A number of amateur and professional sports organizations use routine screening tests to determine if athletes are using performance-enhancing drugs. Jennifer Smith, president of an amateur athletic union, has asked you to determine the feasibility of screening athletes to determine if they are using performance-enhancing drugs. Amateur athletes are increasingly denied participation or deprived of victories if they are found to be users.

As part of the study, you propose the following scenario for analysis. Suppose that 10% of the athletes seeking participation in the athletic union have used performanceenhancing drugs. In addition, suppose that a test is available that correctly identifies an athlete’s drug usage 90% of the time. If an athlete is a drug user, the probability is 0.90 that the athlete is correctly identified by the test as a drug user. Similarly, if the athlete is not a drug user, the probability is 0.90 that the athlete is correctly identified as not using performance-enhancing drugs.

We should note that there are potential ethical and possible legal questions concerning the use of these tests. Here, we are concerned about the feasibility of using such a test if one has decided that such a test is proper, given the legal and value systems.