Self-referencial hint.

You are working hard on a probability question, but have no clue on how to solve it. Your friend who has already found the answer provides you with the following accurate hint:

The answer to that question is the probability that the answer is 1.

You are now left with \(N\) possible answers to that question, just from your friend's hint. Assuming you pick one of the \(N\) answers randomly, the probability that your answer is correct can be expressed as \( \frac{a}{b} \) where \(a\) and \(b\) are coprime positive integers. Find \(a + b\).

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