# Probability / Probability density

Quick question:

I just started reading Feynman's Lectures and in one section (6-4) he says that for a system in which a particle (in 1 dimension) can move in either direction (with equal prob. of either direction). For each 'step' that the particle takes, the distance it moves can be any length such that the average length is, say, 1, then the probability of the particle being any specific distance away from its starting position is zero.

Is this because there are theoretically an infinite number of lengths that the particle can step, and thus the probability for any specific distance approaches 1/infinity?

(note - I haven't taken any quantum physics classes yet, which I imagine is where this stuff may be taught)