Question

In a certain Algebra 2 class of 29 students, 13 of them play basketball and 14 of them play baseball. There are 10 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?

Answer 1

Total students = 29. Let B = basketball (13), S = baseball (14), and N = neither (10). Then |B ∪ S| = 29 − 10 = 19. By inclusion–exclusion,

19 = |B| + |S| − |B ∩ S| = 13 + 14 − |B ∩ S| = 27 − |B ∩ S|,

so |B ∩ S| = 8. The probability a random student plays both is 8/29.