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A truth serum has the property that 90% of the guilty suspects are properly judged while,...

A truth serum has the property that 90% of the guilty suspects are properly judged while, of course, 10% of the guilty suspects are improperly found innocent. On the other hand, innocent suspects are misjudged 1% of the time. If the suspect was selected from a group of suspects of which only 5% have ever committed a crime, and the serum indicates that the suspect is guilty, what is the probability that the suspect is innocent?

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Answer #1

Given,

P(Guilty) = 0.05

So P(Innocent) = 1 - 0.05 = 0.95

P(Found guilty | Guilty) = 0.90

P(Found guilty | Innocent) = 0.01

Hence by Bayes' theorem:

P(Innocent | Found guilty)

= 0.1743

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