Many employers require prospective employees to take a drug test. A positive result on this test suggests that the prospective employee uses illegal drugs. However, not all people who test positive use illegal drugs. The test result could be a false positive. A negative test result could be a false negative if the person really does use illegal drugs. Suppose that 4% of prospective employees use drugs, and that the drug test has a false positive rate of 5% and a false negative rate of 10%. An employer chooses a prospective employee at random. a) Draw a tree diagram to model this random process.

b) Find the probability that the drug test is positive. c) If the prospective employee's drug test result is positive, find the probability that she or he uses illegal drugs.