# Solving a Brilliant Math Problem

Probability Level 5

The probability that Katarina will correctly solve a given Brilliant math problem is $\frac{1}{8}$. The probability that Layla will solve the same problem correctly is $\frac{1}{12}$. Given that they are both incorrect, the probability that they will give the same incorrect numerical result is $\frac{1}{1001}$.

Suppose Katarina and Layla solve a Brilliant math problem independently and get the same numerical result. The probability that they get the correct answer, given that they got the same numerical result, can be written as $\frac{a}{b}$, where $a$ and $b$ are coprime positive integers. Find $a + b$.

Details and assumptions

Clarification: When both of them solve the question correctly, they got the same numerical result.

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