Talking through the birthday problem with kids

Today is my birthday – I figured there was no better way to celebrate than to talk through the birthday problem with the boys.

We’ve talked about it before – here’s what they remembered:

Now . . . how to we tackle this problem? Getting started proved to be a little difficult:

Now that we figured out how to approach the problem, we dove into the calculations. This step also proved to be challenging, but eventually they were able to see how the calculation worked.

Finally we wrote a little [ bug filled ] program on Mathematica and played around with the results.

It is always fun to share a famous problem with the boys.

Talking a bit more about my son’s probability problem

Yesterday we did a fun project on a probability problem / game my son was working on. The game involves rolling three 10-sided dice and adding up the numbers. Repeat the process until you’ve seen one of the sums 40 times. Yesterday 15 was the winner:

Here’s yesterday’s project:

A probability and stats problem with dice my younger son was working on today

I wrote a short program on Mathematica to play my son’s game 1,000,000 times. I was interested to see how each of the boys would interpret the results.

Here’s what my older son had to say:

Here’s what my younger son had to say:

It is interesting to hear what kids have to say about the various probabilities and distributions. The results of the 1,000,000 simulations are probably pretty surprising. This problem that my son made up is actually a pretty fun problem to explore with kids.