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Assume there is a diagnostic blood test to detect use of a performance enhancing drug.  This test will be administered to all Olympic athletes prior to competition.  The test is not perfect, but the following information is known:
–          Among drug users, 98% had a positive test (true positive).
–          Among individuals not using the drug, 5% had a positive test (false positive).
–          Assume that 1% of athletes actually use the drug (prevalence of drug use).
(a)   What is the probability of a randomly chosen athlete getting a positive test result?
(b)   Given that an athlete tests positive, what is the probability that he/she really is using the drug?
(c)    BONUS (1pt):  Assuming the prevalence is correct (1%), what percentage of false positives would be allowable in order for the probability in (b) to be 0.9?