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