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A medical company claims it has a test that is 95% effective in determining whether an athlete is using a steroid or not. Suppose this test is given to a group of athletes in which 10% of the athletes are using steroids.What is the probability that a randomly chosen athlete actually uses steroids, given that the athlete's test is positive?

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Answer:

Probability = 10% = 1/10

Step-by-step explanation:

Prob (Medical company determines steroids use) Ā = P(D) = 95%

Prob (Group athletes use steroids) = P(S) Ā = 10%

Prob (athlete use steroids & medical determines steroid use) = P (D āˆ© S) = 95% x 10% = 9.5%

Conditional Prob Ā [ P (S) I P (D) ] = P (S Ā āˆ© D) / P (D)

= 9.5% / 95% = 10% , ie = 1/10

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