Consider an N x N grid. Denote one corner as point A, and the opposite corner as point B. George is walking from A to B, and Lennie is walking from B to A. All paths are equally likely, as long as they follow the grid and never move away from the destination. (Hence George's path can never move down or left, and Lennie's path can never move up or right.)

What is the probability that George and Lennie collide?

If George runs and thus moves three times faster than Lennie, what is the probability of collision?

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