1. Drug use among athletes remains a problem at Olympic competitions. Detection is not foolproof due to the inaccuracy of tests. Suppose a test is carried out for a particular drug on a population of 1,000 athletes of which there are 100 drug users. 50 of these drug users would test positive. Of the non-drug users, 9 would test positive.

a. (1) Calculate the probability that a known drug user will test positive.

b. (3) Calculate the probability that a known non-drug user will test negative.

c. (5) Find the probability that if an athlete tests positive, the athlete really is a drug user.

d. (5) Find the probability that if an athlete tests negative, the athlete really is a non-drug user.

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