Introducing some basic ideas about the Poisson distribution to my younger son

For our project today, I though it would be fun to talk about the Poisson distribution. For me it is one of the most interesting and important ideas in probability. This question, for instance, is fascinating -> If a random event happens on average once per time period, what is the probability that it happens twice?

I started the introduction with a version of the idea I mentioned above and asked my son for some estimates of what he thought the answer would be:

Then we looked at some simulations. Here I’m looking at the idea of a random event that happens on average once per year and chopping the year up into 52 weeks:

Next I chopped the year up into 365 days – would we get different answers?

This project turned out to be a little more interesting to my son than I was expecting – I’m looking forward to exploring Poisson distributions a bit more next week.