A random walker takes a step of unit length towards right or left at any discrete time step. Starting from x = 0 at time t = 0, it goes right to reach x = 1 at t = 1. Hereafter if it repeats the direction taken in the previous step with probability p, the probability that it is again at x = 1 at t = 3 is

1
1 - p
2
(1 - p)2
3
2p(1 - p)
4
4p2(1 - p)

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