Galton Board
The Galton board is a tool for visualizing the principles by which the binomial distribution is created. Early Galton boards were made with wooden poles and beads that rolled down. Francis Galton, who created the Galton board, is known as the nephew of Charles Darwin, famous for his theory of evolution.
Galton board. (2023, June 5). In Wikipedia. https://en.wikipedia.org/wiki/Galton_board
When a marble encounters each pole, it has two possibilities: it rolls to the left or right. In this way, the binomial distribution refers to the cumulative distribution of results when trials with two cases are repeated independently. The 'binomial distribution' has the same appearance as the 'normal distribution' if the probability of a trial is constant, each trial is independent, and the number of trials is sufficiently large.
However, in order to achieve a complete binomial distribution, the probability of a marble branching to the left or right is constant at 1/2, and each process must be independent of each other. However, these ideal conditions cannot be achieved with a Galton board. Therefore, it is not possible to create a complete 'binomial distribution' with a Galton board.