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 {p: 5, s: 3, d: 4}. What is the expected number of occurrences of the pattern 'sp+' 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 6 letters from the multiset {b: 3, j: 4, n: 2, h: 3}. What is the expected number of occurrences of the pattern 'n+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.25
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {x: 3, k: 6, g: 3} 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"
}
] |
0.68
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {m: 8, b: 4}. What is the expected number of occurrences of the pattern 'm.*m' 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 {w: 3, q: 3, m: 4, u: 2}. What is the expected number of occurrences of the pattern 'u+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.25
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {q: 2, e: 3, u: 4, n: 1, v: 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"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {g: 7, i: 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"
}
] |
2.27
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {n: 4, z: 2, a: 6}, what is the expected number of times the pattern 'zn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.39
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {c: 3, r: 4, a: 3, q: 2}, what is the expected number of times the pattern 'r*c' appears? Round 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 {v: 3, o: 2, d: 1, x: 3, y: 3} to form a word, what is the expected number of matches of the pattern 'x+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.4
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {e: 7, j: 1, g: 4}. What is the expected number of occurrences of the pattern 'e.*j' 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 6 letters from the multiset {w: 3, h: 3, z: 4, o: 2}. 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"
}
] |
1.27
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {s: 1, y: 7, d: 4}. What is the expected number of occurrences of the pattern 'y+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.87
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {r: 2, f: 2, b: 2, i: 6} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.23
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {m: 7, b: 5} to form a word, what is the expected number of matches of the pattern 'mm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {u: 5, x: 2, h: 3, p: 2}. What is the expected number of occurrences of the pattern 'hx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.75
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {x: 3, u: 3, e: 1, a: 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"
}
] |
0.68
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 2, s: 3, c: 1, z: 6}, 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"
}
] |
3.41
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {e: 3, w: 2, j: 3, h: 4} to form a word, what is the expected number of matches of the pattern 'w.*w'? 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 {l: 7, q: 1, m: 1, k: 3}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {y: 2, z: 3, i: 5, m: 2}. What is the expected number of occurrences of the pattern 'z.*z' 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 {g: 1, d: 4, m: 2, n: 3, k: 2} to form a word, what is the expected number of matches of the pattern 'd+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.58
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {a: 4, y: 3, k: 2, u: 3} to form a word, what is the expected number of matches of the pattern 'y+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.4
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {k: 6, c: 6}. What is the expected number of occurrences of the pattern 'ck*' in each word? Round your answer 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 {t: 7, z: 5}, what is the expected number of times the pattern 'z+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.88
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 6, f: 3, s: 3}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.41
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {c: 5, h: 3, z: 4}. What is the expected number of occurrences of the pattern 'cz*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.47
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {w: 4, c: 8} to form a word, what is the expected number of matches of the pattern 'cw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.56
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {o: 2, d: 2, m: 4, r: 3, j: 1} to form a word, what is the expected number of matches of the pattern 'mo*'? Round 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 6 by randomly selecting letters from the multiset {z: 6, a: 3, p: 3}, 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"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {k: 1, j: 2, s: 2, i: 3, l: 4} to form a word, what is the expected number of matches of the pattern 's*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.75
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {w: 1, n: 4, z: 5, i: 2}. 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"
}
] |
0.57
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {u: 3, h: 5, o: 2, b: 2} 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"
}
] |
0.68
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 3, d: 9}, 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"
}
] |
8.18
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {f: 1, n: 4, o: 7} 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"
}
] |
4.77
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {t: 6, s: 3, h: 3}. What is the expected number of occurrences of the pattern 'h*s' 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 {t: 5, w: 1, f: 1, g: 2, n: 3}. What is the expected number of occurrences of the pattern 'w+g' 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": "If you form a word of length 6 by randomly selecting letters from the multiset {f: 7, k: 5}, what is the expected number of times the pattern 'f*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.83
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {n: 3, f: 6, q: 3} to form a word, what is the expected number of matches of the pattern 'q.*q'? 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 {n: 3, v: 5, p: 2, e: 2}, what is the expected number of times the pattern 'vn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.17
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {x: 3, c: 2, v: 4, z: 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"
}
] |
0.23
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {n: 3, f: 2, s: 3, a: 1, p: 3} to form a word, what is the expected number of matches of the pattern 'f.*a'? 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 {h: 1, a: 2, f: 3, g: 5, z: 1}, what is the expected number of times the pattern 'ah+' 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 6 letters from the multiset {v: 3, u: 3, s: 2, l: 4} to form a word, what is the expected number of matches of the pattern 'vs+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.25
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {c: 5, x: 1, j: 1, m: 5} to form a word, what is the expected number of matches of the pattern 'xm+'? 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 {q: 4, k: 2, w: 6}. What is the expected number of occurrences of the pattern 'qw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.43
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {q: 2, h: 2, e: 1, u: 5, b: 2} to form a word, what is the expected number of matches of the pattern 'e*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.08
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {n: 2, j: 4, v: 3, c: 3}, what is the expected number of times the pattern 'n+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.25
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {z: 6, g: 6}. What is the expected number of occurrences of the pattern 'z*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.14
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {j: 5, k: 5, d: 2} to form a word, what is the expected number of matches of the pattern 'j+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.34
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {m: 5, d: 5, p: 2}, what is the expected number of times the pattern 'dm+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.34
