messages
listlengths 1
1
| ground_truth
stringclasses 108
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {l: 4, y: 8}, what is the expected number of times the pattern 'y+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.41
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {s: 1, y: 2, o: 5, t: 3, a: 1}, what is the expected number of times the pattern 'y+a' 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 {l: 5, b: 7} to form a word, what is the expected number of matches of the pattern 'l+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.88
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {p: 6, l: 2, f: 4} to form a word, what is the expected number of matches of the pattern 'l.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.91
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {t: 2, w: 2, j: 3, q: 5}. What is the expected number of occurrences of the pattern 'tw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.16
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {b: 7, c: 5} to form a word, what is the expected number of matches of the pattern 'cc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.47
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {a: 5, h: 2, p: 1, k: 4}, what is the expected number of times the pattern 'h*k' appears? 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 {g: 5, t: 7}, 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"
}
] |
2.33
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {o: 5, e: 7} to form a word, what is the expected number of matches of the pattern 'oe+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {a: 11, c: 1}. 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"
}
] |
12.5
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {i: 4, e: 8} to form a word, what is the expected number of matches of the pattern 'ie*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.41
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {s: 1, d: 11}. What is the expected number of occurrences of the pattern 's.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.25
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 2, z: 3, o: 5, p: 2}, what is the expected number of times the pattern 'pz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.27
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 2, i: 2, h: 2, o: 3, g: 3}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.23
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {w: 3, n: 7, p: 2}, what is the expected number of times the pattern 'n+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.4
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {d: 1, u: 1, h: 3, s: 3, q: 4} to form a word, what is the expected number of matches of the pattern 'u+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.11
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 9, m: 3}, what is the expected number of times the pattern 'm*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.7
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {v: 3, u: 4, i: 3, r: 2}, what is the expected number of times the pattern 'u*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.39
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {r: 8, i: 4}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6.36
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {u: 4, n: 4, c: 4}, what is the expected number of times the pattern 'c.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.82
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {i: 4, h: 3, l: 5}. What is the expected number of occurrences of the pattern 'hi*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.08
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {d: 7, k: 5} to form a word, what is the expected number of matches of the pattern 'kd+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {o: 4, q: 3, g: 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"
}
] |
2.08
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 1, h: 1, z: 2, g: 3, k: 5}, what is the expected number of times the pattern 'j*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.08
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {t: 4, g: 5, o: 3}. 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"
}
] |
1.36
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 3, m: 3, e: 2, q: 2, w: 2}, what is the expected number of times the pattern 'mw+' appears? 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 {z: 4, b: 2, x: 2, r: 4} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.23
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {x: 3, d: 3, t: 6}. What is the expected number of occurrences of the pattern 't*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.57
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 5, d: 5, l: 2}, what is the expected number of times the pattern 'h.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.14
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {h: 5, z: 3, g: 2, r: 2}. What is the expected number of occurrences of the pattern 'r*z' 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": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 7, k: 2, o: 3}, 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"
}
] |
0.68
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {s: 7, o: 5}. 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"
}
] |
2.27
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {o: 3, p: 3, a: 6}, what is the expected number of times the pattern 'a.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.05
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {n: 3, t: 1, x: 2, b: 2, p: 4} to form a word, what is the expected number of matches of the pattern 'xt+'? 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 6 letters from the multiset {y: 5, f: 4, i: 3}. What is the expected number of occurrences of the pattern 'f+y' 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": "If you form a word of length 6 by randomly selecting letters from the multiset {d: 5, i: 7}, what is the expected number of times the pattern 'd*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.38
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {a: 5, y: 2, u: 1, t: 2, i: 2}. What is the expected number of occurrences of the pattern 'y.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.14
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {m: 6, e: 6} to form a word, what is the expected number of matches of the pattern 'm.*m'? 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: 7, u: 5}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.77
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {e: 3, v: 4, i: 1, p: 2, l: 2}. What is the expected number of occurrences of the pattern 'ie+' 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": "Form a word by randomly choosing 6 letters from the multiset {x: 2, r: 3, h: 1, d: 4, j: 2}. What is the expected number of occurrences of the pattern 'rd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.08
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {u: 5, g: 2, z: 5} to form a word, what is the expected number of matches of the pattern 'g*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.91
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {m: 5, v: 7} to form a word, what is the expected number of matches of the pattern 'm.*v'? Round 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 {v: 3, i: 2, l: 3, x: 3, d: 1} to form a word, what is the expected number of matches of the pattern 'l.*i'? 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 {d: 4, z: 2, f: 3, y: 1, x: 2}. What is the expected number of occurrences of the pattern 'dx+' 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 6 letters from the multiset {v: 3, b: 2, l: 4, z: 3} to form a word, what is the expected number of matches of the pattern 'zz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.75
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {s: 1, r: 2, j: 4, z: 5}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.23
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {c: 6, j: 6}, 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"
}
] |
3.41
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {b: 2, f: 5, m: 2, r: 2, y: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.27
