# Law of large numbers

The law of large numbers states that if an experiment is repeated again and again, the probability of an event obtained from the relative frequency will get closer and closer to the theoretical or actual probability.

For example, using theoretical probability, we know that the probability of getting tails is 1/2 or 50%. We draw this conclusion because there are two outcomes and only 1 outcome will give tails.

## Using the law of large numbers and the relative frequency

If you do not want to use the theoretical probability and you have time to perform the experiment, you could actually get a coin and toss it 100 times.

The coin may land on tails 35 times for example.

The relative frequency is 35/100. Your sample size was small, so the answer was not very close to the actual probability.

If now, you increase your sample size to 1000 or even 10000, you are using the **law of large numbers**. In other words, you are choosing a sample size that is large so your probability can be as close as possible to the theoretical probability.

The coin may land on tails 485 times if you toss it 1000 times

The relative frequency is 485/1000 = 0.485 and 0.485 is closer to 0.5

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