sunyiyou/math_combinatory_pattern_matching_level_2

messages listlengths 1 1	ground_truth stringclasses 38 values	dataset stringclasses 1 value
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, n: 2, l: 3}. What is the expected number of occurrences of the pattern 'n*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	1.95	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, y: 1, l: 1, g: 1, m: 2}, what is the expected number of times the pattern 'lg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.07	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {n: 4, g: 1, y: 1}. What is the expected number of occurrences of the pattern 'g*y' 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 3 letters from the multiset {b: 2, i: 1, s: 1, m: 1, a: 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}", "role": "user" } ]	0.0	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {b: 2, i: 1, w: 1, q: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'iq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.07	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {y: 1, d: 3, r: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.6	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, b: 3, p: 1}, what is the expected number of times the pattern 'j.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.2	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {b: 2, m: 4} to form a word, what is the expected number of matches of the pattern 'm*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	1.73	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, a: 1, u: 1, g: 2}, 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}", "role": "user" } ]	0.13	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {g: 1, t: 1, u: 1, n: 1, a: 2} 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}", "role": "user" } ]	0.0	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, f: 1, e: 3, j: 1}, what is the expected number of times the pattern 'eh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.2	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, n: 1, b: 4}, what is the expected number of times the pattern 'n*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.5	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {n: 3, k: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'nb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.45	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {j: 1, a: 2, g: 3} to form a word, what is the expected number of matches of the pattern 'a+g'? 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 3 letters from the multiset {q: 2, p: 4}. What is the expected number of occurrences of the pattern 'q*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	2.6	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, s: 2, u: 3}, what is the expected number of times the pattern 'x.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.2	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {t: 2, n: 1, g: 1, b: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'jg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.07	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {r: 2, v: 2, m: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'v*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.65	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, s: 2, n: 2}, what is the expected number of times the pattern 'nv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.3	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, m: 1, f: 2, h: 1}, what is the expected number of times the pattern 'w*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.65	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {o: 2, l: 1, d: 3} to form a word, what is the expected number of matches of the pattern 'od*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	1.5	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, x: 1, w: 2, t: 1, k: 1}, what is the expected number of times the pattern 't+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.07	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {m: 2, i: 1, k: 1, d: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'dm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.15	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 3, c: 3}, 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}", "role": "user" } ]	2.25	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {l: 2, i: 1, f: 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}", "role": "user" } ]	0.2	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, x: 1, u: 3}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.0	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {b: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.6	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {f: 1, g: 1, v: 2, u: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'uf*'? Round 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 3 letters from the multiset {z: 1, p: 1, g: 1, r: 1, j: 2}. What is the expected number of occurrences of the pattern 'z.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.1	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, m: 2, o: 2, i: 1}. What is the expected number of occurrences of the pattern 'i*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	1.13	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {t: 1, q: 2, m: 3} to form a word, what is the expected number of matches of the pattern 't*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	1.13	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, i: 3, s: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.0	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, n: 1, r: 1, o: 1, g: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.0	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, y: 3}. What is the expected number of occurrences of the pattern 'ya+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.75	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, p: 2, x: 3}. What is the expected number of occurrences of the pattern 'p+x' 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": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, u: 3}, what is the expected number of times the pattern 'h.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.9	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {z: 2, v: 1, e: 1, o: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'eo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.57	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {e: 1, g: 1, k: 1, i: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'i+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.15	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, x: 2, t: 2, a: 1}, what is the expected number of times the pattern 'a+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.13	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, z: 1, k: 1, q: 1, h: 2}. What is the expected number of occurrences of the pattern 'cq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.07	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, z: 3, r: 1}. What is the expected number of occurrences of the pattern 'z.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.6	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {e: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.2	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, w: 5}. What is the expected number of occurrences of the pattern 'n*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	2.83	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, m: 3}. What is the expected number of occurrences of the pattern 'm.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.9	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, y: 1, b: 2, i: 1, m: 1}, what is the expected number of times the pattern 'mb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.65	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, o: 5}, what is the expected number of times the pattern 'o*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	1.0	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {e: 1, g: 1, h: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'yh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	1.3	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {p: 4, o: 2}. What is the expected number of occurrences of the pattern 'p+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.73	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, d: 3, o: 2}. What is the expected number of occurrences of the pattern 'l+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.2	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, o: 1, u: 2, n: 1, a: 1}. What is the expected number of occurrences of the pattern 'u.