A truth serum given to a suspect is known to be 94 percent reliable when the per

Question

A truth serum given to a suspect is known to be 94 percent reliable when the person is guilty and 98 percent reliable when the person is innocent. In other words, 6 percent of the guilty are judged innocent by the serum and 2 percent of the innocent are judged guilty. If the suspect was selected from a group of suspects of which only 8 percent are guilty of having committed a crime, and the serum indicates that the suspect is guilty of having committed a crime, what is the probability that the suspect is innocent? (Round your answer to 3 decimal places.)

Probability          

Explanation / Answer

Let G shows the event that person is guilty and I shows the event that person is innocent. So

P(G) = 0.08, P(I)= 1-0.08=0.92

Let P shows the event that test gives innocent result and N shows the event that test gives guilty result. So

P(N|G) = 0.94, P(P | I) = 0.98

Here we need to find the probability P(I |N).

By the complement rule,

P(N |I) = 1 - P(P|I) = 0.02

By the Baye's theorem,

P(I |N) = [ P(N|I ) P(I) ] [ P(N | I)P(I) + P(N|G)P(G) ] = [ 0.02 * 0.92] / [ 0.02 *0.92 + 0.94 * 0.08 ] = 0.0184 / 0.0936 = 0.197

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