Applications of probability
Qualification dates
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This module introduces models to describe patterns of events that occur in time (such as earthquakes) and space (for instance, the occurrence of a plant species). You’ll study situations that occur only at discrete time points, including the gambler’s ruin, and develop probability models for situations where events may occur at any time, such as the spread of an epidemic. The module ends with other situations involving probability, including genetics and changes in stock market prices.
What you will study
This module in probability and its applications emphasises probability modelling and developing the properties of the models. A considerable amount of mathematics is sometimes required for this development, but we do not always give formal proofs, particularly if the proof does not illuminate the probabilistic ideas.
The module consists of five books.
The first one, which is introductory, revises and develops ideas about probability and introduces some techniques that will be used frequently in the module.
The second book develops models for events occurring in time, including the Poisson process and several extensions of it, and patterns in space, including models for random scatter and clustering of objects.
The third book develops models for processes in which events can occur only at discrete time points, such as a Bernoulli process. This includes practical situations such as the ruin of a gambler and the extinction of a family surname.
In the fourth book, probability models are developed for situations in which events can occur at any time. Examples include queues, the spread of epidemics, and the change in the size of a population due to births and deaths.
In the fifth book, models are developed for various situations, including genetics, the renewal of components, and the change in stock market prices.
You can find the full content list on the Open mathematics and statistics website.
You will learn
Successful study of this module should enhance your skills in understanding mathematical arguments, expressing problems in mathematical language, finding solutions to problems and interpreting mathematical results in real-world terms.
Professional recognition
This module may help you to gain membership of the Institute of Mathematics and its Applications (IMA). For further information, see the IMA website.
This module may also help you to apply for the professional award of Graduate Statistician conferred by The Royal Statistical Society (RSS).
Entry requirements
There is no formal pre-requisite study, but you must have the required mathematical skills.
You can check you’re ready for M343 and see the topics it covers here.
Talk to an advisor if you’re not sure if you’re ready.
Preparatory work
You should aim to be confident and fluent with the concepts covered in the Are you ready? quiz here, and follow the advice in the quiz.
The key topics to revise include:
- calculus
- differential equations
- matrices.
You’ll also find it useful to be familiar with the following topics:
- probability functions
- probability density functions
- the binomial, Poisson, geometric, exponential and normal distributions
- the Poisson process.
An OU level 2 module in mathematics is ideal preparation, and Analysing data (M248) is also useful.
What's included
You’ll have access to a module website, which includes:
- a week-by-week study planner
- course-specific module materials
- audio and video content
- assessment details, instructions and guidance
- online tutorial access
- access to student and tutor group forums.
You’ll be provided with printed books covering the content of the module, including explanations, examples and activities to aid your understanding of the concepts and associated skills and techniques. You’ll also receive a printed module handbook.
You will need
Calculator with the usual mathematical functions (exp, log, sin, cos), but not necessarily with statistical functions.
Computing requirements
- Primary device – A desktop or laptop computer. It’s possible to access some materials on a mobile phone, tablet or Chromebook; however, they will not be suitable as your primary device.
- Peripheral device – Headphones/earphones with a built-in microphone for online tutorials.
- Our OU Study app operates on supported versions of Android and iOS.
- Operating systems – Windows 11 or latest supported macOS. Microsoft will no longer support Windows 10 as of 14 October 2025.
- Internet access – Broadband or mobile connection.
- Browser – Google Chrome and Microsoft Edge are recommended. Mozilla Firefox and Safari may be suitable.