# Maths (probability) question

aeytgr | 12:20 Tue 31st Aug 2004 | Quizzes & Puzzles
I have heard a maths problem I am puzzling over. I know that the probability of two people (out of a group of ONLY two people) having the same birthday is 1/365. I would like to know the probability of AT LEAST two people out of a group of three people having the same birthday. PS. I seem to have found by using a roundabout method that the probability is 3/365 - 2/(365 x 365) but I don't know why or how to get to that result from first principles. Pushing my luck, if anyone could provide a general formula for AT LEAST two people sharing the same birthday from a group of X people that would be great. Thanks in advance

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You work out the probability that they all have different birthdays and subtract it from 1. Thus you're looking for 1-((364/365)x(363/365)).
I started typing out the theory, but there is a full explanation here http://mathforum.org/dr.math/faq/faq.birthdayprob.html So in a school class of more that 23, there is a better than evens chance that two have the same birthday. Do you remember the tale of the mathematics teacher who announced this to his new class, but hadn't noticed that there was a pair of twins in the front row?

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