Suppose that an employer plans to hire eight people from a group of fourteen equally qualified people, of whom four are minority candidates. If the employer does not know which candidates are minority candidates, and if she selects her employees at random, what is the probability that exactly one minority candidate is hired? Round your answer to four decimal places.

Question

Suppose that an employer plans to hire eight people from a group of fourteen equally qualified people, of whom four are minority candidates. If the employer does not know which candidates are minority candidates, and if she selects her employees at random, what is the probability that exactly one minority candidate is hired? Round your answer to four decimal places. ​

Quizplus · Accepted Answer

There are two parts to this problem. First, we need to determine the number of ways to select exactly one minority candidate out of four, and second, we need to determine the number of ways to select seven non-minority candidates out of ten.

The number of ways to select exactly one minority candidate out of four is C(4,1) = 4.

The number of ways to select seven non-minority candidates out of ten is C(10,7) = 120.

The total number of ways to select eight people out of fourteen is C(14,8) = 3003.

Therefore, the probability of selecting exactly one minority candidate is:

P = (number of ways to select one minority candidate) × (number of ways to select seven non-minority candidates) / (total number of ways to select eight people)

P = (4 × 120) / 3003 ≈ 0.1592

Rounded to four decimal places, the answer is 0.1592, which corresponds to choice C.

Suppose That an Employer Plans to Hire Eight People from a Group