Question

Suppose John has a torn tendon and is facing surgery to repair it. The surgeon explains the risks to John; infection occurs in 3% of operations, the repair fails in 14% of operations, and both infection AND failure occur together in 0.57% of operations. What percentage, P, of these operations succeed and are free from infection?

Round to the nearest two decimal places.

Answer 1

The percentage, P, of these operations succeed and are free from infection is 83.57%.

Explanation:

Suppose John has a tendon surgery to repair it.

The risks to John:

Infection occurs after the operation in 3% of cases, the repair operation fails in 14% of cases, and both infection and failure of operation occur together in 0.57% of cases.

Therefore, chances of infection or chances of failure of operation or chances of both the cases will be (14 + 3 - 0.57) % = 16.43%.

Hence, the percentage, P, of these operations succeed without infection is (100 - 16.43) % = 83.57%. (Answer)