Probability Lab (Coins & Dice)
Flip coins and roll dice thousands of times and compare results with theory.
About the Probability Lab (Coins & Dice)
Free probability simulator. Flip coins, roll one die or two dice, run 1 to 1000 trials at once and compare the histogram with the theoretical probability. See the law of large numbers. Built for math, the probability lab (coins & dice) runs instantly in your browser: change a setting or drag an object and the result updates at once, so you learn by trying things out rather than only reading about them.
Flip coins and roll dice thousands of times and compare results with theory. Use it to explore math ideas at your own pace, then check what you found against the key ideas further down this page.
How to use the Probability Lab (Coins & Dice)
- Use the controls to change What to roll, Track this outcome. The simulation reacts instantly.
- Pick an option such as Coin, One die, Two dice (sum) to switch modes or load an example.
- Press "×1", "×10", "×100", "×1000" to start, reset or change what is happening.
- Where you see a glowing handle, object, weight or atom, drag it with your mouse or finger. Everything responds in real time.
- Watch the readouts and graphs update as you experiment, and compare what you see with the key ideas below.
Things to try
- Flip 1000 coins and watch the heads percentage settle.
- Roll two dice 1000 times.
- Track a different outcome.
- Compare experiment and theory.
Key ideas you can learn
- Experimental results wobble in small samples but settle toward the theoretical probability.
- With two dice, 7 is the most likely sum because it has the most combinations.
- Each flip or roll is independent: past results do not change the next one.
Where this is used in the real world
Probability underlies insurance, weather forecasts, medical trials, games and machine learning. Understanding randomness helps you avoid common mistakes.
Who is this simulation for?
Algebra, geometry, trigonometry and calculus students, teachers preparing demonstrations, and self-learners who want to see the maths move.
For teachers: project it on the board, let students predict what will happen, then run it together. For students: change one thing at a time and write down what changes.
Frequently asked questions
What is the law of large numbers?
As you repeat a random experiment more times, the observed frequency gets closer to the theoretical probability.
Why is 7 the most common sum of two dice?
Six of the 36 equally likely outcomes add to 7, more than any other sum.
Is the Probability Lab (Coins & Dice) free to use?
Yes. It is completely free, with no signup, no download and no ads inside the simulation. It runs in your web browser.
Does the Probability Lab (Coins & Dice) work on a phone or tablet?
Yes. It uses touch as well as the mouse, so you can drag objects with your finger. A larger screen makes the controls easier to see.