The plant manager for the local electric utility company wants to know the reliability of one of his small hydroelectric power generating systems.This system is comprised of two components: a generator which has a random failure rate of one in every two years of operation; and a transformer which has a random failure rate of one in every five years of operation.If he were to add both a backup generator and a backup transformer,with the same failure rates,what would be the probability that this system would perform reliably for a period of one year?
A)0.48
B)0.60
C)0.72
D)0.75
E)0.96

Question

Quizplus · Accepted Answer

To find the probability that the system will perform reliably for a year with a backup generator and a backup transformer, we need to find the probability that both the primary generator and transformer do not fail, or that both the primary and backup generators and transformers do not fail.

Probability of primary generator and transformer not failing in one year: (1 - 1/2) * (1 - 1/5) = 0.4 * 0.8 = 0.32

Probability of all four generators and transformers not failing in one year: (1 - 1/2)^2 * (1 - 1/5)^2 = 0.6 * 0.64 = 0.384

Therefore, the probability that the system will perform reliably for a year with backup generators and transformers is 0.32 + 0.384 = 0.704 or 0.72 to the nearest hundredth. Thus, the best choice is (C).

The Plant Manager for the Local Electric Utility Company Wants