id
stringlengths 39
39
| setting_key
stringclasses 1
value | setting_name
stringclasses 0
values | messages
listlengths 1
1
| ground_truth
stringclasses 126
values | dataset
stringclasses 1
value |
|---|---|---|---|---|---|
combinatory_pattern_matching_train_0000
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {s: 1, x: 1, t: 1, i: 1}. What is the expected number of occurrences of the pattern 's.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.08
|
math
|
combinatory_pattern_matching_train_0001
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {f: 1, m: 3, j: 2}. 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0002
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 1, z: 1, c: 1, n: 1}, what is the expected number of times the pattern 'z.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.08
|
math
|
combinatory_pattern_matching_train_0003
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, v: 1, c: 1, q: 1}. What is the expected number of occurrences of the pattern 'c.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.25
|
math
|
combinatory_pattern_matching_train_0004
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, j: 2}. What is the expected number of occurrences of the pattern 'r+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.83
|
math
|
combinatory_pattern_matching_train_0005
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, f: 2, b: 1, e: 1}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0006
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {m: 1, q: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'qf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.17
|
math
|
combinatory_pattern_matching_train_0007
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 3, g: 2}, what is the expected number of times the pattern 'cg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
math
|
combinatory_pattern_matching_train_0008
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {b: 3, h: 2}. What is the expected number of occurrences of the pattern 'h*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.5
|
math
|
combinatory_pattern_matching_train_0009
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {y: 1, l: 2, v: 2}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
math
|
combinatory_pattern_matching_train_0010
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, j: 1, d: 2, e: 1}. What is the expected number of occurrences of the pattern 'qd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.83
|
math
|
combinatory_pattern_matching_train_0011
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {r: 1, n: 1, a: 1, k: 1, c: 1}, 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0012
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, b: 1}, 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0013
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, u: 1, y: 1}, what is the expected number of times the pattern 'ut*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.17
|
math
|
combinatory_pattern_matching_train_0014
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, z: 3, l: 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}"
}
] |
0.6
|
math
|
combinatory_pattern_matching_train_0015
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, y: 2, k: 3}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.6
|
math
|
combinatory_pattern_matching_train_0016
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 1, o: 2, g: 1}, what is the expected number of times the pattern 'f*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.58
|
math
|
combinatory_pattern_matching_train_0017
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, x: 2, r: 1, a: 1}, what is the expected number of times the pattern 'rx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.65
|
math
|
combinatory_pattern_matching_train_0018
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {a: 3, f: 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}"
}
] |
0.3
|
math
|
combinatory_pattern_matching_train_0019
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {t: 1, d: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'd.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
math
|
combinatory_pattern_matching_train_0020
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {n: 1, s: 1, l: 1, g: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0021
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 4, i: 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}"
}
] |
1.2
|
math
|
combinatory_pattern_matching_train_0022
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {t: 2, x: 2} to form a word, what is the expected number of matches of the pattern 't.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.33
|
math
|
combinatory_pattern_matching_train_0023
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 3, o: 1, e: 1}, 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0024
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {j: 2, s: 2}, what is the expected number of times the pattern 'j+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.33
|
math
|
combinatory_pattern_matching_train_0025
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 1, d: 2, w: 1, b: 1}, 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0026
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {f: 2, b: 4} to form a word, what is the expected number of matches of the pattern 'fb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.73
|
math
|
combinatory_pattern_matching_train_0027
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, s: 1, o: 2, d: 2}. What is the expected number of occurrences of the pattern 'y.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
math
|
combinatory_pattern_matching_train_0028
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, b: 1, f: 1, a: 1, d: 1}, what is the expected number of times the pattern 'df+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
math
|
combinatory_pattern_matching_train_0029
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, s: 2, z: 1, h: 1}, what is the expected number of times the pattern 'uz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.13
|
math
|
combinatory_pattern_matching_train_0030
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 3, y: 3}, 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}"
}
] |
0.3
|
math
|
combinatory_pattern_matching_train_0031
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, m: 1, h: 2, a: 1}. What is the expected number of occurrences of the pattern 'v.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.15
|
math
|
combinatory_pattern_matching_train_0032
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 2, j: 4}, what is the expected number of times the pattern 'jh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.6
|
math
|
combinatory_pattern_matching_train_0033
