Part 2 of studying Futility Closet’s “Paradox of the Second Ace” with kids

Yesterday we did an introductory project for kids on Futility Closet’s Paradox of the Second Ace:

Here’s that project:

Introducing the boys to Futility Closet’s Paradox of the Second Ace

Today we continued the project and calculated the two probabilities in the “paradox.” These calculations are pretty challenging ones for kids, but even with the counting challenges, this was a really fun project.

I started by reminding them of the problem and getting their thoughts from yesterday:

Now we calculated the probability of having a second ace given that you have at least one ace. It took a while to find the right counting ideas, but once they did the calculation went pretty quickly. The counting technique that we used here was case by case counting:

Next we moved to the 2nd problem -> If you have the Ace of Spades, what is the probability that you have more than one ace? The counting technique that we used here was complimentary counting:

Finally, I asked the boys to reflect on the problem – was it still a “paradox” in their minds or did it make a bit more sense now that we worked through it?

I really loved talking through this problem with the boys – thanks to John Cook for sharing it and to Futility Closet for writing about it originally!