is that exactly how the question was phrased?

there is a subtlety in the question that i am not able to decipher, but that's ok, everyone knows i'm not that good with probability.

Let be the event that the patient survives the surgery

Let be the event the patient recovers from the heart damage

If what you want is the probability that the patient survives the surgery AND recovers from the heart damage, then that is given by:

If what you want is the probability that a patient will recover from the heart damage, GIVEN they survived the surgery, then that is given by:

based on how you phrased the question, I'd say you want the first answer, but something in the back of my mind is saying you want the second answer. I don't know which voice to listen to!

EDIT: I have decided to go with rualin's voice, he seems to know his stuff judging from his past posts. So go with the first answer, and better yet, use his notation