Question 84441
It is known that steroids give users an advantage in athletic contests, but it is also known that steriod use is banned in athletes.  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 98% accurate.  
If 90% 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?
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P(fail|user)=0.98
P(pass|nonuser)=0.98
P(nonuser)=0.90
P(user)=0.10
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Your Problem:
P(user and fail)= P(fail | user)*P(user)
                = 0.98*0.90
                = 0.882
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Cheers,
Stan H.