The concept of Joint-Probability

As a mathematical construct, probability is one of the few which feels intuitive. It’s not like Linear Algebra, which requires some imagination to think in n-dimensional spaces.

But… add another word in front of it, and you get something that seems to make no sense.

Yup. I took a Probability and Random Processes course in my undergrad, and Joint-Probability was the most difficult concept to wrap my head around. Let’s have a look at it through a unique example.


Simply put, joint probability defines the probability of simultaneous occurrence of two things.

Honestly, the best way to explain joint-probability is through an example.

The big bang theory, Season 5, Episode 5

Someone has to go up with the telescope as a payload specialist, and guess who that someone is..
Mohammed Li

The genius Sheldon Cooper, has a simple logic behind his guess.

He guessed Mohammed Li by using probability. He states that it is common knowledge that Mohammed is the most common first name, and Li is the most common last name.

Thus, combining the two, he got the most common… hey… wait a second…Mohammed Li is a almost impossible name. It is definitely not the most common name.

Why do people face difficulty with it then??

It’s now clear as to what Joint-Probability is and does.

The bigger question is, how is it that undergrad students don’t understand a simple concept like this.

Well, in my course, probability was taught as a measure. From the set-theoretic definitions and axioms of probability. Measure Theory is a topic in advanced mathematics.

Thus, Joint-Probability was introduced using the Joint CDF(Cumulative Distribution Function), and its derivative was the Joint Probability Density.

Thus, the math was conveyed, but the meaning was not.

I love The Big Bang Theory, and this post was not made with any intent to pin-point any negatives about the show.

Originally published at on June 5, 2016.