Statistics: The Birthday Paradox

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 n randomly 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.

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

Click to visit The Birthday Paradox Experiment website

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!