Referring to the previous problem, find the same probabilities through the counting argument explained in this section. Start with 100,000 athletes and divide them into the various categories.
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?