And we have an right answer! Thanks to both Eddie and John for their right answer. Very well done!

You are at a party with a friend and 30 people are present including you and the friend. Your friend wants to make a wager with you if there are two people that share their birthday date, he will give you 100$, however, you shall give him 100$ if nobody shares their birth date. Would you accept the wager ? Explain why.

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The answer is that ‘Yes’, you would want to take the bet with your friend. That is, because with 30 people in a party, there is a 70% chance that two of them will share their birthday date. The idea is as follows (From John’s answer):

For the first person, the chances that he has a unique birthday is

365/365

For the second person his/her chances are 364/365 etc.

So the chances that all 30 have a unique birthday is

(365*364*363*362*…337*336)/365^30

which gives a number very close to 30%.

Therefore, the probability of at least two person sharing a birthday is 100-30 = 70%.

This is based on what is called the Birthday Paradox. Check out the Wikipedia entry on the subject for more details: Birthday Paradox. Interestingly enough, the Birthday Paradox is not a Paradox in the sense that we know them. It was called a Paradox because it is so counter intuitive…

Hope you enjoyed this puzzle! 🙂