Question

Suppose John has a torn tendon and is facing surgery to repair it. The surgeon explains the risks to John: infection occurs in 2% of operations, the repair fails in 12% of operations, and both infection and failure occur together in 1.28% of operations. What percentage, ?, of these operations succeed and are free from infection? Please round your answer to the nearest two decimal places.

Answer 1

Solution:

From given information, we have

P(infection) = 0.02

P(repair fails) = 0.12

P(infection and repair fails) = 0.0128

P(infection or repair fails) = 0.02 + 0.12 - 0.0128 = 0.1272

[By using probability rule: P(A or B) = P(A) + P(B) – P(A and B)]

P(operations succeed and are free from infection) = 1 - P(infection or repair fails)

[By using probability rule: P(A’ and B’) = 1 – P(A or B)]

P(operations succeed and are free from infection) = 1 - 0.1272

P(operations succeed and are free from infection) = 0.8728

Required probability = 0.8728

Required percentage = 87.28%