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% of applicants who turn out to be successful managers pass the test and 90% of applicants who turn out not to be successful managers fail the test.
If an applicant passes the aptitude test for managers, what is the probability that the applicant will succeed in a management position?
What is the probability an applicant does not pass the test and is a successful manager?