10 Many colleges face the problem of whether athletes should be tested for drug use. Define c1 = Cost if athlete is falsely accused of drug use c2 = Cost if a drug user is not identified c3 = Cost due to invasion of privacy if a nonuser is tested Suppose that 5% of all athletes are drug users, and that the test used is 90% reliable. This means that if an athlete uses drugs, there is a 90% chance that the test will detect it, and if the athlete does not use drugs, there is a 90% chance that the test will show no drug use.
a If c1 = 10, c2 = 5, and c3 = 1, should the college test athletes for drugs?
b Prove that if c1 > c2 > c3, then the college should not test for drugs.