is a proven mathematical theorem that links probabilities to frequencies
the law states that:
- as the number of identically distributed, randomly generated variables increases, their sample mean (average) approaches their theoretical mean
- as you continue to repeat the same process, the relative frequency of occurrence of a particular outcome will get closer and closer to that outcome’s probability
- in repeated independent tests with the same actual probability p of a particular outcome in each test, the chance that the fraction of times that outcome occurs differs from p converges to 0 as the number of trials goes to infinity
For example, if you flip a fair coin 10 times, it’s not that unlikely to get 7 heads, instead of the “expected” 5. In this case, the relative frequency of heads would be 7/10 or 0.7. But if you flip the same coin 1000 times, the relative frequency of heads will be much closer to 0.5. What the law of large numbers says is that, as you increase the number of flips, the relative frequency of heads will get closer and closer to 0.5.

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