The Birthday Paradox

Did you know if you gather in a room with 23 people, someone there will share the same birthday as you? How is that possible you say? In a room of just 23 people there is a 50% chance that you will find a birthday twin. That percentage jumps to 99% when 75 people gather in the same room. Although this may sound impossible it is true!

According to the Birthday Paradox, which is counter-intuitive, our brains are not able to yet compute the power of exponents needed to comprehend this “paradox”. We learn possibilities or outcomes in linear mindsets, but here we have something different.

Lets Do the Math!

Remember the objective is to find ATLEAST one match, not to match all 23 people.

Example 1: Yes, We could take a randomized room of 23 people and match them up with each other for every possible outcome. Doing this could be tedious, but effective.

Example 2:  With 23 people in a room, we would have 253 possible pairings. (22x23=253)

The chance of 2 people having the same birthday is (364/365) ²⁵³ =.4995 or a little over 50%.

Yes, there is a 50% chance that someone there may not have your birthday, but it is like a coin toss. There is a 50% chance to get heads or tails. But the more you flip the coin the higher the percentage to get your preferred coin toss outcome. Same with the Birthday Paradox, the more pairings or possible outcomes, the higher percentage to find your Birthday Twin!