Having my son talk through an interesting probability problem from Pasquale Cirillo

Last week I learned about an really interesting probability problem from Pasquale Cirillo:

Today I asked him to think about the problem while I was out and when I got back home he walked me through his solution:

The last video shows his general approach – now he calculated the asnwer:

To wrap up I showed him how to modify his original argument just a bit to avoid the infinite series calculation. This is a much shorter way to solve the problem, but does require a bit more mathematical sophistication:

I really love the problem and think that it is a great one to share with kids. Even if kids can’t quite solve it, it would be really fun to hear their thought process and how they might estimate the probability of winning.