Question

Suppose that 0.9% of male professional golfers use steroids, and that Max is a male professional golfer who has been randomly selected to take a drug test. The test he has been asked to take has a false positive rate of 1% and a false negative rate of 10%. Use Bayes’ rule to calculate the probability that Max actually uses steroids if he tests positive for steroid use. Give your answer as a decimal precise to three decimal places. ?= P=

Answer 1

Let A denote the event that Max test positive, denote the event that he uses steroid and denote the event that he does not use steroids.

Given that 0.9% of professional golfers use steroids. That is, . So, probability that the golfers do not use steroids is

Also given that the test has a false postive rate of 1% and false negative rate of 10%. That is, and

Given that Max test postive and we have to find the probability that he actually uses steroid. That is, required probability is

By Bayes' theorem,

That is,

9