There’s a 50 per cent chance that, in any group of 23 people, two people will share a birthday. First, we need to work out the probability that everyone in the group has a unique birthday.
Considering a ‘group’ of just one person, the chance is 100 per cent. If we add another person, there’s just one birthday that they could share with person one, so their probability of having a unique birthday is 364/365. For person three, it’s 363/365. And so on, until person 23, for whom the probability of a unique birthday is 343/365.
To find the probability of everyone in the group having a unique birthday, multiply all 23 probabilities together, giving 0.493.
So the probability of a shared birthday is 1 – 0.493 = 0.507, or 50.7 per cent.
Read more:
- What are the chances of having two identical snooker games?
- What are the odds of shuffling a deck of cards into the right order?
Subscribe to BBC Science Focus Magazine for fascinating new Q&As every month and follow @sciencefocusQA on Twitter for your daily dose of fun facts.
Authors
Robert is a science writer and visiting professor of science at Aston University. He likes maths, West End musicals and hamsters.
