A local FedEx/Kinkos has three black-and-white copy machines and two color copiers. Based on historical data, the chances that each black-and-white copier will be down for repairs is 0.10. The color copiers are more of a problem and are down 20% of the time each. If a customer wants both a color copy and a black-and-white copy, what is the probability that the necessary machines will be available? (Assume that the color copier can also be used to make a black- and-white copy if needed.)
A) 0.04
B) 0.96
C) 0.47
D) 0.42

Question

Quizplus · Accepted Answer

The probability that a black-and-white copier is available is 1 - (0.10)^3, since all three would have to be down for none to be available. This equals 1 - 0.001 = 0.999. For the color copiers, the probability that at least one is available is 1 - (0.20)^2, since both would have to be down for none to be available. This equals 1 - 0.04 = 0.96. Since the events are independent, the combined probability is 0.999 * 0.96 = 0.95904, which rounds to 0.96, indicating that there is a 96% chance the necessary machines will be available.

A Local FedEx/Kinkos Has Three Black-And-White Copy Machines and Two