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_0900
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, z: 4}. What is the expected number of occurrences of the pattern 'kz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.74
|
math
|
combinatory_pattern_matching_train_0901
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, e: 1, a: 1, y: 3, p: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0902
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {o: 1, c: 2, h: 1, n: 1, s: 1} 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0903
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {o: 3, j: 3} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.6
|
math
|
combinatory_pattern_matching_train_0904
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 1, w: 1, y: 1, o: 2, c: 1}, what is the expected number of times the pattern 'u.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
math
|
combinatory_pattern_matching_train_0905
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {d: 3, h: 2, n: 2}. 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}"
}
] |
0.86
|
math
|
combinatory_pattern_matching_train_0906
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {v: 1, h: 2, f: 3} to form a word, what is the expected number of matches of the pattern 'f*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.17
|
math
|
combinatory_pattern_matching_train_0907
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {s: 2, g: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'v*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.6
|
math
|
combinatory_pattern_matching_train_0908
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {g: 1, r: 4, j: 3} to form a word, what is the expected number of matches of the pattern 'rj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.0
|
math
|
combinatory_pattern_matching_train_0909
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {d: 1, n: 1, c: 2, o: 2, b: 2} 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}"
}
] |
1.11
|
math
|
combinatory_pattern_matching_train_0910
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, z: 4, v: 1}, what is the expected number of times the pattern 'mz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.66
|
math
|
combinatory_pattern_matching_train_0911
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {f: 1, w: 1, k: 3, j: 1}. What is the expected number of occurrences of the pattern 'fk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.08
|
math
|
combinatory_pattern_matching_train_0912
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 4, x: 2}, what is the expected number of times the pattern 'x+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.93
|
math
|
combinatory_pattern_matching_train_0913
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {a: 2, d: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'k+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.47
|
math
|
combinatory_pattern_matching_train_0914
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 1, m: 1, t: 1, i: 2, g: 1}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0915
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, s: 1, o: 2, c: 1, e: 1}, what is the expected number of times the pattern 'e*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.48
|
math
|
combinatory_pattern_matching_train_0916
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 4, w: 1, e: 1, s: 2}, what is the expected number of times the pattern 'sh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.36
|
math
|
combinatory_pattern_matching_train_0917
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, v: 1, g: 4}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.86
|
math
|
combinatory_pattern_matching_train_0918
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {k: 4, w: 2}. What is the expected number of occurrences of the pattern 'wk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.67
|
math
|
combinatory_pattern_matching_train_0919
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {n: 1, l: 1, z: 2, i: 3} to form a word, what is the expected number of matches of the pattern 'l+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.07
|
math
|
combinatory_pattern_matching_train_0920
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {r: 3, t: 1, o: 3, q: 1} to form a word, what is the expected number of matches of the pattern 't.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.32
|
math
|
combinatory_pattern_matching_train_0921
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 2, t: 1, c: 1, n: 1, i: 2}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0922
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {x: 1, a: 1, u: 2, c: 2}. What is the expected number of occurrences of the pattern 'x.*a' 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_0923
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {a: 2, l: 1, x: 2, i: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'i.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.29
|
math
|
combinatory_pattern_matching_train_0924
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, p: 3}. What is the expected number of occurrences of the pattern 'xp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.25
|
math
|
combinatory_pattern_matching_train_0925
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {a: 4, j: 3} to form a word, what is the expected number of matches of the pattern 'aj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.4
|
math
|
combinatory_pattern_matching_train_0926
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, n: 1, b: 4}, what is the expected number of times the pattern 'nb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.55
|
math
|
combinatory_pattern_matching_train_0927
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {f: 1, d: 3, e: 3, n: 1} to form a word, what is the expected number of matches of the pattern 'ed*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.1
|
math
|
combinatory_pattern_matching_train_0928
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {a: 3, h: 2, e: 1, z: 1}. What is the expected number of occurrences of the pattern 'h*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.73
|
math
|
combinatory_pattern_matching_train_0929
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 2, z: 1, f: 2, s: 1, j: 2}, what is the expected number of times the pattern 'e*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.62
|
math
|
combinatory_pattern_matching_train_0930
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {r: 1, o: 1, f: 3, e: 2} to form a word, what is the expected number of matches of the pattern 'e*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.53
|
math
|
combinatory_pattern_matching_train_0931
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {c: 2, b: 2, y: 2}. What is the expected number of occurrences of the pattern 'cy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.47
|
math
|
combinatory_pattern_matching_train_0932
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, b: 1, z: 3, n: 1}. What is the expected number of occurrences of the pattern 'z*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.75
|
math
|
combinatory_pattern_matching_train_0933
