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 exactly two of the tested players are 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 that exactly two out of the five tested players have taken a performance-enhancing drug can be calculated using the binomial probability formula:
P(X = 2) = (C(3,2) * C(11,3)) / C(14,5)
where C(n,r) represents the number of combinations of n items taken r at a time.

Simplifying this expression gives:
P(X = 2) = (3 * 165) / 2002
P(X = 2) = 495 / 2002
P(X = 2) ≈ 0.2473

Therefore, the best choice is B, with a probability of 0.2473.

Suppose a Baseball Team Has 14 Players on the Roster