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.

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

Step-by-step 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)