Probabilities in painted cube...

A wooden cube - after being painted all over - has been cut into \(1000\) smaller equal cubes. These were thoroughly mixed in a bag, from which one was produced and tossed. What is the probability that a painted side turned up? The answer can be written as \(\frac{m}{n}\) where \(m\) and \( n\) are coprime positive integers. Find \(m+n\).

not original problem

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