Using a John Allen Paulos problem to discuss probability and expected value with my younger son

I saw a neat problem from John Allen Paulos earlier in the week:

Today my older son was working on a different math project, so I thought I’d use Paulos’s problem for a nice project with my younger son.

I started by introducing the problem (and forgetting to zoom out after introducing it – sorry about the middle 3 min of this video . . . .). Despite the filming goof, you’ll see my son head down a path that illustrates a common counting mistake.

Now we found that our probabilities didn’t add up to 1, so we tried to found out where we went wrong. Fortunately, my son was able to track down the error.

The next part of the project was discussing the expected amount we’d win playing this game. I didn’t define “expected value” but my son was able to come up with a good way of thinking about the concept.

Finally, we went to the computer to write a little program in Mathematica. This part of the project turned out to be a nice lesson in both simulations and in statistics.