Question

Your dog Alfred is sitting in the corner A of a square ABCD. A bone is placed in the center O of the square. We assume that Alfred moves randomly, following the segments created by OABCD. We call pn the probability for Alfred to reach the bone in the center O for the first time after n moves.
(1) Compute p1 and then pn.
(2) We call En the event "Alfred reached the bone at least once after n moves" and Sn its associated probability. Find the link between Sn and pn.
(3) Compute Sn. Could you have predicted this result more easily? (4) Compute limn→∞ Sn and comment the result. Compute limn→∞ Sn and comment the result.​

Answer 1

Answer:

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