Probability 1 lecture notes

Author

Clare Wallace

Published

October 2, 2025

Welcome to Probability 1

Welcome to Probability 1! These lecture notes contain all the mathematical content you’ll need to know to succeed in Probability this year.

If you have questions about any of the content here, try one of the following:

ask a friend!
ask me! I like to answer emails, and I am often in my office (MCS3060): you can (and should) pop by to see if I’m around. You can do this during my official office hours (Mondays, 10-12) for a guaranteed speedy response, but you definitely shouldn’t wait until then, especially if it’s a short or quick question.
Google it, or try a textbook. There are some good ones on the reading list (see below).

These notes have been developed over the years by several members of the Statistics and Probability groups, including (most recently) Debleena Thacker and Andrew Wade.

Warning

There could still be typos. If you find one, let me know about it and you can have a free bag of Skittles.

How to use these notes

The notes contain all the mathematical content for the course. In lectures, we will start at the beginning and work our way through the whole document, until we reach the end (hopefully, this will happen exactly at the end of term).

Throughout the notes, there are boxes like this one:

💪 Try it out

You can do the “Introductory” exercises on the problem sheet already.

These contain examples you can work through to check your understanding. Wherever possible, I’ve also worked examples into the text, but there are some places where I want to give you an extra example. These come in purple boxes.

Content that’s particularly important for the course is highlighted in red:

🔑 Key idea

Probability is cooler than statistics

while advanced material is highlighted in blue:

Advanced content

Probability is almost surely cooler than statistics.

You’ll also find textbook recommendations, with the relevant sections:

📖 Textbook references

If you want more help with this section, check out:

Appendix A.1 in (Blitzstein and Hwang 2019);
Appendix B in (Anderson, Seppäläinen, and Valkó 2018);
or the Appendix to Chapter 0 in (Stirzaker 2003).

The library has lots of good books on introductory probability, and there are even more available online/to buy. The following four textbooks are a good starting point:

(Blitzstein and Hwang 2019) covers the material in depth and uses simulation code to illustrate the theory.
(Anderson, Seppäläinen, and Valkó 2018) covers just about everything in the course at about the right level of detail.
(Stirzaker 2003) is concise and the most mathematically advanced, and will be useful for students taking 2H probability.
(DeGroot and Schervish 2013) has a statistical perspective, covering this course as well as a lot of Statistics.