Suppose you are using an underwater probe to search for a sunken ship. At any time in the search, your probe is located at some point (x,y) in a grid, where the distance between lines in the grid is some convenient unit such as 100 meters. The sunken ship is at some unknown location on the grid, (X,Y). If your probe is at (x,y), you will move it to one of the eight nearby grid points (x-1,y-1), (x-1,y), (x-1,y+1), (x,y+1), (x,y +1), (x+1,y-1), (x+1,y), or (x+1,y+1), with probability 1/8 each, for the next search. If you start at (0,0) and the ship is at (5,2), use simulation to estimate the probability that you will find the ship in 100 moves or fewer.
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