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 Weird Walk (Posted on 2009-01-17)
Jorge has lost his car keys! He's not using a very efficient search; in fact, he's doing a random walk. He starts at 0, and moves 1 unit to the left or right, with equal probability. On the next step, he moves 2 units to the left or right, again with equal probability. For subsequent turns he follows the pattern 1, 2, 1, 2 etc.

His keys, in truth, were right under his nose at point 0. Assuming that he'll spot them the next time he sees them, what is the probability that Jorge will eventually return to 0?

Note: For purposes of the problem, assume that Jorge is not looking while he is merely passing through a point. For example, he will not look for his keys while he passes through 0.

 No Solution Yet Submitted by K Sengupta Rating: 4.5000 (2 votes)

 Subject Author Date re: solution and exploration Charlie 2009-01-18 13:24:31 re: huh? Charlie 2009-01-18 13:06:45 huh? Steve Herman 2009-01-18 00:22:45 solution and exploration Charlie 2009-01-17 16:39:01

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