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## Homework Statement

Say a drunk starts making his steps of equal distance from a lamppost. Assuming that each of the steps are of equal distance, and N as the total number of steps, what is the probability of him/her ending at the lamppost? Find the probability when N is even and also for odd.

## Homework Equations

P

_{N}(a) = ( N! p

^{(N+m)/2}q

^{(N-m)/2}) / [{(N+m)/2}! {(N-m)/2}!]

whree,

a = integer

p = probability of drunk being in the right side of the lamppost

q = probability of drunk being in the left side of the lamppost

## The Attempt at a Solution

Derivation of the equation is quite straightforward. I am worried about my answer for this particular problem however. Since the drunk starts from the lamppost (x=0), when the N is even, he can land back to the lamppost. However, if N is odd, he can not land back at 0 (as he/she has to land back to an odd number). I do not know if my understanding is correct. Any clue ?

Berkeley