A company has developed a drug test to detect steroid use by athletes. The test is accurate 95% of the time when an athlete has taken steroids. It is 97% accu- rate when an athlete hasn't taken steroids. Suppose that the drug test will be used in a population of athletes in which 10% have actually taken steroids. Let's choose an athlete at random and administer the drug test.

Question:

(a) Suppose that the chosen athlete tests positive. What's the probability that he or she actually used steroids? Show your work.