Probabilistic Steps (Random Walk) Again!

Probability Level 5

A man is standing on an infinite ladder. In one move, he can either go up (with probability 0.40.4), down (with probability 0.50.5) or stay where he is (with probability 0.10.1).

Find the probability that after 1111 moves he is one step away from his initial position.

Inspired by this problem.

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