Question: In the drug testing, assume there are three possible test results: positive, negative, and inconclusive. For a drug user, the probabilities of these outcomes are 0.65, 0.06, and 0.29. For a nonuser, they are 0.03, 0.72, and 0.25. Use Bayes' rule to find a table of all posterior probabilities. (The prior probability of being a drug user is still 0.05.) Then answer the following.
a. What is the posterior probability that the athlete is a drug user,
(1) given that her test results are positive,
(2) given that her test results are negative, and
(3) given that her drug results are inconclusive?
b. What is the probability of observing a positive test result, a negative test result, or an inconclusive test result?