Table of Contents
About Coin Flipping
Coin flipping is the simplest random experiment and the foundation of probability theory. A fair coin has equal probability of heads (H) and tails (T). It is used for making random decisions, demonstrating probability concepts, and as the building block for more complex statistical models (Bernoulli trials).
The coin flip is a Bernoulli trial with p=0.5. Multiple flips follow the binomial distribution, and by the law of large numbers, the proportion of heads converges to 0.5 as the number of flips increases.
Mathematics
Is a Real Coin Fair?
| Study | Finding |
|---|---|
| Diaconis et al. 2007 | Coins land same-side-up 51% |
| Murray & Teare 1993 | US penny: 50.1% heads |
- Real coins are very close to fair but have tiny biases due to weight distribution.
- Spinning a coin on a table is more biased than flipping in the air.
FAQ
What is the gambler's fallacy?
The mistaken belief that past results affect future independent events. After 10 heads in a row, the next flip is still 50/50 for a fair coin. Each flip is independent.
How many flips to detect a biased coin?
To detect a bias of 0.51 vs 0.50 at 95% confidence, you need approximately 10,000 flips. Small biases require very large samples to detect.