4.80 Medical Diagnostics Medical case histories indicate that different illnesses may produce identi- cal symptoms. Suppose a particular set of symptoms, which we will denote as event H, occurs only when any one of three illnesses A, B, or C-occurs. (For the sake of simplicity, we will assume that illnesses A, B, and C are mutually exclusive.) Studies show these probabilities of getting the three illnesses: P(A) = 0.01 P(B) = 0.005 P(C)=0.02 The probabilities of developing the symptoms H, given a specific illness, are P(H|A) = 0.90 P(HB) 0.95 = P(HC)=0.75 Assuming that an ill person shows the symptoms H, what is the probability that the person has illness A?