a. Suppose a certain drug test is 99% accurate, that is, the test will correctly identify a drug user as testing positive 99% of the time, and will correctly identify a non-user as testing negative 99% of the time. This would seem to be a relatively accurate test, but Bayes' theorem will reveal a potential flaw. Let's assume a corporation decides to test its employees for opium use, and 0.5% of the employees use the drug. You want to know the probability that, given a positive drug test, an employee is actually a drug user.

b. Suppose that 8 % of all bicycle racers use steroids, that a bicyclist who uses steroids tests positive for steroids 96 % of the time, and that a bicyclist who does not use steroids tests positive for steroids 9 % of the time. What is the probability that a randomly selected bicyclist who tests positive for steroids actually uses steroids?