Toss a coin onto a grid of squares. The chance of it landing entirely inside one square (not crossing a line) depends on the size of the coin and the size of the squares — and the answer involves both length and area.
Flip a coin and watch heads/tails settle towards 50/50.
Goal: 20% heads, exactly. The more flips, the closer you get.
Set it up
- Rule a grid of equal squares, each side just a little bigger than your coin.
- Drop the coin from a low height — about 10 cm — over the grid.
- Score a hit only if the coin touches no grid line.
- Repeat 20+ times and compare your hit rate to the predicted ((s − 2r)/s)².
Square side s = 3 cm, coin radius r = 1 cm. What's the chance of a clean landing?
This is a cousin of Buffon's needle — drop a needle on lined paper and the chance it crosses a line involves π. Geometry and probability, holding hands.
How to do it
On a sheet of paper, rule a grid of squares. Each square should be just a bit bigger than your coin. Toss the coin from a small height ten times — count how often it lands fully inside one square (not crossing any line).
If the square has side s and the coin has radius r, the coin lands fully inside one square only if its centre is at least r from every edge. That's a smaller square of side s − 2r — so the probability is ((s − 2r)/s)².