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# (16) Birthday paradoxJan 19, 2013

What is the probability of anyone in a class of 30 having the same birthday? There are many people who answer 30/365=8.2 %, but the correct answer is 70.6 %. This is because you calculate the probability of someone having the same birthday as you, and this problem is called birthday paradox. In order to find the correct answer, you need to calculate the probability of at least one pair having the same birthday. However, this calculation is complicated, and it is easier to calculate the probability of any pair not having the same birthday. This method is called proof by contradiction. The correct answer of the probability of someone having the same birthday as you is 7.6 %, which is less than estimated 8.2 %. Even if the number of class increases to 500 or 1000 people, the probability of someone having the same birthday as you will not reach 100 %. This fact may be called birthday paradox.

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