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, l: 3, o: 1, z: 1}, what is the expected number of times the pattern 'z.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
math
|
combinatory_pattern_matching_train_0934
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {s: 1, i: 1, z: 2, a: 3, k: 1}. What is the expected number of occurrences of the pattern 'k.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.21
|
math
|
combinatory_pattern_matching_train_0935
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {i: 1, j: 2, h: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'i.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.4
|
math
|
combinatory_pattern_matching_train_0936
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {f: 1, r: 1, j: 1, c: 2, p: 1}. What is the expected number of occurrences of the pattern 'c+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.23
|
math
|
combinatory_pattern_matching_train_0937
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {q: 4, g: 3}. What is the expected number of occurrences of the pattern 'g*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3.4
|
math
|
combinatory_pattern_matching_train_0938
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {i: 3, b: 3, v: 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}"
}
] |
0.86
|
math
|
combinatory_pattern_matching_train_0939
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {c: 5, k: 1, g: 2} 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}"
}
] |
1.07
|
math
|
combinatory_pattern_matching_train_0940
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {i: 1, e: 1, a: 1, h: 3}. 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0941
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, l: 1, g: 3, a: 1, d: 2}, what is the expected number of times the pattern 'ha*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.41
|
math
|
combinatory_pattern_matching_train_0942
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, r: 3, f: 3}, what is the expected number of times the pattern 'sr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.17
|
math
|
combinatory_pattern_matching_train_0943
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {o: 2, e: 1, w: 4}. 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}"
}
] |
1.71
|
math
|
combinatory_pattern_matching_train_0944
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, p: 2, t: 3, u: 1}. 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}"
}
] |
0.32
|
math
|
combinatory_pattern_matching_train_0945
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, v: 2, q: 2, r: 3}. What is the expected number of occurrences of the pattern 'ri*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.23
|
math
|
combinatory_pattern_matching_train_0946
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, m: 1, w: 2, s: 2, n: 1}, what is the expected number of times the pattern 'ns+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.08
|
math
|
combinatory_pattern_matching_train_0947
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {p: 2, o: 2, h: 1, y: 2}. What is the expected number of occurrences of the pattern 'ho+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.16
|
math
|
combinatory_pattern_matching_train_0948
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 1, n: 1, s: 1, r: 1, l: 2}, what is the expected number of times the pattern 'l*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.9
|
math
|
combinatory_pattern_matching_train_0949
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {g: 4, c: 4} to form a word, what is the expected number of matches of the pattern 'cg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3.2
|
math
|
combinatory_pattern_matching_train_0950
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 1, y: 1, i: 2, f: 2}, what is the expected number of times the pattern 'fi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.8
|
math
|
combinatory_pattern_matching_train_0951
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 2, i: 2, v: 2, a: 2}, what is the expected number of times the pattern 'ia*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.24
|
math
|
combinatory_pattern_matching_train_0952
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {g: 2, t: 4} 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}"
}
] |
2.4
|
math
|
combinatory_pattern_matching_train_0953
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {a: 7, o: 1} to form a word, what is the expected number of matches of the pattern 'oa*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.25
|
math
|
combinatory_pattern_matching_train_0954
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {i: 1, r: 2, m: 1, o: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'ji*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.57
|
math
|
combinatory_pattern_matching_train_0955
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {b: 2, z: 5} 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}"
}
] |
1.24
|
math
|
combinatory_pattern_matching_train_0956
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, s: 3, r: 1, y: 1}, what is the expected number of times the pattern 'kr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.07
|
math
|
combinatory_pattern_matching_train_0957
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, z: 1, t: 3, l: 1}, what is the expected number of times the pattern 'tl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.11
|
math
|
combinatory_pattern_matching_train_0958
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {f: 4, 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}"
}
] |
2.4
|
math
|
combinatory_pattern_matching_train_0959
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {d: 2, t: 1, h: 2, e: 2, v: 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_0960
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 5, i: 1}, what is the expected number of times the pattern 'i*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.83
|
math
|
combinatory_pattern_matching_train_0961
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {w: 1, f: 3, r: 4} to form a word, what is the expected number of matches of the pattern 'f.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.29
|
math
|
combinatory_pattern_matching_train_0962
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {m: 4, w: 3}. 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}"
}
] |
2.4
|
math
|
combinatory_pattern_matching_train_0963
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, p: 1, i: 4}, what is the expected number of times the pattern 'i+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.18
|
math
|
combinatory_pattern_matching_train_0964
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {y: 2, w: 3, o: 2} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.29
|
math
|
combinatory_pattern_matching_train_0965
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, o: 1, x: 2}. 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}"
}
] |
0.75
|
math
|
combinatory_pattern_matching_train_0966
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {i: 2, v: 5} 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}"
}
] |
0.14
|
math
|
combinatory_pattern_matching_train_0967
