A truth serum has the property that 90% of the guilty suspectsare properly judge

Question

A truth serum has the property that 90% of the guilty suspectsare properly judged while, of course, 10% of guilty suspects areimproperly found innocent. On the other hand, innocent suspects aremisjudged 1 % of the time. If the suspect was selected from a groupof suspects of whom only 5% have ever committed a crime, and theserum indicates that he is guilty, what is the probability that heis innocent?

A truth serum has the property that 90% of the guilty suspectsare properly judged while, of course, 10% of guilty suspects areimproperly found innocent. On the other hand, innocent suspects aremisjudged 1 % of the time. If the suspect was selected from a groupof suspects of whom only 5% have ever committed a crime, and theserum indicates that he is guilty, what is the probability that heis innocent?

Explanation / Answer

The proabaility is P(inncent| guility)=(0.05*0.9*0.1)/(0.9*0.1+0.1*0.99) = 0.0238

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