(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant 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

3. 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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Random Walk ( Drunk Instance)

**Physics Forums | Science Articles, Homework Help, Discussion**