Suppose that 1% of all Olympic athletes use steroids or other performance-enhancing drugs. Because drug
use is a serious violation of Olympic rules, the International Olympic Committee has implemented random
drug tests. Let us assume that the test will report positive with probability 0.9 if the athlete uses drugs,
and with probability 0.15 if the athlete does not use drugs.
a) A randomly selected athlete has a positive drug test. What is the probability that he uses drugs?