Probabilistic Structure of the Galton Board

There are three probabilistic levels in the Galton board:
1. Peg level: Bernoulli random variables.
2. Ball level: Sum of Bernoulli variables ⇒ Binomial distribution.
3. Experiment level: Average over many balls ⇒ Normal distribution (CLT).
The bell-shaped histogram of a Galton board is explained primarily by the binomial distribution of a single ball, while a large number of balls ensures a
smooth empirical approximation to this distribution.