We are up to problem #8 in Mosteller’s 50 Challenging Problems in Probability.

The problem today is a classic -> What is the probability that you would be dealt a bridge hand with 13 cards of the same suit from a well-shuffled deck of cards?

We started off by taking a quick look at the problem and getting a few ideas from the boys about how to solve it. One question that came up was whether or not the method used to deal the cards would matter:

The first cut at solving the problem involved dealing the cards in a circle – so what I’d think of as the standard way to deal cards:

Next up we took a little detour into choosing numbers because some of the details of how those numbers worked were a little fuzzy. It was a nice review and I was happy that the boys had recognized that the choosing numbers were somehow related to problem:

Finally, we wrapped up by checking to see if the probability changed when we used a different method of dealing.

I think this is a great question for kids to think through. The thoughts from the boys here are probably representative of some of both the struggles and connections that kids will have thinking through this problem.