A truth serum given to a suspect is known to be 82 percent reliable when the...

A truth serum given to a suspect is known to be 82 percent reliable when the person is guilty and 94 percent reliable when the person is innocent. In other words, 18 percent of the guilty are judged innocent by the serum and 6 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:

(0.841 is incorrect, taken from a different post of this question)

Expert Solution

P(suspect is guilty) = 0.08

P(judged innocent | guilty) = 0.18

P(judged guilty | guilty) = 1 -0.18 = 0.82

P(judged guilty | innocent) = 0.06

P(judged guilty) = P(judged guilty | guilty) * P(guilty) + P(judged guilty | innocent) * P(innocent)

= 0.82 * 0.08 + 0.06 * (1 - 0.08)

= 0.1208

P(innocent | judged guilty) = P(judged guilty | innocent) * P(innocent) / P(judged guilty)

= 0.06 * (1 - 0.08) / 0.1208

= 0.457 (ans)

orchestra answered 2 years ago

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