Walking through problem #7 from Mosteller’s 50 Challenging Problems in Probability

We’ve been going through Mosteller’s 50 Challenging problems in Probability this school year. Today we looked at problem #7.

The problem is about gambling on a roulette wheel. Specifically a wheel with 38 spaces for which you get 35 times your money (plus your bet) back if you guess the number correctly.

Here’s the problem and some initial thought from the boys:

At the end of the last video the boys had a plan for how to solve the problem. That plan and the solution to the problem are here:

To end the project I had the boys spend some time writing a computer program to simulate the game. Writing this code was a nice project for them and running it gave us a nice chance to talk about the problem from a different angle:

This was a fun project, but I think I need to add a second section to it tomorrow to clarify that just because you have a decent chance of being ahead, doesn’t mean the game has a positive expected value.