Talking through a Bayes’ Theorem problem

My younger son is reading Jordan Ellenberg’s How not to be Wrong and the chapter talking about Bayes’ Theorem caught his attention this week. Looking around for something related to talk about in a project, I found this interesting problem on Wikipedia:

Before talking through that problem, though, we talked about the roulette wheel example from Ellenberg’s book:

Next we began to talk through the problem from Wikipedia. This part of the project shows the initial reaction and some thoughts on the problem from the boys:

Finally, with the initial thoughts out of the way we moved on to solving the problem. My older son was seeing these ideas cold, but what was really neat to me in this part is that the ideas from Ellenberg’s book really helped my younger son see how to solve this problem:

I feel like I got a bit lucky with this project. The ideas about updating probabilities looked a bit too difficult to go through in a 15 minute project – especially since my older son was seeing them for the first time. With this introduction, though, I think we can compute / verify the updated probabilities in the roulette wheel example from Ellenberg’s book in a project tomorrow.