5.30 A. Goranson and J. Hall (Aeronautical Journal, November 1980, pp. 279–280) explain that the probability of detecting a crack in an airplane wing is the product of p1, the probability of inspecting a plane with a wing crack; p2, the probability of inspecting the detail in which the crack is located; and p3, the probability of detecting the damage.

a What assumptions justify the multiplication of these probabilities?

b Suppose p1  0.9, p2  0.8, and p3  0.5 for a certain fleet of planes. If three planes are inspected from this fleet, find the probability that a wing crack will be detected in at least one of them.