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# At a certain stage of a criminal investigation, the inspector in-charge is 60% convince of the guilt of a certain suspect. Suppose now a piece of evidence that shows the criminal has brown hair is uncovered. If the inspector in-charge is convinced that the suspect is not guilty then there is 20% chance that he/she has brown hair. What is the probability that the inspector in-charge is convinced that the suspect is guilty given he/she has brown hair?

SHAIK AASIF AHAMED
6 years ago
Hello student,
•G: event that the suspect is guilty
•C: event that he possesses the characteristic of the criminal
•P(G|C) is ?
•P(G|C) = P(GC)/P(C)
= P(C|G)P(G) / [P(C|G)P(G) + P(C|Gc)P(Gc)]
= 1(.6)/[1(.6) + (.15)(.4)] ≈ .91
Thanks and Regards
Shaik Aasif