Probability & Statistics Visualizer

🪙 Coin Flip Simulator — Law of Large Numbers

Flip a coin 10 times — you might get 7 heads. Flip 1,000 times — you'll be very close to 50%. This is the "Law of Large Numbers." More trials = more predictable outcome.

Hit the button to run all 5 simulation sizes at once.

🔔 Normal Distribution — The Bell Curve

Tons of things in nature follow a bell curve: heights, test scores, measurement errors. The curve tells you how likely any value is. About 68% of values fall within 1 standard deviation (σ) of the mean — and 99.7% within 3σ!

🎰 Expected Value — Should You Play the Lottery?

Expected value (EV) tells you the average outcome if you played many, many times. Almost all lotteries have negative EV — you lose money on average. See it yourself!

🧬 Bayes' Theorem — The Medical Test Paradox

A test is 99% accurate. You test positive. What's the chance you actually have the disease? Probably much less than 99%! This is Bayes' theorem — it factors in how rare the disease is. A rare disease + lots of people tested = lots of false positives.