(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

When the test for steroids is given to soccer players, 98% of players taking steroids test positive and 0.5% of the players not taking steroids test positive. Suppose that 5% of soccer players take steroids, what is the probability that a player who tests positive takes steroids.

2. Relevant equations and attempt at solution

p: tests positive

s: uses steroids

pr(s) = .05

pr(P|S) = .98

inclusion exclusion pr(p) = Pr(P|S)*Pr(S) + Pr(P|not S) * Pr(not S) = .98*.5 + .005 *.95 = .05375

Bayes Theorem: [Pr(S | P) = Pr(P | S) * Pr(S)]/Pr(p)

plugging in...

Pr(S | P) = .91

My question: Is 91% a plausible answer to this problem? Its the first one I've ever done using Bayes rule.

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# Bayes Theorem probability of steroids

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