Question

The chance that doctor A will diagnose a disease X correctly is 65%. The chances that a patient will die by his treatment after correct diagnosis is 45% and the chance of death by wrong diagnosis is 75%.

Hint: Let E1 denote the event that disease X is diagnosed, E2 denote the event disease X is NOT correctly diagnosed, E denote the event that a patient who had disease X dies. Then you can use the Law of Total Probability and Bayes’ theorem to answer the following two questions.

a)Using the above information, calculate the probability that a patient who had disease X will die.

b)Given that a patient of doctor A who had disease X died, what is the chance that his disease was diagnosed correctly?

Answer 1