Medical Case Histories Indicate That Different Illnesses May Produce Identical

Essay

Medical case histories indicate that different illnesses may produce identical symptoms. Suppose a particular set of symptoms, which we will denote as event H, occurs only when any one of these 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 the probabilities of getting the three illnesses are as follows: P(A) = 0.015, P(B) = 0.005, and P(C) = 0.025. The probabilities of developing the symptoms H, given a specific illness, are P(H/A) = 0.85, P(H/B) = 0.90, and P(H/C) = 0.70.
Assuming that an ill person shows the symptoms H, what is the probability that the person has illness A?