Hi there, I'm currently trying to figure out a probability question..

A patient with a failing heart has been told that the probability of having a heart transplant is 0.38, the probability of surviving more than 12 months given that a transplant is performed is 0.85, and the probability of surviving more than 12 months given that a transplant is not performed is 0.30

determine the probability that a transplant was performed given that the patient survived more than 12 months.

I figured it's a conditional probability thing, so the thought the equation would be:

Pr (A|B) = Pr(A intersect B)/Pr (B)

with, A being the patient has a transplant and B being the patient surviving >12 months

One of the prior questions is find the probability the patient survives more than 12 months, which I calculated as 0.509, which I think plays a part in it but I can’t seem to calculate a right answer….A friend gave me his and he got .635, but I can't figure out how as it doesn't fit into the equation above...Just wondering if anyone could help at all?

Thanks