Applications of probability

This module introduces models to describe patterns of events that occur in time (such as earthquakes), and in space (for instance, the occurrence of a species of plant). Situations that occur only at discrete time points, including the ruin of a gambler, are studied. Probability models are developed for those situations, such as the spread of an epidemic, in which events may occur at any time. The module ends with other situations involving probability including genetics and changes in stockmarket prices. You are expected to be reasonably competent in calculus and algebra.

Course facts
About this course:
Course code M343
Credits 30
OU Level 3
SCQF level 10
FHEQ level 6
Course work includes:
3 Tutor-marked assignments (TMAs)
4 Interactive computer-marked assignments (iCMAs)
No residential school

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 six 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.

Computer simulations are used to illustrate some of the phenomena studied, and associated activities are included in a separate book.

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.


You need no pre-requisites to study Applications of probability. However, we recommend that you are familiar with the following mathematical topics:

  • calculus
  • algebra
  • differential equations
  • matrices

We recommend you also have previous basic knowledge of probability; we'll include some revision of the following topics:

  • probability functions
  • probability density functions
  • the binomial, Poisson, geometric, exponential and normal distributions
  • the Poisson process

Check you're ready to study Applications of probability with our self-assessed quiz.

Talk to an advisor if you're still not sure if you're ready.

Preparatory work

Essential mathematics 1 (MST124) and Essential mathematics 2 (MST125) are ideal preparation to reach the mathematical competence level we recommend for studying Applications of probability. However, we recommend also completing one of our OU level 2 mathematics modules.

Analysing data (M248) teaches the probability knowledge we recommend you to have before starting Applications of probability. The first book of Applications of probability includes a thorough revision of this knowledge, so we recommend you study it early if you haven't completed Analysing data.

If you have a disability or additional requirement

This module may be very challenging if you have severely impaired sight. Almost all the texts contain detailed diagrams and there are a few data tables.

Adobe Portable Document Format (PDF) versions of printed material are available. Some Adobe PDF components (such as equations) may not be available or fully accessible using a screen reader and mathematical materials may be particularly difficult to read in this way.

Study materials

What's included

Books, web-based software, website.

You will need

Calculator with the usual mathematical functions (exp, log, sin, cos), but not necessarily with statistical functions.

Computing requirements

You will need a device with internet access to study this module as a web browser is used to access learning materials and activities. Any other computer-based activities you will need to carry out, such as word processing, using spreadsheets, taking part in online forums, and submitting files to the university for assessment, are specified in the module materials. If any additional software is needed for these tasks it will either be provided or is freely available. You may need administrative privileges to install software required for this module. Windows 10 S is not suitable as it restricts software installation to software available in the Windows Application Store.

Suitable devices are:

  • A Windows desktop or laptop running Windows 7 or later operating system
  • A Macintosh desktop or laptop running OS X 10.8 or later operating system.

Some software will not run on Linux, iOS or Android devices.

A netbook, tablet, smartphone or Linux computer that supports one of the browsers listed below may be suitable. However, these devices may not be suitable for some activities. If you intend to use one of these devices please ensure you have access to a suitable desktop or laptop device that uses the Windows or OS X operating system in case you are unable to carry out all activities on your mobile device.

Recent versions of the following browsers are suitable for carrying out web-based activities:

  • Safari
  • Chrome
  • Firefox
  • Edge

Or Internet Explorer 9 and above.

Using a browser upgraded to the latest version will maximise security when accessing the internet.

Using company or library computers may prevent you accessing some internet materials or installing additional software.

To be able to talk and listen in our online discussions you will need both a microphone and speakers/headphones.

Devices with small screens may make it difficult to view the material provided and carry out the activities. However, a device that has a resolution of at least 1024 pixels horizontally and also at least 768 pixels vertically should be adequate.

See our Skills for OU study website for further information about computing skills for study and educational deals for buying Microsoft Office software.

Teaching and assessment

Support from your tutor

You will have a tutor who will help you with the study material and mark and comment on your written work, and whom you can ask for advice and guidance. We may also be able to offer group tutorials or day schools that you are encouraged, but not obliged, to attend. Where your tutorials are held will depend on the distribution of students taking the module.

Contact us if you want to know more about study with The Open University before you register.


The assessment details for this module can be found in the facts box above. Although your scores on the TMAs and iCMAs will not contribute directly to your final grade, you will need to successfully complete at least 2 of the 3 TMAs and 3 of the 4 iCMAs. You will be given more information when you begin the module.

You can choose whether to submit your tutor-marked assignments (TMAs) on paper or online through the eTMA system. You may want to use the eTMA system for some of your assignments but submit on paper for others. This is entirely your choice.

Future availability

The details given here are for the module that starts in October 2017. It starts once a year – in October.

This course is expected to start for the last time in October 2022.

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).