Suppose a baseball team has 14 players on the roster who are not members of the pitching staff. Of those 14 players, assume that three have recently taken a performance-enhancing drug. Suppose the league decides to randomly test five members of the team. What is the probability that at least one of the tested players is found to have taken a performance-enhancing drug?
A) 0.2308
B) 0.2473
C) 0.4945
D) 0.7692

Question

Quizplus · Accepted Answer

The probability of at least one player being found to have taken a performance-enhancing drug is easier to calculate by finding the complement, which is the probability that none of the tested players have taken the drug, and then subtracting that from 1. There are 11 players who haven't taken the drug, so the probability of selecting 5 of these from the total 14 without selecting any of the 3 who did take the drug is (11 choose 5) / (14 choose 5). This gives 1 - (462/600) = 1 - 0.77 = 0.2308 for the complement, so the probability of at least one being found is 1 - 0.2308 = 0.7692.

Suppose a Baseball Team Has 14 Players on the Roster