• # Question: If there are 85 students in a statistics class and we assume that there are 365 days in a year, what is the probability that at least two students in the class have the same birthday (assuming birthdays are distributed independently)?

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• Cathal Cummins answered on 21 Nov 2013:

Good question — the chances are EXTREMELY high. That at least two share the same birthday, the chances are

0.99997599731169891027795113052661898132590850175219624597954970956747155681436320867937208967404349287120157457635255148

or

99.9975997%

How close is that to certainty? Well suppose certainty is represented by a metre stick — 0cm being impossible and 100cm being certainty. How far away from the 100cm mark would we be? We would be less than a human hair’s width from the 100cm mark!!

A more interesting number than 85 is 87 people because 87 people in a room is the number of people needed to give a 0.5 (i.e. a flip of a coin) chance that at least THREE people share the same birthday. 🙂