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?
                   

2 years ago

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                                        Hello student,
Please find the answer to your question below
P(C)=P(C∣G)P(G)+P(C∣Gc)P(Gc)=(1)(0.6)+(0.2)(0.4)=0.68
This is then used to update the inspector's belief in the suspect's guilt posterior to discovering that the suspect does have that characteristic.
P(G∣C)=(P(G)P(C∣G))/P(C)
=1(0.6)/0.68
=0.882
So the probability that the inspector in-charge is convinced that the suspect is guilty given he/she has brown hair is 0.882
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