EXAMPLE 4.41

Adequate sleep and exercise. Suppose that 40% of adults get enough sleep and 46% exercise regularly. What is the probability that an adult gets enough sleep or exercises regularly? To find this probability, we also need to know the percent who get enough sleep and exercise. Let’s assume that 24% do both.

We will use the notation of the general addition rule for unions of two events. Let A be the event that an adult gets enough sleep, and let B be the event that a person exercises regularly. We are given that P(A) = 0.40, P(B) = 0.46, and P(A and B) = 0.24. Therefore,

P(A or B) = P(A) + P(B) − P(A and B)

= 0.40 + 0.46 − 0.24

= 0.62

The probability that an adult gets enough sleep or exercises regularly is 0.62, or 62%.