2 Bayes Theorem 2 Question:: From 2011 to 2015, more than a thousand Russian ath

Question

2 Bayes Theorem 2 Question:: From 2011 to 2015, more than a thousand Russian athletes in various sports, including summer, winter, and Para lympic sports, benefited from a state-run doping program. A new drug test being considered by the International Olympic Committee can detect the presence of a banned substance when it has been taken by the subject 98% the time. However, the test also registers a "false positive" in 4'% of the population that has never taken the banned substance a. If 4% of the athletes in question are taking the banned substance (96% are not taking it what is the probability that a random person that has a positive drug test is actually taking the banned substance?

Explanation / Answer

We have

Given

P( Detect Substance/ Actually Take it) = 0.98

P( Detect Substance/Not Actually Take it) = 0.04

P( Taking Substance) = 0.04

P( Not taking Substance) = 0.96

We need to calculate

P( Taking Substance/Detect) = (0.98*0.04)/(0.98*0.04+0.96*0.04) = 0.5052 ( rounded to four places of decimal)

So, answer is 0.5052

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