A star is placed in the bottom right hand corner of a grid. You toss a coin and

• if it is heads you move the star one square up
• if it is tails you move the star one square to the left

If after tossing the coin the star would move off the grid you stop.

What is the probability that you end up in the top left-hand corner of the grid for 2 x 2, 3 x 3, 4 x 4 and n x n grids?