Coin Flip Simulator
probabilitysimulationlaw of large numbers
The law of large numbers tells us that as we repeat an experiment more and more times, the observed frequency of an outcome will converge to its true probability. A fair coin has a 50% chance of landing heads — but you might not see exactly 50% on any given set of flips.
This simulator lets you run batches of coin flips and watch the running proportion of heads stabilize toward 0.5 over time. Try flipping 10 coins and notice the variance. Then flip 1,000 and watch how much tighter the distribution gets.
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What to notice
- Small samples are noisy. With 10 flips, getting 7 heads (70%) is totally normal.
- Large samples converge. With 10,000 flips, you'll almost always land within a percent or two of 50%.
- Each flip is independent. Past results don't influence future flips — there's no "due" outcome.
This is the foundation of frequentist probability and why statistical studies need adequate sample sizes to be meaningful.