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.2	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {l: 1, k: 1, s: 2, o: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'q+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.07	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {n: 5, d: 1} to form a word, what is the expected number of matches of the pattern 'dn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	1.0	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, w: 1, h: 1, p: 1, v: 1}. What is the expected number of occurrences of the pattern 'kh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.13	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, v: 3}. What is the expected number of occurrences of the pattern 'vf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.75	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, f: 2, b: 1, g: 1}. What is the expected number of occurrences of the pattern 'g+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.13	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, m: 3}, what is the expected number of times the pattern 'm.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.9	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, r: 1, d: 1, l: 1, m: 1}. What is the expected number of occurrences of the pattern 'rt+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.15	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, m: 2, z: 2, w: 1}, what is the expected number of times the pattern 'w+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.07	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, b: 2, e: 1, r: 2}. What is the expected number of occurrences of the pattern 'p.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.2	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {i: 4, b: 2} 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}", "role": "user" } ]	1.2	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {l: 1, q: 1, k: 1, e: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'i+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.07	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, z: 3}. 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}", "role": "user" } ]	0.9	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, r: 2, e: 1}, what is the expected number of times the pattern 'e+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.13	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, x: 1, h: 2, b: 2}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.2	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {w: 3, s: 3} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.6	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {y: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'yy+'? 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 3 letters from the multiset {c: 1, h: 1, s: 1, v: 2, x: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.2	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {l: 2, h: 1, x: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'hl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.15	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {r: 1, f: 1, k: 2, z: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'm+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.07	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, j: 2, c: 1, u: 1, y: 1}. What is the expected number of occurrences of the pattern 'ug+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.07	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, p: 1, f: 1, d: 1, o: 1}, what is the expected number of times the pattern 'dp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.57	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {z: 2, b: 1, n: 1, t: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'q+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.07	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, d: 4, s: 1}. 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" } ]	0.0	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, e: 1, c: 1, x: 2}, what is the expected number of times the pattern 'ew*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.65	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {q: 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" } ]	0.6	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, c: 4}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.2	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 5, l: 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}", "role": "user" } ]	2.0	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {z: 4, u: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	1.2	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, u: 1, l: 2}. What is the expected number of occurrences of the pattern 'lw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	1.5	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, x: 1, g: 1, p: 1, l: 2}. What is the expected number of occurrences of the pattern 'g.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.2	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, k: 1, u: 2, q: 1}. What is the expected number of occurrences of the pattern 'jk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.13	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, z: 1, y: 1, o: 2}, 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" } ]	0.0	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {a: 1, v: 2, o: 1, r: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.0	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, k: 1, s: 1, o: 2}, what is the expected number of times the pattern 'yo+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.3	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, r: 2, u: 2}. What is the expected number of occurrences of the pattern 'r+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.3	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, w: 1, h: 3, i: 1}, what is the expected number of times the pattern 'hu*' appears? Round 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 3 letters from the multiset {v: 1, u: 1, q: 1, r: 2, a: 1}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.0	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, n: 2}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.2	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {u: 1, d: 2, k: 2, r: 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}", "role": "user" } ]	0.0	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {q: 1, y: 1, i: 2, t: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'ty+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.07	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, l: 2}. What is the expected number of occurrences of the pattern 'ul+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.6	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {t: 2, p: 2, n: 2} to form a word, what is the expected number of matches of the pattern 't*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	1.3	MATH
[ { "content": "When randomly selecting 3 letters from the multiset {k: 2, i: 1, u: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'u*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.57	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, z: 2, b: 1, g: 1, q: 1}, what is the expected number of times the pattern 'ff+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.0	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {p: 3, n: 2, d: 1}. What is the expected number of occurrences of the pattern 'np*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	1.5	MATH
[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, k: 1, i: 1, a: 2, g: 1}, what is the expected number of times the pattern 'd*g' appears? Round 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 3 letters from the multiset {d: 2, r: 1, i: 1, m: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.2	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, r: 1, n: 1, o: 1, d: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.0	MATH
[ { "content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, y: 1, l: 1, t: 1, k: 1}. What is the expected number of occurrences of the pattern 'k*l' 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 3 letters from the multiset {i: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'u.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	0.9	MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, n: 2, l: 3}. What is the expected number of occurrences of the pattern 'n*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

