Some of you might remember that a while back I gave a talk at an offsite where I used the classic birthday problem as a motivating example when discussing the potential pitfalls when of looking back at data and identifying coincidences that seem too unlikely to have occurred by chance.
The problem is this: what’s the least number of people you need in a room for there to be a 50% chance or more that at least 2 people have the same birthday? And the answer, which seems surprisingly low to most people, is 23.
In honour of this occasion I’d like to give you a variant of the classic birthday problem:
What’s the least number of people you need in a room for there to be a 50% chance or more that everyone in the room has the same birthday as someone else in the room?
They don’t all have to have the same single birthday, but there must be no one in the room who has a unique birthday.
So, just to be clear: with 23 people we know there’s a 50% chance that at least 2 people will share a birthday. But it’s very unlikely in that case that everyone in the room shares a birthday with someone else in the room. On the other hand, if we squeezed the whole population of the world – 7.8 billion people – into a single room, it’s pretty much guaranteed that everyone will share a birthday with someone else in the room. So to get a 50% chance that everyone in the room shares a birthday, we’ll have to fill it with somewhere between 23 and 7.8 billion people. But how many?
The exact calculation isn’t very easy, so I’m not expecting you to actually do it. But I am interested in what you might guess this number to be. So, can I ask you please to have a guess and send me your answer via this survey? The answers will be anonymous, but I think it might be interesting to see how accurate, collectively, we are at guessing the answer a problem of this type. So, please don’t be shy, just click to the survey, enter your best guess, and hit return. In a future post I’ll give the actual answer and summarise the answers that you send me.