The surgeon explains the risks to you: infection occurs in 3% of such operations, the repair fails in 16%, and both infection and failure occur together in 1%. what percent of these operations succeed and are free from infection?

P (fail U infection) = P (fail) + P (infection) - P (fail AND infection)

==>

0.03 + 0.16 - 0.01 = -.18

==>

P (success AND infection-free)

==>

1 - 0.18 = 0.82

==>

Therefore, 82 percent of these operations succeed and are free from infection.