# Sharing problem #21 from Mosteller’s Fifty Challenging Problems in Probability with my kids

I found a neat problem in Mosteller’s Fifty Challenging Problems in Probability to share with the boys this morning:

In terms of “what kids learning math look like” this is one of the most interesting projects we’ve done. The problem turned out to be basically accessible to the boys, but pretty close to the end of what they could solve. Eventually they got there, though. I feel like this post could be useful for both the math and for seeing how kids think about math as they are learning it.

I started with a quick introduction to the problem and asked for their initial thoughts:

The first thing the boys wanted to do is look at the replacement and no replacement strategies with the urn with three blocks:

Next they looked at the two strategies in the urn with 201 blocks. We pretended the chances of each block were 50/50 to simplify the math a little:

Now things started going in a direction that was a bit different from what I was expecting. I thought we were just about to wrap up, but it turned out that the right way forward wasn’t yet clear in their minds. But even though things aren’t yet clear to them, you’ll see that they are making progress towards the answer:

Next we were able to combine the two decisions trees and start looking at how often our decision rule would lead us to picking the correct urn. Towards the end of this video suddenly the ideas in the problem become clear to the boys:

Here we finish the calculation of guessing right with our strategy – with the problem now making sense to them the calculation goes pretty quickly: