A company administers an “aptitude test for managers” to aid in selecting new management trainees. Prior experience suggests that 60 percent of all applicants for management trainee positions would be successful if they were hired. Furthermore, past experience with the aptitude test indicates that 85 percent of applicants who turn out to be successful managers pass the test and 90 percent of applicants who do not turn out to be successful managers fail the test.
a. If an applicant passes the “aptitude test for managers,” what is the probability that the applicant will succeed in a management position?
b. Based on your answer to part a, do you think that the “aptitude test for managers” is a valuable way to screen applicants for management trainee positions? Explain.