In: Math
You have torn a tendon and are facing surgery to repair it. The
surgeon explains the risks to you: infection occurs in 4% of such
operations, the repair fails in 14%, and both infection and failure
occur together in 2%. What percent of these operations succeed and
are free from infection?
A : Event of infect occurs
B : Event of repair fails
Given,
infection occurs in 4% of such operations, the repair fails in 14%, and both infection and failure occur together in 2%
i.e
P(A) = 4/100 = 0.04
P(B) = 14/100 = 0.14
P(A and B) = 2/100 = 0.02
: Event of free from infection
: Event of operation succeed
Probability of operation succeed and free from infection = P( and )
P( and ) = P()
P() = 1 - P(A or B)
P(A or B) = P(A) + P(B) - P(A and B) = 0.04 + 0.14 - 0.02 = 0.16
P() = 1 - P(A or B) = 1 - 0.16 = 0.84
P( and ) = P() = 0.84
Probability of these operations succeed and are free from infection = P( and ) = 0.84
Percent of these operations succeed and are free from infection = 100 x 0.84 = 84%
Percent of these operations succeed and are free from infection = 84%