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, k: 1, b: 1, x: 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}"
}
] |
0.57
|
math
|
combinatory_pattern_matching_train_0034
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, u: 2, e: 2}. What is the expected number of occurrences of the pattern 'e.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.6
|
math
|
combinatory_pattern_matching_train_0035
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 1, g: 2, i: 2, r: 1}, what is the expected number of times the pattern 'r+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.07
|
math
|
combinatory_pattern_matching_train_0036
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, l: 2, h: 1, f: 1, c: 1}. 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}"
}
] |
0.1
|
math
|
combinatory_pattern_matching_train_0037
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, d: 2, l: 1, r: 1, y: 1}, what is the expected number of times the pattern 'd.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
math
|
combinatory_pattern_matching_train_0038
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {o: 1, w: 3, g: 1}, 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}"
}
] |
1.35
|
math
|
combinatory_pattern_matching_train_0039
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, c: 1, p: 2, q: 1}, 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0040
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, l: 1, i: 1, x: 1}, what is the expected number of times the pattern 'i+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.17
|
math
|
combinatory_pattern_matching_train_0041
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {v: 1, l: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'vl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.67
|
math
|
combinatory_pattern_matching_train_0042
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {o: 1, i: 1, c: 1, g: 1, y: 1} 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0043
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {l: 4, q: 1} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.6
|
math
|
combinatory_pattern_matching_train_0044
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {t: 1, z: 1, c: 1, n: 1, x: 1}, what is the expected number of times the pattern 'cz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.05
|
math
|
combinatory_pattern_matching_train_0045
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {l: 4, x: 1}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.6
|
math
|
combinatory_pattern_matching_train_0046
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, p: 1, u: 1, a: 1, c: 1}. 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0047
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {c: 1, n: 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}"
}
] |
0.5
|
math
|
combinatory_pattern_matching_train_0048
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {w: 1, u: 2, p: 2}. What is the expected number of occurrences of the pattern 'pw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.9
|
math
|
combinatory_pattern_matching_train_0049
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, x: 3, r: 1, l: 1}, what is the expected number of times the pattern 'k+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.07
|
math
|
combinatory_pattern_matching_train_0050
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {v: 1, k: 3} to form a word, what is the expected number of matches of the pattern 'k*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.75
|
math
|
combinatory_pattern_matching_train_0051
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {r: 1, m: 1, j: 2}, what is the expected number of times the pattern 'r.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.08
|
math
|
combinatory_pattern_matching_train_0052
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {u: 2, s: 1, y: 2}, what is the expected number of times the pattern 's.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
math
|
combinatory_pattern_matching_train_0053
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {k: 1, w: 2, o: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'w*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.4
|
math
|
combinatory_pattern_matching_train_0054
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {r: 1, n: 2, w: 2, t: 1}. 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}"
}
] |
0.07
|
math
|
combinatory_pattern_matching_train_0055
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {g: 1, r: 1, q: 1, t: 1}, what is the expected number of times the pattern 'tg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.08
|
math
|
combinatory_pattern_matching_train_0056
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {m: 1, c: 2, z: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'm*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.4
|
math
|
combinatory_pattern_matching_train_0057
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {w: 1, b: 1, c: 1, u: 1} 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0058
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {o: 1, p: 1, r: 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0059
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {q: 2, y: 3}, what is the expected number of times the pattern 'yq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
math
|
combinatory_pattern_matching_train_0060
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {r: 1, b: 4}, 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0061
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {c: 1, r: 1, t: 2, q: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'c*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.57
|
math
|
combinatory_pattern_matching_train_0062
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {k: 3, u: 2} to form a word, what is the expected number of matches of the pattern 'k*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.1
|
math
|
combinatory_pattern_matching_train_0063
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 2, b: 3}, what is the expected number of times the pattern 'eb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.1
|
math
|
combinatory_pattern_matching_train_0064
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {u: 4, n: 2}. What is the expected number of occurrences of the pattern 'n+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.27
|
math
|
combinatory_pattern_matching_train_0065
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {i: 2, r: 2, t: 2} to form a word, what is the expected number of matches of the pattern 'rt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.8
|
math
|
combinatory_pattern_matching_train_0066
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {a: 2, g: 3, u: 1} 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0067
