Medical case histories indicate that different illnesses may produce identical symptom. 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 these probabilities of getting the three illnesses: The probabilities of developing the symptoms H, given a specific illness, are:
Assuming that an ill person shows the symptoms H, what is the probability that the person has illness A?
Round your answer to four decimal places.
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