🎯 Galton Board — Binomial Distribution & CLT

Balls drop through a triangular peg board, deflecting left or right at each peg with probability p. The bin heights trace the binomial distribution B(n, p), which converges to a Gaussian as n→∞.

Balls dropped

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Observed mean

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Observed σ

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Theoretical σ = √(np·q)

Rows (n) 10

Prob left (p) 0.50

Ball speed 4

Balls / drop 3

Galton Board (Bean Machine) — Invented by Francis Galton (1889). Each ball encounters n rows of pegs; at each peg it deflects left with probability p (right with probability q = 1−p). The number of right deflections k follows B(n, p) with mean np and variance np·q. By the Central Limit Theorem, as n→∞ this converges to a normal distribution N(np, √(npq)) regardless of p.