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4 35 Conditional probabilities can be useful in diagnosing disease Suppose that three differ ent...

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4 35 Conditional probabilities can be useful in diagnosing disease Suppose that three differ ent closely related diseases A1 A2 and A3 occur in 25 15 and 12 of the population In addition suppose that any one of three mutually exclusive symptom states B B2 and B3 may be associated with each of these diseases Experience shows that the likelihood P BA of hav ing a given symptom state when the disease is present is as shown in the following table Find the probability of disease A2 given symptoms B B2 B3 and B4 respectively Symptom State Bj B B B3 B4 no symptoms Disease State A A 08 18 06 68 A2 17 12 07 64 A3 10 14 08 68

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