EXAMPLE 3.3.4

An office employs seven women and five men. Two employees will be randomly

selected for drug screening. What is the probability that both employees will be men?

SOLUTION

If two people are randomly selected from a set of 12 people, the number of different outcomes is C(12,2) = 66.

There are 66 outcomes possible in this experiment.

The number of two-person groups in which both people are men is the number of ways to choose two men from the set of five men, which is C(5,2) = 10.

Thus,

P(two men are selected) = 10/66 or roughly .152.