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The Birthday Paradox (or) How to win a bet with 23 people

July 27th, 2008 · No Comments

Birthday cake (image courtesy of Art Brazee)

Birthday cake (image courtesy of Art Brazee)

If you had a room of 23 people, what would you say the odds are that two or more of the people share a birthday? It turns out that the odds are greater than 50%. It’s known as the “Birthday Paradox” or the “Birthday Proplem and today I didn’t just learn about the maths – I learned how to make a little coin on it, too.

A friend of mine was telling me of a trainer who regularly stands before workshops of 30 or so participants. Early in the day, he suggests to his audience that at least two people in the room probably share a birthday. To prove his confidence, he proposes a wager – $1 from each participant, which he will double if all participants birthdays are unique. Now if the room had 57 participants there is a greater-than-99% chance he’d keep the money, but even with 30 participants there’s a better than even chance that he’ll pocket the cash.

Ok, so it’s not a good enough trick to quit your day job on, but it could be a nice way to raise a few coins for charity!

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