Problem 4: Imagine a drunk tightrope walker, in the middle of a really long tigh

Question

Problem 4: Imagine a drunk tightrope walker, in the middle of a really long tightrope, who manages to keep his balance, but takes a step forward with probability p and takes a step back with probability (1 p). a. What is the probability that after two steps the tightrope walker will be at the same place on the rope? 1 b. What is the probability that after three steps, the tightrope walker will be one step forward from where he began? c. Given that after three steps he has managed to move ahead one step, what is the probability that the first step he took was a step forward?

Explanation / Answer

a) T (foward, backward) or (backward, forward).
Those each have probabilities p*(1-p),

so the answer is 2p(1-p).

b) need 2 steps forward and 1 step backward, in any order.

There are 3 ways to arrange i.e FFB,

the answer is 3(1-p)p^2

c) percentage or fraction of the arrangements of FFB begin with an F

there are two ways so 2(1-p)p^2

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