How could it be so probable?

Akul and Mayank attempt the same question. Their chances of solving the question are \( \frac 18\) and \(\frac 1{12} \). Given that they made a mistake, the odds against making the same mistake are \(1000:1\). If they obtain the same result, find the probability that they are correct.

IF the probability is in the form of \( \frac ab \) for coprime positive integer, find the value of \(a+b\).

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