You are at a party with 24 other people so there are 25 peop

You are at a party with 24 other people (so there are 25 people at the party altogether, including yourself). What is the probability that some pair of people at the party share a birthday? What if there were 35 people? Explain how one computes this probability.

Supposing the people walk into the room one at a time.

The probability you have a unique birthday different from everyone so far is 365/365 (you\'re first into the room).
The probability the second person has a different birthday is 364/365.
The probability the third person has a different birthday is 363/365
... fourth person ... 362/365
... fifth person ... 361/365
etc.

For 25 people the probability of *not* sharing a birthday is:
365/365 * 364/365 * 363/365 * ... * 342/365 * 341/365

Or ,
....... 365!
------------------------
(365-25)! 365^25

P(at least one shared birthday with 25 people)
= 1 - 365! / (340! * 365^25)
56.9%

Replacing 25 with 35:

P(at least one shared birthday with 35 people)
= 1 - 365! / (330! * 365^35)
81.4%

You are at a party with 24 other people (so there are 25 people at the party altogether, including yourself). What is the probability that some pair of people a

You are at a party with 24 other people so there are 25 peop

Solution

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