I saw a great thread on twitter last week – actually in the reverse order in which the tweets appeared. First I saw from Vincent Pantaloni:

With the N candies experiment, mark K=17, recapture n=17 among which k=2 are marked, you can calculate a first estimate using k/n=K/N which gives N=K/(k/n)=17/(2/17)=144.https://t.co/ZPw7QW5tGa

I thought it would be fun to do a project on this idea with the boys. Unlike a few (or maybe most) of our introductory statistics exercises, the program here was likely going to be too hard for the kids to write themselves, so I just wrote it myself and the boys played with it at the end.

To start I had them look at Pantaloni’s tweet:

Next we looked at Webb’s tweet – this one requires a bit more explanation, but the boys were able to understand what Webb’s animation was showing:

Now I spent 5 min explaining how the program I wrote worked. Since my simulation was quite a bit more simplified than the prior two (and also didn’t have any animation), I wanted to be sure they understood what I was doing before we dove in:

For the first run of my simulation, we looked at a 5000 trials of a pond with 1,500 fish and sampling from 4% of the pond From the conversation here you can hear that the boys are gaining a pretty good understanding of the process and are also able to make sense of the distribution of outcomes:

Finally, we looked at 5000 trials of a pond with 750 fish and sampling from 16% of the pond. Again the boys did a nice job explaining the results.

At the end we talked about why this sort of sampling problem can be really difficult.