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 occurrence of more that one of these illnesses is impossible and that:
P(I1) = .01, P(I2) = .005, P(I3) = .02.
The probabilities of developing the set of symptoms H , given each of these illnesses, are known to be
P (H|I1) = .90, P (H|I2) = .95, P (H|I3) = .75
Assuming that an ill person exhibits the symptoms, H, what is the probability that the person has illness I1?