Question

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 the three illnesses- a; B; or C-occurs. (For 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(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?

          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 the three illnesses- a; B; or C-occurs. (For 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(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?

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 the three illnesses- a; B; or C-occurs. (For 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(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?

Added by Eric G.

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