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {l: 1, b: 3} to form a word, what is the expected number of matches of the pattern 'l+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0068
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {p: 1, l: 3, u: 1, a: 1}, what is the expected number of times the pattern 'u*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.1
|
math
|
combinatory_pattern_matching_train_0069
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {e: 1, o: 1, q: 1, k: 1} 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0070
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {g: 1, x: 1, j: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'g+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
math
|
combinatory_pattern_matching_train_0071
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, z: 1, w: 2, j: 1, d: 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}"
}
] |
0.13
|
math
|
combinatory_pattern_matching_train_0072
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 1, z: 1, s: 2}, what is the expected number of times the pattern 'es+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.17
|
math
|
combinatory_pattern_matching_train_0073
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, k: 3, t: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.9
|
math
|
combinatory_pattern_matching_train_0074
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {q: 1, k: 1, p: 1, g: 1, w: 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0075
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {k: 2, d: 3} 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}"
}
] |
1.1
|
math
|
combinatory_pattern_matching_train_0076
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {c: 1, v: 1, h: 1, g: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'g*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.45
|
math
|
combinatory_pattern_matching_train_0077
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {g: 3, z: 3}. What is the expected number of occurrences of the pattern 'g*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.3
|
math
|
combinatory_pattern_matching_train_0078
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {b: 2, e: 3} 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}"
}
] |
2.5
|
math
|
combinatory_pattern_matching_train_0079
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, e: 1, d: 2, h: 1}. What is the expected number of occurrences of the pattern 'h*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.13
|
math
|
combinatory_pattern_matching_train_0080
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {l: 2, x: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'al+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.17
|
math
|
combinatory_pattern_matching_train_0081
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {z: 1, a: 2, n: 1}. What is the expected number of occurrences of the pattern 'zn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.58
|
math
|
combinatory_pattern_matching_train_0082
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {j: 2, c: 3} to form a word, what is the expected number of matches of the pattern 'c.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.9
|
math
|
combinatory_pattern_matching_train_0083
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, x: 1, t: 2}. What is the expected number of occurrences of the pattern 'x+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.13
|
math
|
combinatory_pattern_matching_train_0084
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {x: 2, t: 2, r: 2}, 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}"
}
] |
0.07
|
math
|
combinatory_pattern_matching_train_0085
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, w: 1, s: 2}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.5
|
math
|
combinatory_pattern_matching_train_0086
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {z: 4, h: 1}, what is the expected number of times the pattern 'z+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
math
|
combinatory_pattern_matching_train_0087
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 4, u: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.8
|
math
|
combinatory_pattern_matching_train_0088
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, u: 1}, what is the expected number of times the pattern 'zu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.75
|
math
|
combinatory_pattern_matching_train_0089
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {y: 1, d: 3} to form a word, what is the expected number of matches of the pattern 'yd+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.75
|
math
|
combinatory_pattern_matching_train_0090
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, b: 2, m: 1, z: 1}. What is the expected number of occurrences of the pattern 'm.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
math
|
combinatory_pattern_matching_train_0091
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, n: 2}, 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}"
}
] |
0.9
|
math
|
combinatory_pattern_matching_train_0092
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 1, s: 1, v: 1, o: 1, z: 1}, what is the expected number of times the pattern 's.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.05
|
math
|
combinatory_pattern_matching_train_0093
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {q: 1, j: 1, k: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'k.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.25
|
math
|
combinatory_pattern_matching_train_0094
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, w: 1, j: 1, f: 1, y: 1}, what is the expected number of times the pattern 'jy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.7
|
math
|
combinatory_pattern_matching_train_0095
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {j: 1, e: 1, c: 1, t: 1, b: 1}, what is the expected number of times the pattern 't.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.05
|
math
|
combinatory_pattern_matching_train_0096
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {q: 3, t: 1} 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0097
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {q: 1, n: 1, t: 1, l: 1, o: 2}, 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}"
}
] |
0.07
|
math
|
combinatory_pattern_matching_train_0098
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, y: 1, w: 1, a: 1}, what is the expected number of times the pattern 'a*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.92
|
math
|
combinatory_pattern_matching_train_0099
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {x: 1, t: 1, h: 2, o: 1}. What is the expected number of occurrences of the pattern 'h+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
math
|
End of preview. Expand
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