Problem 1. (10 marks; 2, 2, 2, 2, 2 ) Medical case histories indicate that different illnesses may produce identical symptoms. Suppose that a particular set of symptoms, denoted H, occurs only when any one of three illnesses, I1, I2, or I3, occurs. Assume that the simultaneous occur- rence of more than one of these illnesses is impossible and that PH 1) = 0.01, P(I2) = 0.005, and 1203) = 0.02. The probabilities of deve10ping the set of symptoms H, given each of these illnesses, are known to be P(H|I1) = 0.90, P(H|I2) = 0.95, P(H|Ig) = 0.75. Answer each of the following questions. You have to show all your work to get full credit. a) Find P(Il n H) = P(H|I1)P(Il) = (0.90)(0.01) = 0.009