You have torn a tendon and are facing surgery to repair it. The surgeon explains the...

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?

Solutions

Expert Solution

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%

milcah answered 1 year ago

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