THIS PROBLEM IS MEANT FOR THE PNC EXPERTS. JUST GIVE IT A TRY ....

On an infinite chessboard (whose squares are labelled by (x,y) where x and y are integers). A king is placed at( 0,0). On each turn ,it has probability of 0.1 of moving to each of the 4 neighboring squares and a probability of 0.05 of moving to each of the 4 diagonally neighboring squares and a probability of 0.4 of not moving . After 2008 turns determine the probability of the king is placed on a square with both coordinates even. An approx. answer is required.

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