I f an athlete is tested for a certain type of drug usage (steroids, say), then the test result is either positive or negative. However, these tests are never perfect. Some athletes who are drug-free...

I f an athlete is tested for a certain type of drug usage (steroids, say), then the test result is either positive or negative. However, these tests are never perfect. Some athletes who are drug-free test positive, and some who are drug users test negative. The former are called false positives; the latter are called false negatives. We assume that 5% of all athletes use drugs, 3% of all tests on drug-free athletes yield false positives, and 7% of all tests on drug users yield false negatives. Suppose a typical athlete is tested. If this athlete tests positive, are we sure that he is a drug user? If he tests negative, are we sure he does not use drugs?

Objective To use Bayes’ rule to revise the probability of being a drug user, given the positive or negative results of the test.