Suppose you are the detective in charge of determining the identity of the perso

Question

Suppose you are the detective in charge of determining the identity of the person who committed a murder. Suppose you know for certain that the guilty culprit is exactly one of three suspects, whom we will call suspects A, B, and C. Based on your prior experience with these individuals, but before processing forensic evidence from the crime scene, you believe the probabilities of guilt for the three suspects are P(A) = 0.8, P(B) = 0.1, and P(C) = 0.1. After processing the available forensic evidence, suppose we have likelihoods for the three suspects of L(A) = 0.05, L(B) = 0.65, and L(C) = 0.30.

a.) What is the posterior probability of guilt for suspect A? Answer to four significant figures.

b.)What is the posterior probability of guilt for suspect B? Answer to four significant figures.

c.) What is the posterior probability of guilt for suspect C? Answer to four significant figures.

Explanation / Answer

Solution:

Here probability of forensic evidence =( A and  forensic evidence + B and  forensic evidence + C and   forensic evidence) = 0.8*0.05 + 0.1*0.65 + 0.1*0.3 = 0.135

a) Hence posterior probability of guilt for suspect A = P(A and forensic evidence) / P( forensic evidence)

= 0.8*0.05/0.135 =0.2963

b) Posterior probability of guilt for suspect B =P(B and forensic evidence)/P( forensic evidence)

= 0.1*0.65/0.135 =0.4815

c)

Posterior probability of guilt for suspect C = P(C and forensic evidence)/P( forensic evidence)

= 0.1*0.30/0.135 =0.2222

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