You have a standard chessboard consisting of \(8 \times 8\) squares, each \(2\) inches on a side. A coin of diameter \(1\) inch is tossed so that its center is uniformly distributed over the board area; any overhang beyond the board boundary or across a gridline counts as failure. What is the probability that the coin lands completely within a single \(2 \times 2\) inch square?
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