Don't Let It Go Away!

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A \(6\times 4\) grid contains \(24\) small squares each of side length \(5\). A coin of diameter \(4\) is thrown on the grid such that it does not cross the outer boundary. The probability that the coin stays inside a small square, that is, doesn't cross an inner boundary line can be represented as \(\dfrac{a}{b}\) where \(\gcd(a,b)=1\). Find \(a+b\).

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