 3}. What is the expected number of occurrences of the pattern 'yx*' 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": "When randomly selecting 5 letters from the multiset {q: 2, i: 3, z: 3, p: 2} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.22
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {l: 5, w: 5} to form a word, what is the expected number of matches of the pattern 'w*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.17
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {m: 2, f: 3, y: 2, a: 1, i: 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"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {r: 3, x: 2, q: 5}, what is the expected number of times the pattern 'r.*q' appears? 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 5 letters from the multiset {o: 4, z: 1, n: 2, f: 2, k: 1}. What is the expected number of occurrences of the pattern 'z*n' 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": "When randomly selecting 5 letters from the multiset {j: 4, f: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'f+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.95
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 2, d: 3, z: 1, l: 4}, what is the expected number of times the pattern 'zb*' appears? Round 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 5 letters from the multiset {n: 3, s: 1, r: 4, a: 2}. What is the expected number of occurrences of the pattern 'a*s' 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": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 3, d: 3, i: 4}, 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"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {a: 1, z: 3, x: 6} to form a word, what is the expected number of matches of the pattern 'z*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.96
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {r: 5, t: 5}. 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"
}
] |
2.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {h: 3, b: 2, w: 2, e: 2, f: 1}. What is the expected number of occurrences of the pattern 'w.*w' 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": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 5, q: 3, r: 2}, 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 {q: 2, w: 2, t: 2, e: 4}, what is the expected number of times the pattern 'wq+' appears? Round 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: 8, e: 2} to form a word, what is the expected number of matches of the pattern 'o+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.56
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {b: 5, i: 5} to form a word, what is the expected number of matches of the pattern 'i+b'? 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 5 letters from the multiset {j: 2, o: 4, h: 1, m: 2, i: 1}. What is the expected number of occurrences of the pattern 'j.*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": "Form a word by randomly choosing 5 letters from the multiset {n: 3, c: 1, z: 3, k: 3}. 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"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {f: 3, t: 5, x: 2} to form a word, what is the expected number of matches of the pattern 'tf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.3
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {l: 7, 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"
}
] |
4.63
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 5, j: 5}, what is the expected number of times the pattern 'j+t' 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 5 by randomly selecting letters from the multiset {v: 5, n: 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"
}
] |
2.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 6, q: 4}, what is the expected number of times the pattern 'i+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.8
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {m: 4, k: 6}. What is the expected number of occurrences of the pattern 'm.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 3, x: 2, e: 2, b: 2, k: 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"
}
] |
1.09
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {p: 2, d: 2, j: 3, n: 3} 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"
}
] |
0.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {p: 2, q: 5, c: 3}. What is the expected number of occurrences of the pattern 'q*p' in each word? Round your answer 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 {c: 1, a: 5, d: 3, t: 1} to form a word, what is the expected number of matches of the pattern 'dt+'? Round 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 5 by randomly selecting letters from the multiset {r: 2, s: 2, i: 1, j: 1, m: 4}, 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"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 5, w: 5}, what is the expected number of times the pattern 'w.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.78
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {n: 2, w: 6, k: 2}. What is the expected number of occurrences of the pattern 'w*n' 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 5 by randomly selecting letters from the multiset {t: 2, c: 4, e: 4}, what is the expected number of times the pattern 'ce*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.95
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {p: 5, a: 5}. What is the expected number of occurrences of the pattern 'ap+' in each word? Round your answer 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 5 by randomly selecting letters from the multiset {t: 2, e: 3, g: 3, o: 2}, what is the expected number of times the pattern 'g+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.32
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 3, l: 2, x: 2, i: 3}, what is the expected number of times the pattern 'c.*c' 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 {x: 1, d: 3, j: 3, b: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {z: 2, a: 2, n: 6}, what is the expected number of times the pattern 'z+n' 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 5 letters from the multiset {q: 2, t: 4, h: 3, i: 1}. What is the expected number of occurrences of the pattern 'q+i' 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": "When randomly selecting 5 letters from the multiset {u: 3, x: 4, c: 3} to form a word, what is the expected number of matches of the pattern 'cx*'? Round 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 {u: 7, b: 3}. What is the expected number of occurrences of the pattern 'u.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.33
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {z: 3, c: 2, i: 5}, what is the expected number of times the pattern 'i.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.11
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {b: 3, g: 3, n: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'g*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.98
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {s: 4, n: 1, k: 1, i: 4} 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"
}
] |
1.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {y: 5, x: 2, t: 3}. What is the expected number of occurrences of the pattern 't+y' 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": "Form a word by randomly choosing 5 letters from the multiset {u: 3, z: 2, d: 3, m: 2}. What is the expected number of occurrences of the pattern 'm+d' 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": "Form a word by randomly choosing 5 letters from the multiset {a: 4, z: 2, u: 4}. 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"
}
] |
1.33
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {z: 4, v: 4, q: 2} to form a word, what is the expected number of matches of the pattern 'qv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.48
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {a: 6, k: 3, y: 1}. 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"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {q: 2, l: 3, m: 5}. What is the expected number of occurrences of the pattern 'ql+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.32
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 7, t: 3}, what is the expected number of times the pattern 'st+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.13
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {c: 2, e: 2, y: 1, b: 3, t: 2}. What is the expected number of occurrences of the pattern 'c.*t' 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": "Form a word by randomly choosing 5 letters from the multiset {a: 1, s: 2, y: 4, c: 3}. 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"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {a: 1, z: 2, l: 2, y: 1, t: 4} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 2, o: 2, i: 2, e: 4}, what is the expected number of times the pattern 'oa+' appears? Round 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 {n: 4, h: 3, s: 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"
}
] |
1.33
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {h: 4, b: 1, f: 1, n: 1, i: 3} 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"
}
] |
0.18
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {t: 6, d: 4}. 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"
}
] |
3.33
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 6, s: 4}, what is the expected number of times the pattern 's+x' appears? Round 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 {o: 2, s: 1, q: 4, f: 2, h: 1}. What is the expected number of occurrences of the pattern 'oq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.48
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {v: 4, j: 1, p: 2, m: 2, k: 1}. What is the expected number of occurrences of the pattern 'm+j' 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": "Form a word by randomly choosing 5 letters from the multiset {c: 1, k: 4, l: 1, n: 3, r: 1}. What is the expected number of occurrences of the pattern 'k+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.24
|
MATH
|
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