Math Help Forum: binomial issue!

the chances that doctor A will diagnose X disease correctly is 60%. the chances that a patient will die by his treatment after correct diagnose is 40% and the chances of death by wrong diagnose is 70%. a patient of doctor A, who had disease X died. what is the chances that his disease was diagnose correctly?

pls help!

Let A be the probability that a patient will die, and the probability that that the doctor will diagnose the disease X correctly.

What you're looking for is the probability

All the probabilities needed are directly given in the text.

I always lay out problems like this with a tree (rather than using the equation from Bayes' Theorem, which always looks more complex than it really is).
First node is "correct diagnosis"/"incorrect diagnosis."
Second node (at the end of each branch from first node) is "die" / "don't die."
Two paths lead to die:
1. correct diagnosis + die, with probability 0.6 x 0.4
2. incorrect diagnosis + die, with probability 0.4 x 0.7
Probability of correct diagnosis is 0.24/0.52.