The random walk model employed to explain gas diffusion can be treated as a binomial distribution similar to coin flips with 50/50 chance that a particle will move in either the +x or the -x direction.
a) If 10 steps are taken, how much more likely is it that the particle didn't move (Δx=0 after 10 steps) compared to the situation where the particle moved 10 steps in the +x direction?
b) If 10 steps are taken, how much more probable is it that particle didn't move compared to condition where the particle ended up four steps in the +x direction? Make sure that your steps add up to 10.