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, given that her test results are positive;

given that her test results are negative; given that her drug results are inconclusive?

b. What is the probability of observing a positive test result; a negative test result; an inconclusive test result?