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {x: 4, w: 2, y: 4, b: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'm*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.15
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {g: 4, h: 2, i: 1, q: 5}. What is the expected number of occurrences of the pattern 'q*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.07
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {r: 3, b: 4, l: 2, h: 1, y: 2}, what is the expected number of times the pattern 'h+h' 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 6 letters from the multiset {r: 7, u: 5} 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"
}
] |
2.27
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {o: 6, t: 6}. What is the expected number of occurrences of the pattern 'o*t' 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": "Form a word by randomly choosing 6 letters from the multiset {e: 6, g: 6}. What is the expected number of occurrences of the pattern 'e+g' 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": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 3, q: 1, f: 4, n: 4}, what is the expected number of times the pattern 'b.*b' appears? 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 {r: 2, j: 3, m: 3, c: 4}, what is the expected number of times the pattern 'mc*' 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 {z: 3, e: 4, a: 5} 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"
}
] |
2.27
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {d: 6, o: 6}. What is the expected number of occurrences of the pattern 'd*o' 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 {m: 4, v: 3, z: 2, f: 3}, what is the expected number of times the pattern 'f*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.27
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {z: 4, t: 2, m: 6}. 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"
}
] |
3.41
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 3, y: 4, z: 1, v: 3, s: 1}, what is the expected number of times the pattern 'y.*b' 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: 2, g: 10}, what is the expected number of times the pattern 'og+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.97
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {g: 6, s: 4, e: 2} to form a word, what is the expected number of matches of the pattern 's+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.17
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {y: 3, o: 3, l: 2, c: 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"
}
] |
0.68
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {f: 6, h: 6}. What is the expected number of occurrences of the pattern 'hf+' 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 6 letters from the multiset {g: 4, p: 4, x: 4} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.36
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 3, d: 3, w: 2, f: 2, r: 2}, what is the expected number of times the pattern 'fw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.16
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 3, r: 2, y: 4, o: 3}, what is the expected number of times the pattern 'o+h' appears? 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 {h: 4, a: 1, f: 7}. What is the expected number of occurrences of the pattern 'a.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.45
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {b: 5, s: 2, t: 5} to form a word, what is the expected number of matches of the pattern 't.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.14
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {x: 5, l: 3, a: 2, w: 2}. What is the expected number of occurrences of the pattern 'a*l' 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 {c: 4, o: 8}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.36
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {v: 3, k: 5, o: 4}. 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"
}
] |
1.36
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {z: 5, j: 7}. What is the expected number of occurrences of the pattern 'jz*' 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": "Form a word by randomly choosing 6 letters from the multiset {n: 4, k: 8}. What is the expected number of occurrences of the pattern 'nk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.41
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {n: 3, l: 3, u: 4, k: 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"
}
] |
0.68
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {r: 3, h: 4, n: 3, z: 2}. 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"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {x: 3, s: 1, k: 4, n: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'n*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.75
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {o: 3, w: 3, j: 3, s: 3}, 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"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {j: 3, z: 2, y: 1, h: 5, u: 1} to form a word, what is the expected number of matches of the pattern 'zj+'? 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 {l: 3, a: 5, p: 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"
}
] |
2.27
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {p: 7, v: 5}, what is the expected number of times the pattern 'vp*' 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 {p: 3, r: 2, h: 3, e: 4} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.36
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {q: 3, i: 2, k: 3, d: 4} 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"
}
] |
1.36
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {n: 3, i: 1, r: 2, w: 5, t: 1}, what is the expected number of times the pattern 'r.*r' appears? 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 {t: 4, z: 5, d: 3}. 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"
}
] |
0.68
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {e: 4, l: 8}, what is the expected number of times the pattern 'l+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.41
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {i: 4, m: 1, q: 5, v: 2} to form a word, what is the expected number of matches of the pattern 'iv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {v: 2, k: 3, f: 1, c: 4, x: 2}. What is the expected number of occurrences of the pattern 'f+c' in each word? Round your answer 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 6 by randomly selecting letters from the multiset {u: 6, f: 3, y: 3}, 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"
}
] |
0.68
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {u: 3, b: 3, l: 6}, what is the expected number of times the pattern 'u+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.25
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {w: 8, m: 4}. What is the expected number of occurrences of the pattern 'mw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.41
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 4, k: 5, v: 3}, 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"
}
] |
0.8
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 5, l: 7}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.27
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {o: 2, p: 8, j: 2}. What is the expected number of occurrences of the pattern 'p.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.82
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {i: 3, k: 1, m: 4, v: 2, t: 2}. 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"
}
] |
1.36
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {w: 2, g: 1, l: 4, z: 3, k: 2} to form a word, what is the expected number of matches of the pattern 'zl+'? 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 {g: 3, u: 4, b: 2, e: 3}. What is the expected number of occurrences of the pattern 'u+g' in each word? Round your answer 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 {e: 1, c: 4, p: 3, y: 4} to form a word, what is the expected number of matches of the pattern 'cp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.53
|
MATH
|
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