What is the essence of the law of large numbers?

1 Answer
Jun 7, 2017

Given enough time, the outcomes of a trial will even out.


The law of large numbers is a probability law which states that the outcomes of two events with the same chance of occurrence, given enough time and trials, will even out into the expected ratio. In this case, the expected ratio is 1:1

Take fair coin flips for example. If you flip a coin 10 times, you may get 7 head and 3 tails, or 9 tails and one heads, or 5 heads and 5 tails. With a number this small, the law of large numbers does not come into account. Interestingly, this is known as the gamblers fallacy, when a person thinks that because an event has happened so many times with a 50/50 chance of it occurring, that the next event must be different. What the gamblers fallacy fails to take into account is that the number must be sufficiently large enough for that kind of thinking to work.

If I took a fair coin and flipped it 1000 times, then the law of large numbers would come into play, and I would find myself with a more or less 1:1 ratio of heads and tails.

That is the essence of the law of large numbers