The probabilities of solving a problem correctly by `A` and `B` are `(1)/(8)` and `(1)/(12)` respectively. Given that they obtain the same answer after solving a problem and the probability of a common mistake by them is `(1)/(1001)`, then probability that their solution is correct is (Assuming that if they commit different mistake, then their answers will differ)
A. `(77)/(96)`
B. `(14)/(15)`
C. `(2)/(5)`
D. `(13)/(14)`