When a test is conducted to determine whether or not someone is infected with a particular virus, an incorrect test result can occur in two ways: A infected person may test negative, or a noninfected person may test positive. The latter is called a false positive test. It has been pointed out that the social consequences of false positive tests for the AIDS virus are particularly serious. Such a false positive test will unnecessarily "stigmatize and fright any healthy people," because "most people consider a positive AIDS test to be sentence to ghastly suffering and death." Meyer and Pauker therefore assert that it is important that a patient who tests positive for the AIDS virus have a high probability of really being infected. In order to focus on the false positive rate of the test, assume throughout this question that we are dealing with a test that properly identifies all persons who really are infected with the AIDS virus. a) Assume that 5% of a population to be tested for the AlIDS virus really is infected and that the test has a false positive rate of 0.5%. Find probability that a person who tests positive really is infected. b) Assume now that a low-risk population is to be tested. Specifically, assume that 0.01% of the population to tested is actually infected with the AIDS virus and that the test has a false positive rate of 0.005% (which is unusually low). Find the probability that a person who tests positive really is infected. c) What would your answer to part (c) be if you assumed a false positive rate of 0.05%? (15 marks)