14 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(1₁) = 0.02, P(1₂) = 0.006, P(13) = 0.04. The probabilities of developing the set of symptoms H, given each of these illnesses, are known to be P(H|I₁) = 0.91, P(H|1₂) = 0.96, P(H|13) = 0.76. Assuming that a person who is ill exhibits the symptoms, H, what is the probability that the person has illness I₁? (Round your answer to four decimal places.)

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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(I ₁) = = 0.02, P(1₂) = 0.006, P(13) = 0.04.
The probabilities of developing the set of symptoms H, given each of these illnesses, are known to be
P(H|I₁) = 0.91, P(H|1₂) = 0.96, P(H|I3) = 0.76.
Assuming that a person who is ill exhibits the symptoms, H, what is the probability that the person has illness I? (Round your answer to four decimal places.)
Transcribed Image Text:14 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(I ₁) = = 0.02, P(1₂) = 0.006, P(13) = 0.04. The probabilities of developing the set of symptoms H, given each of these illnesses, are known to be P(H|I₁) = 0.91, P(H|1₂) = 0.96, P(H|I3) = 0.76. Assuming that a person who is ill exhibits the symptoms, H, what is the probability that the person has illness I? (Round your answer to four decimal places.)
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