Refer to the situation in Exercise 88. Suppose an employee is chosen randomly and that the employee’s test identifes him/her as a drug user. Use Bayes’ theorem to revise the probability that the person chosen is actually a drug user.
In Exercise 88
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.