Birthdays and Probability

I’ve always enjoyed the ability of maths to show us something about the world that just seems wrong. It’s great to be hit with something counter-intuitive and work out what is going on. My favourite example of this is the classic probability puzzle: if you have an average sized class of pupils, what are the chances that at least two of them share a birthday? When first presented with this, most people think that the chances are quite slim – after all, there are 365 days in a year, and a class only has around 30 pupils. Surely it’s not that likely at all?

The tools needed to analyse this are actually quite unsophisticated – it should be within the grasp of a year 8 student. I won’t go into detail here about how to work it out (perhaps you can do it yourself?), but the results, in case you’re not familiar with them, are interesting. You only need a class of 24 people for it to be more likely than not that at least two of them share a birthday, and if your class has 32 pupils (sadly the norm these days), then the chances are around three in four. Try it out with a few classes and see what results you get!

Of course, the only time I had the opportunity to try this out with a mathematics class, which did indeed have 32 pupils, I had hit on the one in four classes where all the pupils had different birthdays. Even the twins, who had managed to be born either side of midnight…