The birthday paradox (also known as the birthday problem) is the probability that in a room of 23 strangers, there is a 50% (50.7% to be precise) chance of two people having the same birthday. In a room of 75 people that probability increases to 99.9%. The statistical oddity was first discovered by mathematician Richard von Mises in 1939.
This statistical oddity is categorized as a paradox because is counter-intuitive. In general, people use division rather than the compounding power of exponents to solve problems of probability. For example, to figure out what the chances are to toss a coin and get 10 heads in a row, the average person calculates this way: If getting one head is 50%, then getting two heads is 50% divided by two (25%); therefore, getting ten heads in a row must be 50% divided by 10 (5%). But the proper way to calculate this problem is through exponents: .50 to the power of 10, which equals .001.
There is a rather simple formula (see for further reading) to determine the chances of two people having the same birthday, but the key is using the power of exponents. But the simplest proof is as a “parlor trick” next time you are at an event of several dozen people. Impress attendees with your mathematical genius.
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For further reading: Don’t You Believe It by Herb Reich (2010)