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 69% 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 surviving surgery

The probability of surviving bypass surgery is \(P(\text{survive}) = 0.57\).

Step2: Find the probability of not making a full recovery given survival

If the probability of making a full recovery given survival is \(0.69\), then the probability of not making a full recovery given survival is \(P(\text{not full recovery}|\text{survive})=1 - 0.69=0.31\).

Step3: Use the multiplication rule for conditional probability

By the formula \(P(A\cap B)=P(A)\times P(B|A)\), where \(A\) is "survive surgery" and \(B\) is "not make a full recovery". So \(P(\text{survive and not full recovery})=P(\text{survive})\times P(\text{not full recovery}|\text{survive})\).
Substitute the values: \(0.57\times0.31 = 0.1767\).

Answer:

\(0.1767\)