There are 100 equally spaced points around a circle. at 99 of the points, there aresheep, and at 1 point, there is a wolf. at each time step, the wolf randomly moves eitherclockwise or counterclockwise by 1 point. if there is a sheep at that point, he eats it. the sheep don’t move. what is the probability that the sheep who is initially oppositethe wolf is the last one remaining?

we have

Step-by-step explanation:

considering circle with 100 points on it and then placing the wolf on one and sheep on rest.

pi = P( sheep on i-th spot  is eaten at last}

As in the question we need to find probability of sheep opposite to the wolf, so p_{51}. observe each last spot is replaced by i-1 after eating

Byy LOTP we know thta

also these pi need to satisfy

some sheep is eaten at last. Distribution is

satisfies above equation, therefore we have

step-by-step explanation:

bob the banana

thats not a system of equations, that is a solution