# Course - Probability

> Source: https://ollybritton.com/notes/uni/prelims/mt22/probability/ · Updated: 2025-10-21 · Tags: uni, course

> An introduction to probability theory, starting from the axioms of a probability space and ending at the weak law of large numbers and Chebyshev's inequality. A lot more than was covered in Stats at A-Level.
> 
> There were some really fun problem sheet questions in this course, like this one from Sheet 1: "Celia the centipede has 100 feet, 100 socks, and 100 shoes. How many orders can she choose from to put on her socks and shoes? (She must put a sock on foot $i$ before putting a shoe on foot $i$.)".

- [Course Webpage](https://courses.maths.ox.ac.uk/course/view.php?id=606)
- [Lecture Notes](https://courses.maths.ox.ac.uk/pluginfile.php/25386/mod_resource/content/6/PrelimsProb_MT22_28Sep2022.pdf)
- Some of the lectures from this course are [available on YouTube](https://www.youtube.com/playlist?list=PL4d5ZtfQonW0B3qW24yAj1u1SuOvgKfP5).
- Other courses this term: [Courses MT22](https://ollybritton.com/notes/uni/prelims/mt22/)

### Notes
- [Notes - Probability MT22, Axioms of probability space](https://ollybritton.com/notes/uni/prelims/mt22/probability/notes/axioms-of-probability-space/)
- [Notes - Probability MT22, Basic definitions](https://ollybritton.com/notes/uni/prelims/mt22/probability/notes/basic-definitions/)
- [Notes - Probability MT22, Partition theorem](https://ollybritton.com/notes/uni/prelims/mt22/probability/notes/partition-theorem/)
- [Notes - Probability MT22, Bayes' theorem](https://ollybritton.com/notes/uni/prelims/mt22/probability/notes/bayes-theorem/)
- [Notes - Probability MT22, Random variables](https://ollybritton.com/notes/uni/prelims/mt22/probability/notes/random-variables/)
- [Notes - Probability MT22, Distributions](https://ollybritton.com/notes/uni/prelims/mt22/probability/notes/distributions/)
- [Notes - Probability MT22, Expectations](https://ollybritton.com/notes/uni/prelims/mt22/probability/notes/expectations/)
- [Notes - Probability MT22, Variance and covariance](https://ollybritton.com/notes/uni/prelims/mt22/probability/notes/variance-and-covariance/)
- [Notes - Probability MT22, Recurrence relations](https://ollybritton.com/notes/uni/prelims/mt22/probability/notes/recurrence-relations/)
- [Notes - Probability MT22, Probability generating functions](https://ollybritton.com/notes/uni/prelims/mt22/probability/notes/probability-generating-functions/)
- [Notes - Probability MT22, Random sums theorem](https://ollybritton.com/notes/uni/prelims/mt22/probability/notes/random-sums-theorem/)
- [Notes - Probability MT22, Moments](https://ollybritton.com/notes/uni/prelims/mt22/probability/notes/moments/)
- [Notes - Probability MT22, Branching processes](https://ollybritton.com/notes/uni/prelims/mt22/probability/notes/branching-processes/)
- [Notes - Probability MT22, Random samples](https://ollybritton.com/notes/uni/prelims/mt22/probability/notes/random-samples/)
- [Notes - Probability MT22, Weak law of large numbers](https://ollybritton.com/notes/uni/prelims/mt22/probability/notes/weak-law-of-large-numbers/)
- [Notes - Probability MT22, Markov's inequality](https://ollybritton.com/notes/uni/prelims/mt22/probability/notes/markovs-inequality/)
- [Notes - Probability MT22, Chebyshev's inequality](https://ollybritton.com/notes/uni/prelims/mt22/probability/notes/chebyshevs-inequality/)
- [Notes - Probability MT22, Misc](https://ollybritton.com/notes/uni/prelims/mt22/probability/notes/misc/)

### Lectures
- [Lecture - Probability, Lecture 1](https://ollybritton.com/notes/uni/prelims/mt22/probability/lectures/1/)
- [Lecture - Probability, Lecture 2](https://ollybritton.com/notes/uni/prelims/mt22/probability/lectures/2/)
- [Lecture - Probability, Lecture 3](https://ollybritton.com/notes/uni/prelims/mt22/probability/lectures/3/)
- [Lecture - Probability MT22, IV](https://ollybritton.com/notes/uni/prelims/mt22/probability/lectures/4/)
- [Lecture - Probability MT22, V](https://ollybritton.com/notes/uni/prelims/mt22/probability/lectures/5/)
- [Lecture - Probability MT22, VI](https://ollybritton.com/notes/uni/prelims/mt22/probability/lectures/6/)
- [Lecture - Probability MT22, VII](https://ollybritton.com/notes/uni/prelims/mt22/probability/lectures/7/)
- [Lecture - Probability MT22, VIII](https://ollybritton.com/notes/uni/prelims/mt22/probability/lectures/8/)
- [Lecture - Probability MT22, IX](https://ollybritton.com/notes/uni/prelims/mt22/probability/lectures/9/)
- [Lecture - Probability, X](https://ollybritton.com/notes/uni/prelims/mt22/probability/lectures/10/)
- [Lecture - Probability MT22, XI](https://ollybritton.com/notes/uni/prelims/mt22/probability/lectures/11/)
- [Lecture - Probability MT22, XII](https://ollybritton.com/notes/uni/prelims/mt22/probability/lectures/12/)
- [Lecture - Probability, XIII](https://ollybritton.com/notes/uni/prelims/mt22/probability/lectures/13/)
- [Lecture - Probability, XIV](https://ollybritton.com/notes/uni/prelims/mt22/probability/lectures/14/)
- [Lecture - Probability, XV](https://ollybritton.com/notes/uni/prelims/mt22/probability/lectures/15/)
- [Lecture - Probability, XVI](https://ollybritton.com/notes/uni/prelims/mt22/probability/lectures/16/)

### Problem Sheets
- [Sheet 1](https://courses.maths.ox.ac.uk/pluginfile.php/25389/mod_resource/content/5/PrelimsProbabilitySheet1_MT22.pdf)
- [Sheet 2](https://courses.maths.ox.ac.uk/mod/resource/view.php?id=4510)
- [Sheet 3](https://courses.maths.ox.ac.uk/mod/resource/view.php?id=4511)
- [Sheet 4](https://courses.maths.ox.ac.uk/mod/resource/view.php?id=4512)
- [Sheet 5](https://courses.maths.ox.ac.uk/mod/resource/view.php?id=4513)
- [Sheet 6](https://courses.maths.ox.ac.uk/mod/resource/view.php?id=4514)
- [Sheet 7](https://courses.maths.ox.ac.uk/mod/resource/view.php?id=4515)
- [Sheet 8](https://courses.maths.ox.ac.uk/mod/resource/view.php?id=4516)

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