Exhibit 5-17.Suppose a baseball team has 14 players on the roster who are not members of the pitching staff.Of those 14 players,assume that 3 have recently taken a performance-enhancing drug.Suppose the league decides to randomly test five members of the team. Refer to Exhibit 5-17.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 of exactly 2 players out of 5 testing positive for the drug can be calculated using the binomial probability formula: 
P(X=2) = (Number of ways to choose 2 players out of 3 who have taken the drug) * (Number of ways to choose 3 players out of 11 who have not taken the drug) / (Number of ways to choose 5 players out of 14)
P(X=2) = (3 choose 2) * (11 choose 3) / (14 choose 5) = (3 * 165) / 2002 ≈ 0.2473
Therefore, the answer is B.