Yesterday we looked at the famous Birthday problem – how many people do you need to have in a room to have a 50/50 chance of two people having the same birthday? That project is here:
Today we continued the project (with just my older son as my younger son was hiking) and studied the problem that originally motivated this project -> If you have 24 students in a class, what is the chance that exactly 3 pairs of students will share a birthday? This is the surprisingly fun situation in my son’s English class.
We will – as I think it standard for the introductory version of this problem – be making the assumption that all birthdays are equally likely. If you want to see a really neat discussion – though not really a math for kids paper! – see the paper in this tweet:
So, to start the project today we first reviewed the main ideas from yesterday:
Next we took a step towards solving the problem by looking at the chance of having exactly 2 pairs. Once piece of the counting here is tricky, so we used the computer to help see what the problem was.
Now we tackled the “exactly 3 pairs problem”:
Finally, I had my son make up a problem to solve – he decided to find the chance of all 24 students pairing up. This problem wasn’t too hard given the prior work. It was also a fun challenge to try to estimate the chance of this happening.