Question 6 Suppose police have enough evidence to believe there is a 10 percent

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Question 6

Suppose police have enough evidence to believe there is a 10 percent chance that a person committed a crime. They do a DNA test and find matching DNA that would occur only one time in 100,000 by chance. What is the probability that the suspect is guilty? We can define events G = {suspect is guilty} and D = {DNA samples match}. Then P(D|G) = 1 and P(D|G^C) = 1/100000. In other words, the DNA test never yields negative when there is actually a match, and it yields a false positive 1/100000. Hope the problem is more clear now. MK

Explanation / Answer

given that there is 10% of chance that a person comitted crime =0.1

DNA would occur only once in 100000 =1/100000

the probbaility that the suspect is guilty is 0.1/100000

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