A man is accused of robbing a bank. Eyewitnesses testify that the robber was 6 feet tall and had…

A man is accused of robbing a bank. Eyewitnesses testify that the robber was 6 feet tall and had red hair and green eyes; the suspect matches this description. Suppose that only 100 of the 100000 people in the town are men who are 6 feet tall with red hair and green eyes, and assume that one of them robbed the bank.

(a) What is the probability that the suspect is innocent, given that he matches the description?

(b) What is the probability that the suspect would match the description, given that he is innocent?

(c) Suppose the police reviewed images of 1000 potential suspects when investigating the case, and every one of the 100000 residents was equally likely to appear in this review. What is the probability that at least one of the 1000 would match the description?

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