It is known that steroids give users an advantage in athletic contests, but it i

Question

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.)

Explanation / Answer

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

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