Random WalkConta...Now, let us find the probability that after three steps the person ends up at position-1.

To find the probability that after three steps the person ends up at position -1, we need to consider all possible paths that lead to this position.

Step 1: The person can either move to position 1 or -1 with equal probability of 1/2.

Step 2: If the person is at position 1, they can either move to position 2 or 0. If they are at position -1, they can either move to position 0 or -2.

Step 3: If the person is at position 0, they can either move to position 1 or -1. If they are at position -2, they can only move to position -1.

The paths that lead to position -1 after three steps are:

1. 1 -> 0 -> -1
2. -1 -> 0 -> -1
3. -1 -> -2 -> -1

The probability for each path is (1/2) * (1/2) * (1/2) = 1/8.

Since there are three such paths, the total probability that the person ends up at position -1 after three steps is 3 * (1/8) = 3/8.