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {i: 8, b: 4}. What is the expected number of occurrences of the pattern 'ii*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
7.74
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {b: 6, m: 6} 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"
}
] |
2.14
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {t: 3, m: 5, g: 4} to form a word, what is the expected number of matches of the pattern 'tm+'? Round 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 {k: 2, s: 7, b: 3} 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"
}
] |
6.0
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 4, i: 8}, 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"
}
] |
6.36
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {e: 3, b: 3, u: 3, l: 1, d: 2} 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"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {g: 4, v: 8} to form a word, what is the expected number of matches of the pattern 'g*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.56
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {m: 4, g: 2, j: 2, o: 4}, what is the expected number of times the pattern 'o+j' 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 6 by randomly selecting letters from the multiset {p: 4, m: 4, x: 1, y: 2, c: 1}, what is the expected number of times the pattern 'cy*' 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 {t: 6, e: 6}. What is the expected number of occurrences of the pattern 't*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.14
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {c: 2, x: 2, z: 3, r: 3, p: 2} 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"
}
] |
0.23
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {s: 5, a: 7}. 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"
}
] |
3.98
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {p: 2, d: 2, l: 3, c: 5}. What is the expected number of occurrences of the pattern 'ld+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.25
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {w: 7, h: 5}. What is the expected number of occurrences of the pattern 'h.*w' 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": "When randomly selecting 6 letters from the multiset {s: 2, d: 7, t: 3} to form a word, what is the expected number of matches of the pattern 't*d'? 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 6 by randomly selecting letters from the multiset {t: 3, f: 2, y: 2, w: 4, v: 1}, what is the expected number of times the pattern 'ft+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.27
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {k: 2, o: 2, y: 2, m: 4, v: 2}, what is the expected number of times the pattern 'v*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.16
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {j: 3, d: 3, y: 3, q: 2, e: 1}. What is the expected number of occurrences of the pattern 'j+y' 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 {i: 2, m: 4, q: 2, z: 4}. What is the expected number of occurrences of the pattern 'm+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.78
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {p: 5, e: 7}. What is the expected number of occurrences of the pattern 'ep*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.37
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {k: 4, w: 2, y: 1, j: 2, p: 3}, what is the expected number of times the pattern 'p+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.13
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {u: 3, d: 5, y: 4}. What is the expected number of occurrences of the pattern 'y+d' in each word? Round your answer 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 {l: 2, p: 3, n: 4, w: 1, s: 2}. What is the expected number of occurrences of the pattern 'l+n' 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": "If you form a word of length 6 by randomly selecting letters from the multiset {o: 7, b: 5}, what is the expected number of times the pattern 'o+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.5
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {b: 3, k: 4, r: 5}. What is the expected number of occurrences of the pattern 'rr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.47
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {o: 3, x: 5, j: 3, y: 1}. 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"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {h: 4, g: 4, w: 4} to form a word, what is the expected number of matches of the pattern 'gw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.78
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {s: 3, a: 2, n: 2, v: 3, q: 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"
}
] |
0.68
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {w: 4, d: 4, p: 4}, what is the expected number of times the pattern 'wp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.78
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {k: 1, u: 3, p: 2, x: 3, r: 3} 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"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {a: 4, d: 3, h: 4, b: 1} 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"
}
] |
1.82
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {x: 5, f: 7}, 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"
}
] |
4.77
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {q: 3, h: 2, z: 3, y: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'y+b'? 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 6 letters from the multiset {q: 2, h: 2, r: 2, d: 2, v: 4}. What is the expected number of occurrences of the pattern 'd*h' 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": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 3, q: 4, u: 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"
}
] |
1.36
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {o: 1, h: 2, g: 4, w: 3, d: 2}, what is the expected number of times the pattern 'g+w' 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 {l: 2, s: 2, b: 3, r: 5}. What is the expected number of occurrences of the pattern 'l.*b' 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 {d: 1, p: 3, u: 3, a: 3, i: 2}, what is the expected number of times the pattern 'pa*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.9
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 6, t: 2, v: 2, a: 2}, what is the expected number of times the pattern 'vd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.71
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {o: 2, y: 2, e: 2, a: 2, m: 4}, what is the expected number of times the pattern 'ye+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.16
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {x: 1, u: 5, f: 3, l: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'lo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.58
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {z: 2, m: 4, r: 4, e: 2} to form a word, what is the expected number of matches of the pattern 'r+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.78
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {o: 4, q: 3, j: 3, v: 2} to form a word, what is the expected number of matches of the pattern 'oj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.53
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {s: 3, n: 1, y: 3, k: 3, h: 2}. What is the expected number of occurrences of the pattern 'k+y' 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": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 3, m: 2, y: 3, a: 2, j: 2}, what is the expected number of times the pattern 'm+a' appears? 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 6 letters from the multiset {y: 3, t: 4, f: 2, p: 2, o: 1}. What is the expected number of occurrences of the pattern 'oy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.13
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {d: 6, x: 4, i: 2} 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"
}
] |
3.41
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {g: 8, z: 4}, what is the expected number of times the pattern 'gz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.56
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {p: 1, s: 2, r: 6, k: 1, v: 2}. What is the expected number of occurrences of the pattern 'p+s' 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
|
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