13. Medical Diagnostics Different illnesses can produce identical 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)=.01 P(B)=.005 P(C)=.02 The probabilities of developing the symptoms H, given a specific illness, are P(HA)=.90 P(HB)=.95 P(HC)=.75 Assuming that an ill person shows the symptoms H, what is the probability that the person has illness A?