# 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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