1.95

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, y: 1, l: 1, g: 1, m: 2}, what is the expected number of times the pattern 'lg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.07

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {n: 4, g: 1, y: 1}. What is the expected number of occurrences of the pattern 'g*y' 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 3 letters from the multiset {b: 2, i: 1, s: 1, m: 1, a: 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}", "role": "user" } ]

0.0

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {b: 2, i: 1, w: 1, q: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'iq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.07

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {y: 1, d: 3, r: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.6

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, b: 3, p: 1}, what is the expected number of times the pattern 'j.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.2

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {b: 2, m: 4} to form a word, what is the expected number of matches of the pattern 'm*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

1.73

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, a: 1, u: 1, g: 2}, 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}", "role": "user" } ]

0.13

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {g: 1, t: 1, u: 1, n: 1, a: 2} 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}", "role": "user" } ]

0.0

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, f: 1, e: 3, j: 1}, what is the expected number of times the pattern 'eh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.2

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, n: 1, b: 4}, what is the expected number of times the pattern 'n*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.5

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {n: 3, k: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'nb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.45

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {j: 1, a: 2, g: 3} to form a word, what is the expected number of matches of the pattern 'a+g'? 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 3 letters from the multiset {q: 2, p: 4}. What is the expected number of occurrences of the pattern 'q*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

2.6

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, s: 2, u: 3}, what is the expected number of times the pattern 'x.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.2

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {t: 2, n: 1, g: 1, b: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'jg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.07

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {r: 2, v: 2, m: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'v*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.65

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, s: 2, n: 2}, what is the expected number of times the pattern 'nv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.3

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, m: 1, f: 2, h: 1}, what is the expected number of times the pattern 'w*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.65

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {o: 2, l: 1, d: 3} to form a word, what is the expected number of matches of the pattern 'od*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

1.5

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, x: 1, w: 2, t: 1, k: 1}, what is the expected number of times the pattern 't+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.07

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {m: 2, i: 1, k: 1, d: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'dm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.15

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 3, c: 3}, 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}", "role": "user" } ]

2.25

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {l: 2, i: 1, f: 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}", "role": "user" } ]

0.2

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, x: 1, u: 3}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.0

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {b: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.6

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {f: 1, g: 1, v: 2, u: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'uf*'? Round 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 3 letters from the multiset {z: 1, p: 1, g: 1, r: 1, j: 2}. What is the expected number of occurrences of the pattern 'z.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.1

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, m: 2, o: 2, i: 1}. What is the expected number of occurrences of the pattern 'i*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

1.13

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {t: 1, q: 2, m: 3} to form a word, what is the expected number of matches of the pattern 't*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

1.13

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, i: 3, s: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.0

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, n: 1, r: 1, o: 1, g: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.0

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, y: 3}. What is the expected number of occurrences of the pattern 'ya+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.75

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, p: 2, x: 3}. What is the expected number of occurrences of the pattern 'p+x' 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": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, u: 3}, what is the expected number of times the pattern 'h.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.9

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {z: 2, v: 1, e: 1, o: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'eo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.57

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {e: 1, g: 1, k: 1, i: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'i+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.15

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, x: 2, t: 2, a: 1}, what is the expected number of times the pattern 'a+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.13

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, z: 1, k: 1, q: 1, h: 2}. What is the expected number of occurrences of the pattern 'cq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.07

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, z: 3, r: 1}. What is the expected number of occurrences of the pattern 'z.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.6

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {e: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.2

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, w: 5}. What is the expected number of occurrences of the pattern 'n*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

2.83

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, m: 3}. What is the expected number of occurrences of the pattern 'm.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.9

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, y: 1, b: 2, i: 1, m: 1}, what is the expected number of times the pattern 'mb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.65

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, o: 5}, what is the expected number of times the pattern 'o*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

1.0

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {e: 1, g: 1, h: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'yh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

1.3

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {p: 4, o: 2}. What is the expected number of occurrences of the pattern 'p+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.73

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, d: 3, o: 2}. What is the expected number of occurrences of the pattern 'l+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.2

