It is known that 5 of a schools athlete population uses dru

It is known that 5 % of a school\'s athlete population uses drugs. The Athletic Director gives a drug test which registers correctly as positive in 84 % of the cases where the drug is present and correctly as negative in 96 % of the cases where the drug is absent. One athlete is randomly selected and tested. Find the probability that the athlete is a drug user, given that the test result is positive. Give your answer as a decimal number, with 4 decimal places.

Solution

The probability that the athlete is a drug user, given that the test result is positive is:

0.05/0.84=0.059