17. The ZAP Electric Co. manufactures electric circuit breakers. The circuit breakers are produced on two different assembly lines in the company’s Spokane plant.

Assembly line I is highly automated and produces 85 percent of the plant’s output. Assembly line II uses older technology that is more labor intensive, producing 15 percent of the plant’s output. The probability that a circuit breaker manufactured on assembly line I is defective is

.04, while the corresponding probability for assembly line II is .01.

As part of its quality control program, ZAP uses a testing device for determining whether a circuit breaker is faulty.

Some important characteristics of the testing device are as follows:

PðAjBÞ ¼ PðAjBÞ ¼ :985;

where A is the event that the testing device indicates that a circuit breaker is faulty and B is the event that the circuit breaker really is faulty.

a. If a circuit breaker is randomly chosen from a bin containing a day’s production and the circuit breaker is actually defective, what is the probability that it was produced on assembly line II?

b. What is the probability that the testing device indicates that a circuit breaker is not faulty, given that the circuit breaker really is faulty?

c. If the testing device is applied to circuit breakers produced on assembly line I, what is the probability that a circuit breaker really is faulty, given that the testing device indicates that the circuit breaker is faulty? Would you say that this is a good testing device?