Question

An airline gathers data on late departures and early arrivals over a month. It finds that the probability of a late departure is 12 percent, the probability of an early arrival is 27 percent, and the probability of both a late departure and an early arrival is 4 percent. Which equation shows how to correctly calculate the probability of a late departure or an early arrival?

P(late departure or early arrival) = 0.12 + 0.04
P(late departure or early arrival) = 0.12 + 0.27
P(late departure or early arrival) = 0.12 + 0.27 – 0.04
P(late departure or early arrival) = 0.27 + 0.04 – 0.12

Answer 1

Use the inclusion–exclusion rule: P(A or B) = P(A) + P(B) − P(A and B). So

P(late or early) = 0.12 + 0.27 − 0.04 = 0.35 (35%).

Thus the correct choice is: P = 0.12 + 0.27 − 0.04.