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, o: 1, u: 2, n: 1, a: 1}. What is the expected number of occurrences of the pattern 'u.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.2

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {l: 1, k: 1, s: 2, o: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'q+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.07

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {n: 5, d: 1} to form a word, what is the expected number of matches of the pattern 'dn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

1.0

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, w: 1, h: 1, p: 1, v: 1}. What is the expected number of occurrences of the pattern 'kh+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.13

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, v: 3}. What is the expected number of occurrences of the pattern 'vf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.75

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, f: 2, b: 1, g: 1}. What is the expected number of occurrences of the pattern 'g+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.13

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, m: 3}, what is the expected number of times the pattern 'm.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.9

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, r: 1, d: 1, l: 1, m: 1}. What is the expected number of occurrences of the pattern 'rt+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.15

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, m: 2, z: 2, w: 1}, what is the expected number of times the pattern 'w+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.07

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, b: 2, e: 1, r: 2}. What is the expected number of occurrences of the pattern 'p.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.2

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {i: 4, b: 2} 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}", "role": "user" } ]

1.2

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {l: 1, q: 1, k: 1, e: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'i+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.07

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, z: 3}. 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}", "role": "user" } ]

0.9

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, r: 2, e: 1}, what is the expected number of times the pattern 'e+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.13

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, x: 1, h: 2, b: 2}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.2

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {w: 3, s: 3} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.6

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {y: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'yy+'? 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 3 letters from the multiset {c: 1, h: 1, s: 1, v: 2, x: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.2

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {l: 2, h: 1, x: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'hl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.15

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {r: 1, f: 1, k: 2, z: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'm+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.07

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, j: 2, c: 1, u: 1, y: 1}. What is the expected number of occurrences of the pattern 'ug+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.07

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, p: 1, f: 1, d: 1, o: 1}, what is the expected number of times the pattern 'dp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.57

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {z: 2, b: 1, n: 1, t: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'q+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.07

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, d: 4, s: 1}. 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" } ]

0.0

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, e: 1, c: 1, x: 2}, what is the expected number of times the pattern 'ew*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.65

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {q: 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" } ]

0.6

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, c: 4}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.2

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 5, l: 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}", "role": "user" } ]

2.0

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {z: 4, u: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

1.2

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, u: 1, l: 2}. What is the expected number of occurrences of the pattern 'lw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

1.5

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, x: 1, g: 1, p: 1, l: 2}. What is the expected number of occurrences of the pattern 'g.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.2

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, k: 1, u: 2, q: 1}. What is the expected number of occurrences of the pattern 'jk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.13

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, z: 1, y: 1, o: 2}, 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" } ]

0.0

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {a: 1, v: 2, o: 1, r: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.0

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, k: 1, s: 1, o: 2}, what is the expected number of times the pattern 'yo+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.3

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, r: 2, u: 2}. What is the expected number of occurrences of the pattern 'r+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.3

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, w: 1, h: 3, i: 1}, what is the expected number of times the pattern 'hu*' appears? Round 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 3 letters from the multiset {v: 1, u: 1, q: 1, r: 2, a: 1}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.0

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, n: 2}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.2

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {u: 1, d: 2, k: 2, r: 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}", "role": "user" } ]

0.0

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {q: 1, y: 1, i: 2, t: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'ty+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.07

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, l: 2}. What is the expected number of occurrences of the pattern 'ul+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.6

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {t: 2, p: 2, n: 2} to form a word, what is the expected number of matches of the pattern 't*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

1.3

MATH

[ { "content": "When randomly selecting 3 letters from the multiset {k: 2, i: 1, u: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'u*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.57

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, z: 2, b: 1, g: 1, q: 1}, what is the expected number of times the pattern 'ff+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.0

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {p: 3, n: 2, d: 1}. What is the expected number of occurrences of the pattern 'np*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

1.5

MATH

[ { "content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, k: 1, i: 1, a: 2, g: 1}, what is the expected number of times the pattern 'd*g' appears? Round 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 3 letters from the multiset {d: 2, r: 1, i: 1, m: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.2

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, r: 1, n: 1, o: 1, d: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.0

MATH

[ { "content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, y: 1, l: 1, t: 1, k: 1}. What is the expected number of occurrences of the pattern 'k*l' 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 3 letters from the multiset {i: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'u.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

0.9

MATH