A laboratory test for steroid use in professional athletes has detection rates g

Question

A laboratory test for steroid use in professional athletes has detection rates given in the following table: (a) A randomly selected professional athlete tests positive for steroid use. If the rate of steroid use among professional athletes is 1 in 100, what is the probability that the athlete has actually been using steroids? (b) If the rate of steroid use among professional athletes is 55% (the percentage in major league baseball, at least according to media reports and former players), what is the probability that the athlete has actually been using steroids given that he had a positive test? (c) Do you think Major League Ball would be justified in suspending a player based on a single positive drug test? Explain your decision.

Explanation / Answer

Given

SU=steroid use

SNU = Steroid not use

TP=Test is positive

TN=Test is negative

A) P(TP | SU ) =0.90

B)

P( SU | TP ) = P(SU)*P(TP | SU) / ( P(SU)*P(TP | SU) + P(SNU)*P(TP | SNU)

=(0.55 * 0.90 ) / (0.55 * 0.90+0.45*0.01 )

= 0.990991

C) Yes off cource see above probability of steroid use and positive test is 0.90 that's we say that playars are suspending probability is 0.90 .

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