Suppose that you have torn a tendon and are facing surgery to repair it. the orthopedic surgeon explains the risks to you. infection occurs in 3% of such operations, the repair fails in 14%, and both infection and failure occur together 1% of the time. what is the probability that the operation is successful for someone who has an operation that is free from infection?

A: outcome has no infection and repair that does not fail

B: outcome has no infection

P(A | B) = P(A and B) / P(B)

For P(A and B) that's the same as P(A).  We fail in .03+.14-.01 of the cases, so

P(A) = 1 - (.03+.14-.01) = 1-.16 = 0.84

P(B) =  1 - .03 = .97

P(A|B) = .84/.97 = .866

86.6%

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!