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 {v: 4, m: 2, r: 2, w: 4}. What is the expected number of occurrences of the pattern 'rv*' in each word? Round your answer 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 {f: 4, o: 5, r: 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"
}
] |
2.27
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {d: 3, z: 2, q: 2, s: 3, h: 2} to form a word, what is the expected number of matches of the pattern 'q*d'? 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 {r: 2, b: 7, a: 3}. What is the expected number of occurrences of the pattern 'a*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.43
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {h: 3, f: 4, t: 5} to form a word, what is the expected number of matches of the pattern 'th*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.17
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {c: 5, x: 7}, what is the expected number of times the pattern 'x*c' 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 {i: 3, s: 2, f: 4, a: 3} to form a word, what is the expected number of matches of the pattern 'sa+'? 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 {f: 3, y: 5, u: 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"
}
] |
2.27
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {g: 5, y: 4, a: 3} to form a word, what is the expected number of matches of the pattern 'g*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.07
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {m: 2, y: 2, s: 4, h: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'mh+'? 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 {l: 5, c: 2, o: 1, e: 3, u: 1} 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": "If you form a word of length 6 by randomly selecting letters from the multiset {b: 7, p: 3, r: 2}, what is the expected number of times the pattern 'p.*p' 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 {a: 6, j: 6}. What is the expected number of occurrences of the pattern 'ja*' 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 {i: 1, p: 3, l: 4, t: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'm*t'? 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: 6, h: 2, k: 3, l: 1}. What is the expected number of occurrences of the pattern 'kl+' 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": "When randomly selecting 6 letters from the multiset {l: 2, z: 2, k: 4, e: 1, v: 3} to form a word, what is the expected number of matches of the pattern 'el*'? 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 {i: 4, s: 6, g: 2}. What is the expected number of occurrences of the pattern 'g*i' 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": "Form a word by randomly choosing 6 letters from the multiset {r: 3, f: 4, n: 5}. 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"
}
] |
2.27
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {o: 3, e: 2, s: 3, m: 2, d: 2}. What is the expected number of occurrences of the pattern 'de+' in each word? Round your answer 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 6 by randomly selecting letters from the multiset {p: 3, h: 2, r: 3, j: 2, a: 2}, what is the expected number of times the pattern 'p.*p' 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 {a: 2, g: 1, m: 2, y: 4, z: 3}, what is the expected number of times the pattern 'a*m' appears? Round 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 {i: 5, e: 4, q: 3} to form a word, what is the expected number of matches of the pattern 'ei+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.07
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {m: 2, o: 3, p: 3, q: 4} 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"
}
] |
0.23
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {x: 6, v: 2, r: 3, w: 1}, what is the expected number of times the pattern 'xv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.49
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {c: 2, u: 4, q: 3, f: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'c+u'? Round 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 {v: 3, b: 3, r: 3, y: 3}, what is the expected number of times the pattern 'y.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.02
|
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 'r.*r'? 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 {z: 3, d: 4, p: 5}. What is the expected number of occurrences of the pattern 'd.*p' 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": "Form a word by randomly choosing 6 letters from the multiset {s: 7, b: 2, k: 3}. What is the expected number of occurrences of the pattern 'sb+' 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": "Form a word by randomly choosing 6 letters from the multiset {s: 4, l: 5, o: 3}. What is the expected number of occurrences of the pattern 'ls*' 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 {p: 1, z: 5, q: 3, 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"
}
] |
0.68
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {k: 5, n: 1, r: 4, v: 2}. What is the expected number of occurrences of the pattern 'k.*n' 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 {e: 2, j: 3, r: 2, b: 5} to form a word, what is the expected number of matches of the pattern 'r*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.91
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {f: 2, s: 3, o: 3, e: 4}, 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 {x: 3, j: 9} to form a word, what is the expected number of matches of the pattern 'x.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.07
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {u: 2, s: 2, z: 1, q: 3, c: 4}. 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"
}
] |
1.39
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {z: 5, c: 2, i: 5}, what is the expected number of times the pattern 'i+z' appears? 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 {r: 3, d: 5, e: 4}, what is the expected number of times the pattern 'e.*d' appears? Round 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 {f: 4, w: 2, s: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'ww+'? 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 {h: 4, j: 2, t: 1, y: 3, l: 2} to form a word, what is the expected number of matches of the pattern 'h.*l'? 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 {y: 6, d: 6}. 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"
}
] |
3.41
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {h: 2, q: 4, f: 3, o: 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"
}
] |
1.36
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {t: 5, e: 4, u: 3} to form a word, what is the expected number of matches of the pattern 'eu+'? 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 {f: 2, v: 4, o: 3, j: 3}. What is the expected number of occurrences of the pattern 'v.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.36
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {j: 3, y: 5, f: 2, s: 2} 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"
}
] |
2.27
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {n: 7, x: 5}. What is the expected number of occurrences of the pattern 'nx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.38
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {h: 8, q: 4} to form a word, what is the expected number of matches of the pattern 'q*h'? 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 {a: 5, o: 4, s: 3} to form a word, what is the expected number of matches of the pattern 'os+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.53
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {w: 4, o: 1, s: 4, u: 3} to form a word, what is the expected number of matches of the pattern 'o*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.15
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {y: 4, i: 6, n: 2} to form a word, what is the expected number of matches of the pattern 'in*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.49
