Discussion:
Q: 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 response 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?