2-46 A particular test for the presence of steroids is to be used after a profes

Question

2-46 A particular test for the presence of steroids is to be used after a professional track meet. If steroids are present, the test will accurately indicate this 95% of the time. However, if steroids are not present, the test will indicate this 90% of the time (so it is wrong 10% of the time and predicts the presence of steroids). Based on past data, it is believed that 2% of the athletes do use steroids. This test is adminis- tered to one athlete, and the test is positive for steroids. What is the probability that this person actually used steroids?

Explanation / Answer

Let

S = uses steroids
P = tests positive

Hence,

P(P) = P(S) P(P|S) + P(S') P(P|S') = 0.02*0.95 + (1-0.02)*(1-0.90) = 0.117

hence,

P(S|P) = P(S) P(P|S) / P(P) = 0.02*0.95/0.117 = 0.162393162 [ANSWER]

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