7 Days of Christmas: Day 2

Today, I will be talking about the birthday paradox.

Say you work in an office of 23 people, what is the probability that two people in your office have the same birthday? (Let’s ignore February 29th for the purposes of this problem).

The answer is that there’s a 50% chance! Once a population hits 366 people, it is statistically guaranteed that two people have the same birthday since there are only 365 possible birthdays. Assuming that all birthdays are equally likely, once you have 57 people grouped together, there is a 99% chance that two of them share the same birthday. That sounds crazy doesn’t it! How does this work?

Firstly, we’re going to find the converse probability – the probability that no two people share the same birthday – as this probability is much easier to calculate.

This probability is:

2.png

This means, that since there’s a 49.3% chance that nobody has the same birthday, there’s a 50.7% chance that at least two people have the same birthday.

The probability curve looks like this:

2..png

To read day 1, click here.

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