If an athlete is tested for a certain type of drug usage, then the test will come out either positive or negative. However, thes
e tests are never perfect. Some athletes who are drug free test positive, and some who are drug users test negative. The former are called false positives; the latter are called false negatives. Assume that 5% of all athletes use drugs, 4% of all tests on drug-free athletes yield false positives, and 10% of all tests on drug users yield false negatives. Define the events as follows: Free: an athlete is drug free. User: an athlete is a drug user. Positive: an athlete is tested positive Negative: an athlete is tested negative. Then, we have P(User) - 0.05, P(Positive Free) = 0.04, and P(Negative User) - 0.10, What is the probability that a randomly selected athlete tests positive, P(Positive)? a. 0.083 b. 0.127 c. 0.308 d. 0.312
