# 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.

### Joint-Probability

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

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 **raghuramkrishnaswami.wordpress.com** on June 5, 2016.*