The National Institute for Sports estimates that 11​% of all college athletes use steroids. A new test correctly diagnoses the presence of steroids in 94​% of athletes that have used steroids in the past 18 months. The test gives a positive result to 14​% of athletes who do not use steroids.   What is the probability an athlete uses steroids given that he has a negative​ result?

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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The National Institute for Sports estimates that
11​%
of all college athletes use steroids. A new test correctly diagnoses the presence of steroids in
94​%
of athletes that have used steroids in the past 18 months. The test gives a positive result to
14​%
of athletes who do not use steroids.
 
What is the probability an athlete uses steroids given that he has a negative​ result?
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