In a populaton of 1,000 athletes, suppose 100 are illegally using testosterone. Of the users, suppose 50 would test positive for testosterone. Of the nonusers, suppose 9 would test positive.
A. Given the athlete is a user, find the probability that a drug test for testosterone will yield a positive result.
B. Given the athlete is a nonuser, find the probability that a drug test for testosterone will yield a negative result.
C. If an athlete tests positive for testosterone, use Bayes' Rule to find the probability that the athlete is really doping.