Question

In a certain Algebra 2 class of 23 students, 11 of them play basketball and 6 of them play baseball. There are 8 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 players, S = baseball players. By inclusion–exclusion,
|B ∪ S| = |B| + |S| − |B ∩ S|.

Here |B ∪ S| = 23 − 8 = 15, and |B| + |S| = 11 + 6 = 17, so
17 − |B ∩ S| = 15 ⇒ |B ∩ S| = 2.

Probability = 2/23 ≈ 0.087.