EXAMPLE 7 Probabilities for Driving to Work

In the discussion of Rule 4 (the addition rule for disjoint events, page 351), we determined that 86% of workers drive to work (either alone or in a carpool). Suppose a random sample of two U.S. workers is chosen. What is the probability that they both drive to work? To answer this question, let:

We want . Since the workers were chosen randomly, events and are independent. Therefore, we use the multiplication rule for independent events to determine this probability:

Hence, the likelihood that both workers drive to work is approximately 74%.