The standard test for tuberculosis attempts to identify carriers, that is, people who have been infected by the tuberculin bacteria. The probability of a false negative is 0.08, that is, the probability of the test giving a negative reading to a carrier is P (negative |carrier) = 0.08. The probability of a false positive is 0.04, that is, the probability of the test giving a positive indication when a person is a non-carrier is P (positive |noncarrier) = 0.04. The probability of a random person in the United States having tuber- culosis is 0.0075. Find the probability that a person is a carrier given that the test gives a positive indication.