Ants

Discrete Mathematics Level pending

A square is drawn with points on (2,0) , (0,2) , (0,-2) , (-2,0). An ant is placed on the origin on this graph and moves 4 times randomly, each time moving only one space. for example, its first move could go to (0,1) , then (1,1) , then (1,2) , and lastly (0,2). The ant can move only forwards, backwards, up, or down - no going diagonally. What is the probability that the ant will end up on the sides of the square drawn? Express your answer as a decimal rounded to the nearest ten-thousandths.

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