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Imagine you walk into a room of 22 people, none of whom have a birthday in common. The chances you'll have a unique birthday feel pretty high - there are only 22 days taken by the others, and 343 days free, so you'd fancy your chances that no-one shares your birthday.

This may be one reason the birthday paradox feels counter-intuitive. We tend to view problems like this from our own individual perspective, and for any individual the chances of sharing a birthday are low.

But let's work out the probability that everyone in that group of 23 has a unique birthday.

For person 1, the chances are 100% because every date is clear. For person two, there's one day they would share with person 1, but the other 364 are clear, so their chance of a unique birthday is 364/365. For person 3 it's 363/365, and so on through to person 23, whose probability of having a unique birthday is 343/365.

To find the probability of everyone in the group having unique birthdays, we multiply all those 23 probabilities together, and if we do we end up with a probability of 0.491.

The probability that a birthday is shared is therefore 1 - 0.491, which comes to 0.509, or 50.9%.

But if that is the probability that any two people in a group will share a birthday, what about the probability that you will share a birthday with at least one other person in a group? For that to be greater than 50%, you'd need to have a group of 253 people.