Question

Suppose that you have torn a tendon and are facing surgery to repair it. the orthopedic 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 1% of the time. what is the probability that the operation is successful for someone who has an operation that is free from infection?

Answer 1

A: outcome has no infection and repair that does not fail

B: outcome has no infection

P(A | B) = P(A and B) / P(B)

For P(A and B) that's the same as P(A).  We fail in .03+.14-.01 of the cases, so

P(A) = 1 - (.03+.14-.01) = 1-.16 = 0.84

P(B) =  1 - .03 = .97

P(A|B) = .84/.97 = .866

Answer: 86.6%