Problem 3 (9 points total, 3 points each part) In the US, racial proling 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 ofcer stops a person at random. Let G1 be the event that the person belongs to group 1, 02 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