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Suppose that 20% of the cyclists racing in the Tour de France are using illegal performance...

Suppose that 20% of the cyclists racing in the Tour de France are using illegal performance enhancing drugs. They are tested one week prior to the start of the race. The blood test administered has a 5% false positive rate (that is, the probability of a positive result given the individual is not using an illegal performance enhancing drug is .05). The probability of a positive result given the individual is using an illegal performance enhancing drug is .90. Suppose that a randomly selected Tour de France participant tests positive for using an illegal performance enhancing drug. What is the probability that the individual is not guilty (that is, is not  taking an illegal performance enhancing drug)?

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TOPIC: Application of Bayes' theorem.

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