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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)`.

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The correct Answer is:
D
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