Chapter 8.4, Problem 53E

Employee screening. The management of a company finds that $30\%$ of the administrative assistants hired are unsatisfactory. The personnel director is instructed to devise a test that will improve the situation. One hundred employed administrative assistants are chosen at random and are given the newly constructed test. Out of these, $90\%$ of the satisfactory administrative assistants pass the test and $20\%$ of the unsatisfactory administrative assistants pass. Based on these results, if a person applies for a job, takes the test, and passes it, what is the probability that he or she is a satisfactory administrative assistant? If the applicant fails the test, what is the probability that he or she is a satisfactory administrative assistant?