It is estimated that 2 of the athletes competing in a large

It is estimated that 2% of the athletes competing in a large tournament are users of an illegal drug to enhance performance. The test for this drug is 95% accurate. What is the probability that an athlete who tests positive is actually a user?

Solution

As following Baye\'s theorem

probability that an athlete who tests positive is actually a user = (0.95*0.02)/(0.95*0.02+0.05*0.98) = 0.28