Probability of Drunks Meeting After N Steps

[Philowns]

Here's one of the question to my problem set:

Homework Statement

Two drunks start out together at the origin, each having equal probability of making a step to the left or right along the x-axis. Find the probability that they will meet after N-steps. It is to be understood that the men make their steps simultaneously. (It may be helpful to consider their relative motion.)

Homework Equations

I don't know much about the related equation because we have no reference for this particular subject.

The Attempt at a Solution

 

[HallsofIvy]

I'm not sure why you would need a specific book or equation. Just "reason" it out. If the two people, let's call them "A" and "B", where A is to the right of B, are distance x apart at time t, then there are four equally likely things that can happen:
A and B both move to the right- the distance between them does not change- it is still x.
A and B both move to the left- the distance between them does not change.
A moves to the right and B moves to the left- the distance between them increases, it is x+2.
A moves to the left and B moves to the right- the distance between them decreases, it is x- 2.

You should be able to find the probabililty distribution for x and so find the probability that it is, at some future time, 0.

 

[Philowns]

The reason I need a textbook for probability (physics) because there are a lot harder questions than this. But anyway thanks for the reply. I'll start working on it.