Binomial distribution emerging from random left/right deflections
Galton board (Francis Galton, 1873): balls fall through a triangular array of pegs, deflecting left (prob 1−p) or right (prob p) at each peg. After n rows, the bin counts follow Binomial(n,p). As n→∞ with p=½, by the Central Limit Theorem this converges to a Gaussian N(np, np(1−p)). The quincunx visually demonstrates the CLT from pure geometric randomness.