Explore a Galton board, coin flips, dice and spinners in one place. Run a few trials or thousands, then compare observed results with theoretical probabilities.
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Galton Board
About this simulation
This simulation drops balls through a triangle of pegs. Each peg is a coin flip, so the bin a ball lands in equals its number of right bounces, a binomial distribution. Students set the rows from 4 to 14 and the bias towards the right from 0.2 to 0.8, press Drop 100 balls, empty the bins and show or hide the gold normal curve. Readouts give the balls in bins, the theoretical mean and the standard deviation. Teachers can use it to introduce probability, the binomial distribution and the central limit theorem.
What students can explore
- Press Drop 100 balls several times and watch the bars build up.
- Increase Rows n and see how the pile gets wider and smoother.
- Set Bias p to 0.7 and see how the pile moves to the right.
- Compare the pile with the gold Bell curve and the Mean and Std deviation readouts.
- Press Empty bins and repeat with a different number of rows.
Learning objectives
- 1Explain how many random choices produce a bell-shaped distribution.
- 2Calculate the mean n p and standard deviation of a binomial distribution.
- 3Describe how bias shifts the center of the distribution.
- 4Compare experimental results with a theoretical curve.
Questions teachers ask
Is the Galton board simulation free to use?
Yes. It is completely free and runs in any modern web browser, including on interactive whiteboards, tablets, Chromebooks and phones. There is nothing to install and no sign-up or account is needed.
Why do the balls make a bell curve?
Each ball's final bin is the sum of many independent left or right bounces. Sums of many random choices follow a binomial pattern that looks like the normal curve, as the central limit theorem predicts.
What are the mean and standard deviation?
For n rows and a chance p of bouncing right, the mean is n times p and the standard deviation is the square root of n times p times one minus p. The simulation shows both.
How do I use the Galton board simulation?
Choose rows and bias, press Drop 100 balls a few times, and compare the bars to the gold curve. Then change one setting and drop again.
Embed this simulation
Drop it into your LMS, blog, or class site — free.
<iframe src="https://kiwibee.io/en/simulations/galton-board-3d-simulation/embed" title="Galton Board | KiwiBee" loading="lazy" allowfullscreen style="width:100%;height:min(70vh,620px);min-height:420px;border:0;border-radius:16px"></iframe>Continue exploring
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