Mental Floss

Happy birthday to them!

By David K. Israel

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As you might know, tomorrow is February 12th. It's also the 199th anniversary of Charles Darwin's birth. It's also the 149th anniversary of the publication of Darwin's "The Origin of Species." It's also the 199th anniversary of Abraham Lincoln's birth.

So many things to celebrate tomorrow; where to start?

How about we just concentrate on the wonderful coincidence that Darwin and Lincoln share the same birthday AND year!

I share a birthday with my mother, Bruce Lee and Jimi Hendrix. Not the same year, obviously, just the same day. Every time I go out to a restaurant to celebrate my birthday, it seems someone else is there doing the same thing, stealing my thunder, and often my piece of free birthday cake. An actuary friend explained that if you got 23 people together in a room, there's a 50-50 chance of at least one coincidental birthday.

After the jump, you'll find a complete breakdown for those who are curious to see the math involved. But first, with whom do you share a birthday? We'd love to know, especially if it's the same day AND year.

To figure out the exact probability of finding two people with the same birthday in a given group, it turns out to be easier to ask the opposite question: what is the probability that NO two will share a birthday, i.e., that they will all have different birthdays? With just two people, the probability that they have different birthdays is 364/365, or about .997. If a third person joins them, the probability that this new person has a different birthday from those two (i.e., the probability that all three will have different birthdays) is (364/365) x (363/365), about .992. With a fourth person, the probability that all four have different birthdays is (364/365) x (363/365) x (362/365), which comes out at around .983. And so on. The answers to these multiplications get steadily smaller. When a twenty-third person enters the room, the final fraction that you multiply by is 343/365, and the answer you get drops below .5 for the first time, being approximately .493. This is the probability that all 23 people have a different birthday. So, the probability that at least two people share a birthday is 1 - .493 = .507, just greater than 1/2. Statistics courtesy of Math Guy over at NPR.