A layman's explanation of Law of Large numbers

A layman's explanation of Law of Large numbers

Created time
Dec 18, 2020 1:50 AM
Sandeep Gangarapu

The first step is to nail their intuition for randomness. Here's how I will do it.

I will ask them if I flip a coin once, will it be heads or tails. The answer would be It will be heads! or It can be either! (smart kid). If it is former, I can prove them wrong in 1-3 tries and lay the path for explaining randomness. If it is later, they already have some intuition for randomness.

I will now ask if I flip it 10 times, how many will be heads and tails. The answer will be either It depends! or It will be 5-5 (50%-50%). Now I will demonstrate and ask them to keep track and show that it is not 5-5 (hopefully) and ask them why it wasn't. The general answer will be the way you are flipping, how much energy you are using, how high you are flipping. I will say OH! you mean it's random! ok! Generally, they will understand by now. If not, repeat this and show that the result is different and random.

As they are keeping track, at the end of 6, 8, 10, 12, 14, 18, 20 trials, I will keep asking the proportions of heads to tails and show them how it is converging. I will again summarize that the proportion was 75-25 at 4 trials, 60-40 at 10 trials, and that it would be close to 50-50 at 100 trials and even close at 1000 trials and as the no. of trials increase, they would be indistinguishable.

I will finish by saying that your initial answer of 50%-50% is in fact true, but you can only be sure at large numbers, and not so sure at small numbers.

I will give another example using the average height of kids in their class and how by taking more and more kids into the sample, we can actually get closer and closer to the true value.