Here’s a neat trick to use at a party:

Ask your friends how many people need to be at the party so that two people share a birthday.

The answer’s not 366. It’s not even in the hundreds. It’s about 57. Huh? Let’s explain.

This is called the birthday problem or the birthday paradox. There’s actually a cryptographic effect called the birthday attack. The problem is not whether a specific person shares a birthday, but whether anybody’s birthday is the same as anybody else’s birthday. This distinction changes the calculation of the probability a bit. To further simplify the problem, approach it from the back end and calculate the probability of all birthdays being different. Taken from Wikipedia:

Don’t worry about the math. This equation basically gives the probability that no birthdays are shared, ie the fourth person doesn’t share the birthday with the first three (362/365) all the way up to the nth person not sharing a birthday with the n-1 birthdays.

Since the case of more one or more persons sharing the same birthday is the complement to what has just been calculated we can say that the probability of two people sharing a birthday is:

Which actually hits ~50% at just 23 people and 99% at 57 people. If some of the people attending the party are fractured, shoot for 100 people which is 99.99997%.

Happy birthday to other people in Houston who share the birthdate of July 8th:

JJ Lassberg (@jjlassberg)

Bridgette Penel (@bridgette_penel)

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