1/
Get a cup of coffee.
Let's talk about the Birthday Paradox.
This is a simple exercise in probability.
But from it, we can learn so much about life.
About strategic problem solving.
About non-linear thinking -- convexity, concavity, S curves, etc.
So let's dive in!
2/
Suppose we came across a "30 under 30" Forbes list.
The list features 30 highly accomplished people.
What are the chances that at least 2 of these 30 share the same birthday?
Same birthday means they were born on the same day (eg, Jan 5). But not necessarily the same year.
3/
What if it was a "40 under 40" list?
Or a "50 under 50" list?
Or in general: if we put M people on a list, what are the chances that *some* 2 of them will share the same birthday?
4/
Clearly, this is an exercise in probability.
To solve it, we'll assume 3 things:
1. No Feb 29 birthdays,
2. Each person on our list is *equally likely* to be born on any one of the other 365 days (Jan 1 to Dec 31), and
3. The birthdays are all independent of each other.
5/
Another way to state the problem:
We have M people, and a 365-sided fair die.
Each person is allowed to roll the die once -- and is thereby assigned a number between 1 and 365 (both inclusive).
What are the chances that *some* 2 people will get assigned the same number?