Question

A doctor gives a patient a 6060​% chance of surviving bypass surgery after a heart attack. if the patient survives the​ surgery, then the patient has a 5050​% chance that the heart damage will heal. find the probability that the patient survives the surgery and the heart damage heals.

Answer 1

Let BS be the event that the patient survives bypass surgery. Let H be the event that the heart damage will heal. Then P(BS) = 0.60, and also we have a conditional probability: GIVEN that the patient survives, the probability that the heart damage will heal is 0.5, that is P(H|BS) = 0.5 We want to know P(BS and H). Using the formula of the conditional probability: P(H and BS) = P(H|BS)·P(BS) = (0.6)(0.5) = 0.3