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The Infection occurs in 3% of surgeries, repair fails in 14%, and both infection and failure occur combined in 1% of cases.

Let A signify the occurrence of infection during procedures, and B denote the failure of the repair.

$P\left(A\right)=3/100,P\left(B\right)=14/100,P(Aa<,B)=1/100$

Consider,

$$\begin{gathered} P\left(A^{\text{'}}a^<B^{\text{'}}\right)=P{\left(A{a}^{âˆ\S a}B\right)}^{\text{'}}=1-P\left(A{a}^{âˆ\S }{}^{a}B\right) \\ =1-\left[P\left(A\right)+P\left(B\right)-P\left(A{a}^{âˆ\S }(⊂B)\right]\right. \\ =1-(3/100+14/100-1/100) \\ =1-16/100 \\ =84/100 \\ =0.84 \end{gathered}$$

Option b. is correct

a. The probability that the operation is successful for someone who has an operation that is free from infection 0.8342 is not the correct answer.

c. The probability that the operation is successful for someone who has an operation that is free from infection 0.8600 is not the correct answer.

d. The probability that the operation is successful for someone who has an operation that is free from infection 0.8660 is not the correct answer.

e. The probability that the operation is successful for someone who has an operation that is free from infection 0.9900 is not the correct answer.