Probability Refresher

Purpose: We created this course to cover some topics and techniques in Probability that you may have seen before, to help ease the transition into third level education. We also provide a lot of questions with worked solutions to test yourself, giving several examples of how to turn word problems into something mathematical. We are not expecting you to know everything covered before starting, nor assess what you already know. If you encounter things you don't know, remember or understand, don't panic! Everything will be taught to you again once you arrive, this is just an extra help.

Topics Covered: First, the Background Material section outlines the necessary notation and definitions. The course is then focused on four key areas split into two sections: Tree Diagrams and Conditional Probability, and Random Variables and Probability Distributions. Each section contains definitions, explanations and examples, along with questions for you to try yourself. Solutions are provided in text for the shorter questions and in video for the longer/more difficult ones. Each subsection contains "Key Takeaways".

Intended Learning Outcomes: We would like you to be comfortable with the basic concepts of: conditional probability; using tree diagrams; general probability distributions; and the Binomial and Normal distributions. Understanding the more difficult concepts within these, such as what actually is a random variable, is a bonus. Ideally, attempt each example and question yourself before looking at solutions. The A level Maths questions should have more commonly seen topics while the Further Maths questions may include concepts you haven't seen before. The questions from STEP are intended to be extremely difficult and we do not expect your own solutions to these; just make your best attempt and then have a look at the video solution. It is more important to see the reasonings behind the solutions than simply to get it right or wrong.

Disclaimer: This is the first year of the refresher course and we want to improve it year-on-year. If you have any comments or feedback, or notice any mistakes, please let us know by email: stats.ug.support@warwick.ac.uk

Important Links:

AQA Past Maths Papers: Contains past papers for A level Mathematics.

AQA Past Further Maths Papers: Contains past papers for A level Further Mathematics.

STEP Website: Contains details on the STEP examination as well as past papers and marking schemes.