Pretty much the title.
In: 388
Imagine you have a fair sides coin. If you flip it once and it lands on head. So the average result is 1 (heads=1, tails=0). If you flip it again, you might get another head average is still 1. The third you might get a tails. Now the average is 0.66, much closer to what the true value.
The law of large numbers states, as you take more samples, the average of the samples will get closer to the true value.
This is because the chances of getting 2 heads and 1 tail after 3 flips is 0.375. However getting 20 heads and 10 tails after 30 flips is 0.028. And so on.
You can calculate how likely landing any number of heads is with the formula
0.5^(sample size) * (sample size) choose (no heads)
The choose function states how many different ways you can rearrange the heads in the sample.
So the formula is saying,
number of possibilities that the result happened times likelihood of each possibility.
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