This has always been one of those problems that I have loved exploring. I recently found a website that will model the outcome in a brilliantly beautiful way. Here’s a little more about it from the Birthday Problem Wikipedia page:

In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of

nrandomly chosen people, some pair of them will have the same birthday.

By the pigeonhole principle, the probability reaches 100% when the number of people reaches 367 (since there are only 366 possible birthdays, including February 29). However, 99.9% probability is reached with just 70

people, and 50% probability with 23 people. These conclusions are based on the assumption that each day of the year (excluding February 29) is equally probable for a birthday.

It may seem surprising that the probability is above 50% when there is a pair with the same birthday for a group as small as 23 individuals. This is made more plausible when considering that a comparison will actually be made between every possible pair of people rather than fixing one individual and comparing him or her solely to the rest of the group.

https://en.wikipedia.org/wiki/Birthday_problem

The Pudding’s Russell Goldenberg has created this website to demonstrate this paradox.

Have a visit, have a play and contribute to the data.

I would absolutely use this as a hook the next time I need to tackle statistics with an upper Key Stage 2 class!