Question

a patient has a 57% chance of surviving bypass surgery after a heart attack. if the patient survives the surgery, then the patient has a 72% chance of making a full recovery. find the probability that the patient survives surgery but does not make a full recovery.
the probability that the patient survives the surgery but does not make a full recovery is
(type an integer or a decimal. do not round.)

Explanation:

Step1: Find the probability of not making a full recovery given survival

The probability of making a full recovery given survival is \(72\%=0.72\). So the probability of not making a full recovery given survival is \(1 - 0.72=0.28\).

Step2: Use the multiplication rule for conditional probability

The multiplication rule for conditional probability is \(P(A\cap B)=P(A)\times P(B|A)\). Let \(A\) be the event that the patient survives surgery and \(B\) be the event that the patient does not make a full recovery. We know \(P(A) = 0.57\) and \(P(B|A)=0.28\). Then \(P(A\cap B)=0.57\times0.28\).

$$0.57\times0.28=(0.5 + 0.07)\times0.28=0.5\times0.28+0.07\times0.28=0.14+0.0196 = 0.1596$$

Answer:

\(0.1596\)