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The Birthday Surprise!

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There are 365 days in a year (or 366 in a leap year), and you could have your birthday on any one of them. So you’d think you’d need rather a large number of people in any given setting to have a chance of having someone with the same birthday right?! Wrong!

Making the assumption that all birthdays are equally likely (which I know is probably not true as people tend to avoid Christmas, some aim for start of school year etc), if there are 23 people in a room then there is a 50% chance that two or more people will share a birthday! I think that’s quite crazy. Think about an average size class at school – there’s more than a 50% chance that two kids in the class will share a birthday. I don’t think that you’d immediately think that. What’s more, in a room with 75 people, there’s a 99.9% chance of a matching birthday!

This article Understanding the Birthday Paradox – BetterExplained gives a good explanation for how it works and why it’s true. Probability is one of those areas of Maths that feels a bit bonkers sometimes. You can understand what the probability of a given event is e.g. rolling a 1 on a dice is 1/6, but when events are interrelated, or the order of events matters, or you’re working out whether there are different possibilities for a scenario or a sequence of things that have to happen (i.e. adding or multiplying probabilities) it can get a bit mind boggling. That’s why game theory and probability came sometimes throw up interesting results.

Next time you’re at a large gathering and your kids are bored, get them to go around asking everyone’s birthdays and see what happens…Maths in action (plus keeps them amused)!

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