# Solved: The probability of surviving a certain transplant operation is 0.55. If a patient survives the operation, the probability that his

#### ByDr. Raju Chaudhari

Feb 26, 2021

The probability of surviving a certain transplant operation is 0.55. If a patient survives the operation, the probability that his or her body will reject the transplant within a month is 0.20. What is the probability of surviving both of these critical stages?

#### Solution

Let $S$ be the event that patient survives transplant. Let $R$ be the event that patients body reject the transplant.

The probability of surviving a certain transplant operation is 0.55, i.e., $P(S) = 0.55$.

If a patient survives the operation, the probability that his or her body will reject the transplant within a month is 0.20, i.e., $P(R|S) =0.20$.

Thus $P(R^\prime |S) = 0.80$.

The probability of surviving both of these critical stages is

 \begin{aligned} P(S\cap R^\prime) &= P(R^\prime |S) P(S)\\ &= 0.80\times 0.55\\ &= 0.44 \end{aligned}