Never Stop Learning: Birthday Paradox

Everybody has a birthday, a special day relatively unique to them (at least in their friendship circle). It’s always fun to meet someone who shares the same day, or very close to the same day as yourself. It doesn’t happen too often, for me anyway.

The birthday paradox concerns probability, and states that “in a set of n randomly chosen people, some pair will share a birthday“. To achieve 100% probability, you would need 367 random people, as there are 366 possible birthdays, including February 29th. With 367 people, it is guaranteed that there will be a pair sharing a birthday. Interestingly, however, to achieve 99.9% probability of a pair sharing a birthday, you only need to have 70 people, and to get 50% probability you need just 23 people!

With just 23 people, there is a 50-50 chance that a pair will share a birthday. A coin toss. I’m not going to dive into why this is the case, as we would be here all evening. However I would recommend having a further look into it, maybe start with Wikipedia. Probability itself is a whole interesting world, which is rather counter intuitive, but makes total sense when you think about it.

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