Mathematics: 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?

There are 100 equally spaced points around a circle.

sshaynijaonnahayde

07.01.2022

we have $p_{51} = \frac{1}{100}$

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 $pi = \frac{1}{2}pi-1 + \frac{1}{2}pi + 1, i \epsilon {2,... 99}$

also these pi need to satisfy

$\sum_{i=1}^{100} pi =1$

some sheep is eaten at last. Distribution is

$pi = \frac{1}{100}$

satisfies above equation, therefore we have $p_{51} = \frac{1}{100}$

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ramenbates81

04.06.2020

There are five different ways, in which we can arrange the photos.

Step-by-step explanation:

There are five different ways to arrange the photos.

1. 5 photos in each 4 rows.

2. 4 photos in each 5 rows.

3. 2 photos in each 10 rows.

4. 10 photos in each 2 rows.

5. 20 photos in a single row.

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