You have torn a tendon and are facing surgery to repair it T

You have torn a tendon and are facing surgery to repair it. The surgeon explains the risks to you: infection occurs in 3% of such operations, the repair fails in 14%, and both infection and failure occur together in 1%. What is the probability of infection given that the repair is successful? (Give your answer to four decimal places.)

Solution

P(infection/successful)=P(infection and sucessful)/P(successful)

Let I = the event that the operation results in infection, F = the event that the operation fails. We seek P(I^C and F^C ). We are given that P(I) = .03, P(F) = .14, and P(I and F) = .01. Then P(I^C and F^C ) = 1 P(I or F) = 1 (.03 + .14 .01) = .84.

P(infection/successful)=0.84/1-0.14=0.9767