Random Walks

You can observe the drunken gait.

You can observe the drunken gait.

A drunk person wanders indiscriminately from side to side. A drunk person may come back to the same place many times while walking around trying to reach his destination.

Now suppose a drunk person is at the origin on the number line. Now when a drunk person starts from the origin and wanders 30 times , where is he on the number line ?

However , suppose that a drunk person sways in only two directions , left and right , and moves only one with one sway. Also , assume that a drunk person sways to the left or to the right in half.

Let's mathematically find the probability that the position on the number line when a drunk person staggers 30 times is 0 , the probability that it is 1 , and the probability that it is 2.