Plinko Probability: free math simulation
Drop balls through a Galton board and watch the binomial distribution emerge.
▶ Open the simulationFree, no sign-up. Works on phones, tablets and laptops.
The science
Each ball bounces left or right at random at every peg. The number of right bounces follows a binomial distribution, so most balls land near the middle and few reach the edges. With many balls the histogram approaches a bell curve.
P(k) = C(n, k) pᵏ (1 − p)ⁿ⁻ᵏ
Things to try
- Drop a few balls, then hundreds, and watch the bell shape appear.
- Compare the histogram mean with the centre of the board.
- Predict which bin will fill fastest before you start.
Topics covered
binomial distribution galton board statistics histogram mean
How to use it
Open the simulation, then change the experiment live with the sliders, checkboxes and buttons in the side panel. Drag objects on screen where it makes sense, and use Pause, Step, Speed and Reset in the bottom bar to study every moment.
Frequently asked questions
What does the Plinko Probability simulation show?
Each ball bounces left or right at random at every peg. The number of right bounces follows a binomial distribution, so most balls land near the middle and few reach the edges. With many balls the histogram approaches a bell curve.
What is the key equation?
P(k) = C(n, k) pᵏ (1 − p)ⁿ⁻ᵏ
Is the Plinko Probability simulation free?
Yes. It runs free in any web browser on phones, tablets and laptops, with no sign-up or download.
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