Bolton Securities is about to implement a drug-testing procedure for company employees. In a recent anonymous survey, 20% of Bolton’s employees admitted to using illegal drugs. The random drug testing procedure is not infallible. In fact, about 5% of the time it will produce a false positive —that is, if the person being tested is NOT a drug user, there is a 5% probability that the test will nevertheless identify that person as a drug user. The test also has a probability of .08 of producing a false negative —about 8% of the time a drug user will be identifed as a non user.
a. If an employee is selected at random, how likely is it that the drug test will identify the employee as a drug user?
b. If the test identifes the employee as a drug user, how likely is it that the employee actually is a drug user?