Meeting point

Dec 2019
52
1
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In the following figure, the distance between any two (horizontally and vertically) adjacent points is 1 km.

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Ruprecht starts with his sledge in point X and drives to point Y; the Grinch starts at the same time with his sledge in Y and drives to X. Both sledges drive alongside the grid pictured above with the same constant velocity. Both choose—completely independently of each other—a route of length 11 km. These choices happen completely randomly, i. e. all possible ways of length 11 km from X to Y (and Y to X, resp.) are chosen with the same probability.
What is the probability p (rounded to the third decimal place) that Ruprecht and the Grinch meet each other on their routes? Calculations are required!