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {y: 1, c: 4, s: 3} to form a word, what is the expected number of matches of the pattern 'cs*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.0
|
math
|
combinatory_pattern_matching_train_0968
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {v: 3, x: 5}. What is the expected number of occurrences of the pattern 'x*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.77
|
math
|
combinatory_pattern_matching_train_0969
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {s: 4, o: 3} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.43
|
math
|
combinatory_pattern_matching_train_0970
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {p: 1, w: 2, l: 1, u: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'xu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.07
|
math
|
combinatory_pattern_matching_train_0971
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, t: 2, l: 2}, 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}"
}
] |
0.2
|
math
|
combinatory_pattern_matching_train_0972
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {s: 2, q: 4, n: 1} to form a word, what is the expected number of matches of the pattern 'sq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.5
|
math
|
combinatory_pattern_matching_train_0973
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {o: 3, p: 1, i: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'o*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.85
|
math
|
combinatory_pattern_matching_train_0974
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {y: 2, a: 1, q: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'a+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.13
|
math
|
combinatory_pattern_matching_train_0975
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {f: 4, d: 2}. What is the expected number of occurrences of the pattern 'fd+' 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_0976
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, x: 2, i: 1, l: 1, o: 1}. What is the expected number of occurrences of the pattern 'zx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.21
|
math
|
combinatory_pattern_matching_train_0977
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {r: 4, e: 3}. 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}"
}
] |
1.71
|
math
|
combinatory_pattern_matching_train_0978
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, l: 1, z: 1, t: 2, s: 1}, what is the expected number of times the pattern 'f*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.5
|
math
|
combinatory_pattern_matching_train_0979
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 4, r: 4}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.29
|
math
|
combinatory_pattern_matching_train_0980
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 1, e: 1, v: 1, y: 2, m: 2}, what is the expected number of times the pattern 'qy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.16
|
math
|
combinatory_pattern_matching_train_0981
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 2, n: 2, i: 3, f: 1}, what is the expected number of times the pattern 'ni*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.4
|
math
|
combinatory_pattern_matching_train_0982
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {n: 1, x: 2, i: 1, v: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'x.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
math
|
combinatory_pattern_matching_train_0983
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {o: 3, m: 3} to form a word, what is the expected number of matches of the pattern 'om*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.25
|
math
|
combinatory_pattern_matching_train_0984
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {j: 4, f: 1, k: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.4
|
math
|
combinatory_pattern_matching_train_0985
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, n: 5, c: 2}. What is the expected number of occurrences of the pattern 'n+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.24
|
math
|
combinatory_pattern_matching_train_0986
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {k: 2, d: 4} to form a word, what is the expected number of matches of the pattern 'k*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.6
|
math
|
combinatory_pattern_matching_train_0987
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {l: 6, v: 2}. What is the expected number of occurrences of the pattern 'lv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.71
|
math
|
combinatory_pattern_matching_train_0988
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {z: 1, n: 2, e: 2, f: 2}. What is the expected number of occurrences of the pattern 'nf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.32
|
math
|
combinatory_pattern_matching_train_0989
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, w: 2, l: 1, h: 1, e: 1}, what is the expected number of times the pattern 'el*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.57
|
math
|
combinatory_pattern_matching_train_0990
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, f: 2, b: 2, k: 1, a: 1}. What is the expected number of occurrences of the pattern 'y+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.05
|
math
|
combinatory_pattern_matching_train_0991
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 3, n: 1, i: 1, l: 1}, what is the expected number of times the pattern 'lf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.42
|
math
|
combinatory_pattern_matching_train_0992
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {u: 4, g: 4} 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}"
}
] |
1.29
|
math
|
combinatory_pattern_matching_train_0993
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {r: 2, a: 1, k: 1, q: 1, b: 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_0994
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {j: 1, t: 1, y: 2, b: 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}"
}
] |
0.0
|
math
|
combinatory_pattern_matching_train_0995
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, n: 2, o: 1, v: 1}. What is the expected number of occurrences of the pattern 'vr+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.17
|
math
|
combinatory_pattern_matching_train_0996
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {p: 2, l: 3, d: 2} to form a word, what is the expected number of matches of the pattern 'p*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.47
|
math
|
combinatory_pattern_matching_train_0997
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 2, r: 1, k: 2, n: 1}, what is the expected number of times the pattern 'rk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.23
|
math
|
combinatory_pattern_matching_train_0998
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {i: 4, z: 2, s: 1, j: 1}. What is the expected number of occurrences of the pattern 'is+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.21
|
math
|
combinatory_pattern_matching_train_0999
|
combinatory_pattern_matching
| null |
[
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, q: 3}. What is the expected number of occurrences of the pattern 'dq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.25
|
math
|
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