# Math Help - binomial issue!

1. ## 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!

2. ## Re: binomial issue!

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

What you're looking for is the probability $P(B_X|A)=\frac{P(A|B_X)P(B_X)}{P(A|B_X)P(B_X) + P(A|B^*_X)P(B^*_X)}$

All the probabilities needed are directly given in the text.

3. ## Re: binomial issue!

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."