Job Applicants: Job applicants in both the public and private sector are often finding that pre-employment drug testing is a requirement. The Society for Human Resource Management found that 71% of larger organizations (25,000+ employees) require drug testing of new job applicants. From the applicant's perspective, one primary concern with drug testing is a "false-positive" result. A "false-positive" is an indication of drug use when the individual has indeed not used drugs. Beyond cost considerations, there are issues of defamation and wrongful accusations. From the employer's perspective, one primary concern with drug testing is a "false-negative" result. A "false-negative" is where there is no indication of drug use when the individual has indeed used drugs.
One company uses a cheaper and less accurate test The following is information about the accuracy (or lack thereof) for this test.
• 3% of applicants actually do use drugs.
• Given an individual is using drugs the test returns a positive test result 98% of the time.
• Given an individual is not using drugs, the test returns a negative test result 95% of the time.
(a) What is the probability any applicant has a positive test result?
(b) What is the probability a randomly selected applicant uses drugs and goes through the screening process undetected?
(c) One applicant has a positive test result. Given this information what is the probability this applicant actually does not use drugs?