Galton Board
Version 1.0.0 · Updated 2026-07-28
CORE DEFINITION
The Galton board, also known as a bean machine or quincunx, is a device invented by Francis Galton to demonstrate the central limit theorem. It consists of a vertical board with interleaved pegs. Small balls are dropped from the top and randomly fall left or right when hitting a peg, eventually landing in one of the compartments at the bottom. Assuming there are n rows of pegs, and the probability of a ball falling to the right after hitting a peg is p (p = 0.5 when left and right probabilities are equal), the probability of a ball landing in the k-th compartment follows a binomial distribution: C(n, k) * p^k * (1-p)^(n-k).
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The Galton board, also known as a bean machine or quincunx, is a device invented by Francis Galton to demonstrate the central limit theorem. It consists of a vertical board with interleaved pegs. Small balls are dropped from the top and randomly fall left or right when hitting a peg, eventually landing in one of the compartments at the bottom.
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The Galton board (bean machine) lets balls fall randomly left or right through layers of pegs, eventually accumulating into a bell-shaped (normal) distribution. It visually demonstrates how a large number of independent small random deviations converge to a stable macroscopic distribution (central limit theorem).
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- zh.wikipedia.orghttps://zh.wikipedia.org/wiki/%E9%AB%98%E5%B0%94%E9%A1%BF%E6%9D%BFverified
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