You have torn a tendon and are facing surgery to repair it. the surgeon explains the risks to you: the probability of infection in such operations is 0.03, the probability the repair fails is 0.16, and the probability of both infection and failure is 0.01. what is the probability that the operation succeeds and is free from infection

P(most favorable outcome) = 1 -(0.03 +0.16 -0.01) = 0.82


"repair fails" includes the "infection and failure" case, as does "infection". By adding the probability of "repair fails" and "infection", we count the "infection and failure" case twice. So, we have to subtract the probability of "infection and failure" from the sum of "repaire fails" and "infection" in order to count each bad outcome only once.

The probability of a good outcome is the complement of the probability of a bad outcome.