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.