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

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

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

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