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 correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.