Chapter 6.6, Problem 12E

Exercises 11–15 refer to diagnostic tests. A false negative in a diagnostic test is a test result that is negative even though the patient has the condition. A false positive, on the other hand, is a test result that is positive although the patient does not have the condition.

Drug Screening A drug-testing laboratory produces false negative results 2% of the time and false positive results 5% of the time. Suppose that the laboratory has been hired by a company in which 10% of the employees use drugs.

(a) If an employee tests positive for drug use, what is the probability that they actually use drugs?

(b) What is the probability that a nondrug user will test positive for drug use twice in a row?

(c) What is the probability that someone who tests positive twice in a row is not a drug user?