Galton Board Statistics

Balls fall through n rows of pegs. At each peg the ball goes left or right with probability p. After n rows, the probability of landing in column k is the binomial coefficient C(n,k)·pᵏ·(1-p)ⁿ⁻ᵏ. As n→∞ the histogram converges to a Gaussian — the Central Limit Theorem in action.