Question

In a certain Algebra 2 class of 23 students, 6 of them play basketball and 10 of them play baseball. There are 11 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?

Answer 1

Let B = basketball, S = baseball. By inclusion–exclusion,

Total = |B| + |S| − |B∩S| + |neither|.

So |B∩S| = |B| + |S| + |neither| − Total = 6 + 10 + 11 − 23 = 4.

Probability = 4/23 (≈ 0.1739).