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"Victory goes to the player who makes the next-to-last mistake - Chessmaster Savielly Grigorievitch Tartakower (1887-1956)"

Friday, January 11, 2008

The Birthday Problem...
Does anyone have the same birthday as you? Of course they do. I share mine with Olivia Newton-John, Bryan Ferry and Will Self. But how about within your group of friends?

When I was in the first year of secondary school our maths teacher asked us a question: in a group of randomly chosen people, how big will the group need to be before there is more than a 50/50 chance that some pair of them will have the same birthday?

We all guessed. Wildy. Some said 365. Some said 183. I was second closest though with a guess of 50.

The actual number is surprisingly low. Just 23. That is to say if you have just 23 people in group there is a 50/50 chance that two of them with share the same birthday.

Now this birthday problem asks whether any of the 23 people have a matching birthday with any of the others — not one in particular. To find out the size of the group in which there is a 50/50 chance of someone having the same birthday as you the maths is a bit different and the answer is much bigger. 253.

So it depends of the question you ask. I don't know any people in my group of friends who have the same birthday as me but I do know people within my group of friends who share the same birthday. Which stacks up with the odds.

3 comments:

  1. Anonymous8:05 pm

    Not one, but two of my friends share my birthday on 1 December. And I have far fewer than 253 friends.
    Love from California,
    Bryn

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  2. Two of my other friends have a birthday on 1st December too! 1st March must have been a busy night! LOL

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  3. david (the other one)3:49 pm

    I've got 5 friends who all have the same birthdeay as me, thankfully they're scattered around the world, so we don't always have a get together. Three of us were born the same year too!

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