25. The management of the AJAX Microchip Company

(mentioned in Problem 24) is interested in increasing quality control at the plant, and is considering the purchase of a testing device that can determine when a memory chip is faulty. In particular, the specifications on the device are as follows:

PðAjBÞ ¼PðAjBÞ¼:98;

where A is the event that the testing device indicates that a memory chip is faulty, and B is the event that the memory chip really is faulty.

a. What is the probability that the testing device indicates that a memory chip is not faulty, given that the memory chip really is faulty?

b. If the testing device is applied to the memory chips produced by AJAX’s assembly line I, what is P(B|A), i.e., the probability that a chip really is faulty, given that the testing device indicates the chip is faulty.

c. Suppose AJAX management wants P(B|A) to be .95.

What is the value of r ¼ PðAjBÞ ¼ PðAjBÞ that will ensure this testing accuracy if the test is applied to the chips produced on assembly line I.