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Each bounce is a coin toss. Why do a hundred balls always pile up into the same shape?
Probability lab · Last updated: 16 October 2026
Each bounce is a coin toss. So why do a hundred balls always pile up into the same shape? In this 3D lab, you drop balls through rows of pegs and watch a bell curve build up. It shows how chance, which is unpredictable for one ball, becomes predictable for many.
What you'll discover
- At each peg a ball has an even chance of going left or right, just like tossing a coin.
- Many different paths lead to the middle slots but only one leads to each far edge, so the middle fills up most.
- With more balls, the pile gets closer and closer to a smooth bell-shaped curve.
The science in plain words
The board in this lab is often called a Galton board or bean machine. As a ball falls, it hits a peg in each row and bounces left or right with an equal chance, like a coin toss. Where it lands depends only on how many times it went right in total.
To land at the far left, a ball must go left at every single peg, and there is only one path that does that. To land in the middle, it needs roughly equal numbers of lefts and rights, and there are a great many different ways to arrange those. With 10 rows of pegs there are 1,024 possible paths. Only one ends at each far edge, while 252 end in the centre slot. The number of paths to each slot follows Pascal's triangle, which links probability to counting.
For a single ball, nobody can say where it will land. But when hundreds of balls fall, the random bounces average out and the pile always forms the same shape: tall in the middle, sloping smoothly to the sides. This is the binomial distribution, and with many rows it looks like the normal distribution, or bell curve. Many real measurements that come from adding up lots of small chance effects, such as people's heights or errors in measurements, form similar bell-shaped patterns.
Where it fits
- India, NCERT: A maths topic beyond the NCERT science syllabus for classes 6 to 10.
- United States: Grades 6 to 8
Common questions
What is a Galton board?
A Galton board is a vertical board with rows of pegs. Balls dropped from the top bounce left or right off each peg at random and collect in slots at the bottom. The slots fill up into a bell-shaped pile, showing how random events add up to a predictable pattern.
What is a bell curve?
A bell curve, or normal distribution, is a graph shape that is highest in the middle and slopes down evenly on both sides, like a bell. It appears when many small random effects add together. Heights of people and measurement errors often follow a pattern close to a bell curve.
Why do most balls land in the middle?
There are many more paths to the middle than to the edges. To reach an edge, a ball must bounce the same way at every peg, which is unlikely. To reach the middle it just needs a mix of lefts and rights, and there are many ways to get that mix.
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Try it yourself
The Probability lab is one of the interactive 3D science labs inside Taz. Change one thing, predict what will happen, then run it and watch. Labs open after you sign in.