A warning light in the cockpit of a plane is supposed to ind

A warning light in the cockpit of a plane is supposed to indicate when a hydraulic pump is inoperative. If the pump is inoperative, then there is a probability of 0.992 that the warning light will come on. However, there is a probability of 0.003 that the warning light will come on even when the pump is operating correctly. Furthermore, there is a probability of 0.996 that the pump is operating correctly. Use 5 decimal places.

(a) What is the probability warning light comes on?

(b) If the warning light comes on, what is the probability that the pump really is inoperative?

Solution