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {l: 4, s: 1, i: 2, x: 3, y: 2}. What is the expected number of occurrences of the pattern 'i.*y' 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 {j: 6, y: 6} to form a word, what is the expected number of matches of the pattern 'y.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.09
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {l: 4, i: 8}. What is the expected number of occurrences of the pattern 'l.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.64
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {s: 2, i: 6, r: 4} 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"
}
] |
1.36
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {k: 5, g: 7} 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"
}
] |
2.27
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {j: 1, i: 3, k: 3, m: 5}, what is the expected number of times the pattern 'm+i' appears? 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 {r: 2, b: 2, d: 2, h: 4, u: 2} to form a word, what is the expected number of matches of the pattern 'h*u'? 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 {x: 4, j: 4, k: 4}. What is the expected number of occurrences of the pattern 'x.*j' 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 {k: 6, u: 4, q: 2}. What is the expected number of occurrences of the pattern 'q.*k' 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 {l: 5, f: 3, a: 1, i: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'fa+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.11
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {g: 5, j: 7} to form a word, what is the expected number of matches of the pattern 'j*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.83
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {g: 3, u: 3, v: 3, n: 3}. What is the expected number of occurrences of the pattern 'vu*' 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 {h: 3, n: 3, v: 2, j: 2, k: 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"
}
] |
0.23
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {s: 5, i: 7}. What is the expected number of occurrences of the pattern 'i*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.83
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {u: 3, e: 3, n: 6}, what is the expected number of times the pattern 'e.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.05
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {h: 3, q: 4, u: 2, z: 3}, what is the expected number of times the pattern 'u.*q' appears? 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 {x: 4, i: 5, a: 3}. What is the expected number of occurrences of the pattern 'x*i' 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 {i: 3, z: 2, e: 3, u: 3, o: 1} 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"
}
] |
0.13
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {t: 1, e: 3, f: 2, q: 4, x: 2}, what is the expected number of times the pattern 'e+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.27
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {v: 4, c: 3, j: 5} to form a word, what is the expected number of matches of the pattern 'vc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.53
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {w: 6, g: 2, y: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'g.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.45
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {o: 2, l: 2, x: 5, j: 3}. What is the expected number of occurrences of the pattern 'j*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.17
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {z: 3, c: 3, h: 5, y: 1}. What is the expected number of occurrences of the pattern 'c+z' 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 {e: 6, o: 6}, what is the expected number of times the pattern 'o+e' appears? 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: 2, o: 3, j: 3, m: 4} to form a word, what is the expected number of matches of the pattern 'to*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.27
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {q: 3, j: 4, o: 3, i: 2}. What is the expected number of occurrences of the pattern 'oj*' 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 {h: 1, m: 5, u: 3, z: 3} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.68
|
MATH
|
[
{
"content": "If you form a word of length 6 by randomly selecting letters from the multiset {m: 7, t: 4, c: 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"
}
] |
4.77
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {d: 6, h: 6} to form a word, what is the expected number of matches of the pattern 'dh*'? Round 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 {n: 4, u: 3, o: 3, s: 2} to form a word, what is the expected number of matches of the pattern 'u*s'? 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 {o: 5, i: 7}. What is the expected number of occurrences of the pattern 'io+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.88
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {k: 2, l: 1, e: 3, g: 3, w: 3}. What is the expected number of occurrences of the pattern 'kw+' in each word? Round your answer 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 {t: 3, v: 5, k: 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"
}
] |
0.68
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {y: 3, u: 2, d: 3, x: 1, v: 3} to form a word, what is the expected number of matches of the pattern 'du+'? 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 {a: 8, o: 4} to form a word, what is the expected number of matches of the pattern 'ao*'? 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 {v: 2, q: 3, b: 2, i: 3, l: 2}. 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"
}
] |
1.9
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {j: 1, s: 4, i: 7} 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"
}
] |
1.36
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {t: 4, k: 5, a: 3}. What is the expected number of occurrences of the pattern 'a.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.7
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {l: 4, h: 4, q: 2, d: 1, m: 1}. 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"
}
] |
0.23
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {q: 5, o: 2, p: 5} to form a word, what is the expected number of matches of the pattern 'q.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.14
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {h: 3, p: 3, n: 6} to form a word, what is the expected number of matches of the pattern 'n+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.07
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {f: 5, x: 7}. What is the expected number of occurrences of the pattern 'x*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.83
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {k: 4, t: 2, x: 3, b: 1, s: 2}. What is the expected number of occurrences of the pattern 'xs+' 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 {t: 8, s: 4}, what is the expected number of times the pattern 's+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.56
|
MATH
|
[
{
"content": "When randomly selecting 6 letters from the multiset {y: 6, b: 6} 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"
}
] |
4.61
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {i: 8, q: 4}. What is the expected number of occurrences of the pattern 'i+q' 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": "Form a word by randomly choosing 6 letters from the multiset {u: 6, t: 6}. What is the expected number of occurrences of the pattern 't*u' 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 {y: 4, a: 3, l: 1, v: 2, z: 2}, 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"
}
] |
0.23
|
MATH
|
[
{
"content": "Form a word by randomly choosing 6 letters from the multiset {c: 6, x: 6}. What is the expected number of occurrences of the pattern 'x.*x' 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": "When randomly selecting 6 letters from the multiset {p: 4, d: 5, l: 3} 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"
}
] |
1.36
|
MATH
|
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