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?

Question

Mathematics

Saige Vargas

6 April, 08:32

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?

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Carter Graham · 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%