messages listlengths 1 1 | dataset sequencelengths 1 1 | ground_truth sequencelengths 1 1 | quality int64 10 10 |
|---|---|---|---|
[
{
"content": "Two balls, a red one and a green one, are randomly and independently tossed into bins numbered with positive integers. For each ball, the probability that it is tossed into bin $k$ is given by $p_k = \\frac{1}{k(k+1)}$ for $k = 1, 2, 3, ...$. Calculate the probability that the red ball is tossed i... | [
"math"
] | [
"\\frac{1}{4}"
] | 10 |
[
{
"content": "A sequence of two distinct numbers is extended in two ways: one to form a geometric progression and the other to form an arithmetic progression. The third term of the geometric progression coincides with the tenth term of the arithmetic progression. With which term of the arithmetic progression do... | [
"math"
] | [
"74"
] | 10 |
[
{
"content": "Given that socks cost $4 per pair and a T-shirt costs $5 more than a pair of socks, and each member needs one pair of socks and a shirt for home games and another pair of socks and a shirt for away games, with a total cost of $2366, determine the number of members in the League. Let's think step b... | [
"math"
] | [
"91"
] | 10 |
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