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# We have the same birthday!

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BIRTHDAY PARODOX! What is the formula to prove that if there are 23 people in a room than the chances are that two people have the same birthday?

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Erm. Even if there are only 2 people in a room, chances are the 2 of them have the same birthday... Or do you mean how to calculate the probability of at least 2 out of x people having the same birthday? Well, to know that, you should invert the question: What is the probability that none of those people share birthdays?

That's easy enough to calculate.

There are 365 dates (Feb 29th would actually make it 365.25, but that makes computation a little awkward). The first person has 365 days to choose from. The second has 364 days to choose from, etc... This make the probability of unique days:

365/365 * 364/365 * ... * (366-x)/365
= (365!/(365-x)!) / (365^x)

For 23 people, that would be:
(365!/342!)/(365^23)
which is approximately 50% chance that the people all have unique birthdays

So the chances that they don't have unique days is 100%-50%=50% (surprise)

With 23 people the chances are fifty-fifty that there is at least one day on which at least two people have their birthday.

If you want to know about exactly two people sharing exactly one day, the calculation is a bit different...

Edited by - Kippesoep on January 11, 2002 5:41:14 AM

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Oh my God!

There is here someone who claims to be from Holland. Well, exuse me, but in our language there is no such a thing like kippesoep.
It is: kippeNsoep.

Ok? Ok.

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I refuse to adopt that new spelling. I will never eat pannenkoeken. They will forever be pannekoeken to me.

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