A doctor gives a patient a \( 90 \% \) chance of surviving bypass surgery atter a heart attack. If the patient survives the surgery, then the patient has a \( 30 \% \) chance that the heart damage will heat find the probatilit that the patient survives the surgery and the heart damage heals. The probability is \( \square \) Type an integer or a decimal.)

To find the probability that the patient survives the surgery and the heart damage heals, you multiply the probability of surviving the surgery by the probability that the heart damage heals, given survival. The probability of surviving the surgery is \(0.90\) (or \(90\%\)), and the probability that the heart damage heals after surviving the surgery is \(0.30\) (or \(30\%\)). So, you calculate: \[ P(\text{survive and heal}) = P(\text{survive}) \times P(\text{heal} | \text{survive}) = 0.90 \times 0.30 = 0.27 \] Therefore, the probability that the patient survives the surgery and the heart damage heals is \(0.27\) (or \(27\%\)).