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?