Problem 2 (Bayes' Theorem) Suppose that 4% of the patients tested in a clinic are in- fected with avian influenza. Furthermore, suppose that when a blood test for avian influenza is given, 97% of the patients infected with avian influenza test positive and that 2% of the patients not infected with avian influenza test positive. What is the probability that a) a patient testing positive for avian influenza with this test is infected with it? b) a patient testing positive for avian influenza with this test is not infected with it? c) a patient testing negative for avian influenza with this test is infected with it? d) a patient testing negative for avian influenza with this test is not infected with it?