contestada

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?

Respuesta :

Answer:

we have [tex]p_{51} = \frac{1}{100}[/tex]

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[tex]pi = \frac{1}{2}pi-1 + \frac{1}{2}pi + 1, i \epsilon {2,... 99}[/tex]

also these pi need to satisfy

[tex]\sum_{i=1}^{100} pi =1[/tex]

some sheep is eaten at last. Distribution is

[tex]pi = \frac{1}{100}[/tex]

satisfies above equation, therefore we have [tex]p_{51} = \frac{1}{100}[/tex]

Otras preguntas