Yesterday we did an introductory project on Bayes’ Theorem inspired by chapter 10 of Jordan Ellenberg’s How not to be Wrong:

https://mikesmathpage.wordpress.com/2021/01/23/talking-through-a-bayes-theorem-problem/

Yesterday’s discussion helped the boys understand the problem that Ellenberg is discussion in chapter 10 of his book a bit better (hopefully anyway!). Today we took a crack at replicating the calculations in the book relating to the roulette wheel example.

First we revisited the example from the book to make sure we had a good handle on the problem:

Next we talked through the details of the process that we’ll have to follow to replicate the calculations that Ellenberg does. Following the discussion here the boys did the calculations off camera:

Here we talk through the numbers that the boys found off camera – happily we agreed with the numbers in the book.

At the end of this video I introduce a slight variation on the problem – instead of getting R, R, R, R, R in a test of 5 rolls, we get an alternating sequence of R and B for 20 rolls:

Here are their answers – and a discussion of why they think the answers make sense – for the new case I introduced in part 3 of the project:

This two project combination was really fun. My younger son said that he was confused by the roulette wheel example, but I think after these two projects he understands it. I think it is a challenging example for a 9th grader to understand, but with a little discussion it is an accessible example. It certainly makes for a nice way to share some introductory ideas about Bayesian inference.