Medical case histories indicate that different illnesses may produce identical symptoms. Suppose a particular set of symptoms, which we will denote as event, occurs only when illness A or illness B occurs. (For the sake of simplicity, we will assume that illnesses A and B are mutually exclusive.) Studies show the probabilities of getting the three illnesses as follows:
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(H|B) = 0.95
P(H|C) = 0.75
Assuming that an ill person shows the symptoms H, what is the probability that the person has illness A?