If you have never heard of the Birthday Paradox, what it says is that in a group of 23 random people there is a 50% chance that two of those people share a birthday.  That’s not it just yet, in a group of only 57 people, there is a greater than 99.99% chance that two of those 57 people share a birthday!  That’s pretty wild when you think about it, given that there are 365 days in a year, thus the paradox coming into play.

Image credit: soapylovedeb

Wikipedia goes further into detail, I’ve paraphrased a bit:

In a group of 23 people, comparing the birthday of the first person on the list to the others allows 22 chances for a matching birthday, but comparing every person to all of the others allows 253 distinct chances: in a group of 23 people there are 23×22/2 = 253 pairs. The approximate probability that two people chosen from the entire population at random have the same birthday is 1/365 (ignoring Leap Day, February 29), and presuming all birthdays are equally probable. Although the pairings in a group of 23 people are not statistically equivalent to 253 pairs chosen independently, the birthday paradox becomes less surprising if a group is thought of in terms of the number of possible pairs, rather than the number of individuals.

The paradox does not state that YOU will have the same birthday as someone else in a room.  It states that someone will have the same birthday as someone else.

The math gets somewhat complicated, but you can check it out in more detail: Understanding the Birthday Paradox and Wikipedia’s page.

Stuff like this is really amazing at how the numbers work out.

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