Problem 3
In the U.S., racial profiling describes the practice of law enforcement agencies to search, stop and sometimes arrest people of a particular ethnic group more than their relative number in the population. Suppose that a population in a certain city is composed of 30% belonging to ethnic group 1 and 70% to ethnic group 2. Members of the ethnic groups are visibly different. Court records reveal that crime rate in group 1 is 25% and in group 2 it is 10%. A police officer stops a person at random. Let G1 be the event that the person belongs to group 1, G2 the event that the person belongs to group 2 and C the event that the person is a criminal.
(a) What is the probability that the person is a criminal?
(b) What is the probability that the person is from group 1 if he is a criminal?
(c) What is the probability that the person is from group 2 if she is a criminal?
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