Question

The chance that doctor a will diagnose disease x correctly is 60%. The chance that a patient will die by his treatment after correct diagnosis is 40% and the chance of death after wrong diagnosis is 70%. A patient of doctor a who had disease x died. The probability that his disease was diagnosed correctly is

Answer 1

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Let A be the probability that a patient will die, and Bx

The probability that that the doctor will diagnose the disease X correctly.

P(Bx|A)= P(A|Bx)P(Bx)/P(A|Bx)P(Bx)+P(A|B∗x)P(B∗x)

correct diagnosis + die with probability 0.6 x 0.4

incorrect diagnosis + die, with probability 0.4 x 0.7

Probability of correct diagnosis is 0.24/0.52

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