It is known that steroids give users an advantage in athleti

It is known that steroids give users an advantage in athletic contests, but it is also known that steroid use is banned in athletics. As a result, a steroid testing program has been instituted and athletes are randomly tested. The test procedures are believed to be equally effective on both users and nonusers and claim to be 97.5% accurate. If 84% of the athletes affected by this testing program are clean, what is the probability that the next athlete tested will be a user and fail the test? (Give your answer correct to two decimal places.)

Solution

P(fail|user)=0.975
P(pass|nonuser)=0.975
P(nonuser)=0.84
P(user)=0.16

Therefore,
P(user and fail)= P(fail | user)* P(user)
= 0.975 * 0.16
= 0.156 Answer