England.

# 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 stock market prices. You are expected to be reasonably competent in calculus and algebra.

## Modules count towards OU qualifications

OU qualifications are modular in structure; the credits from this undergraduate module could count towards a certificate of higher education, diploma of higher education, foundation degree or honours degree.

## Module

M343

### Credits

Credits

• Credits measure the student workload required for the successful completion of a module or qualification.
• One credit represents about 10 hours of study over the duration of the course.
• You are awarded credits after you have successfully completed a module.
• For example, if you study a 60-credit module and successfully pass it, you will be awarded 60 credits.
30

### Study level

Across the UK, there are two parallel frameworks for higher education qualifications, the Framework for Higher Education Qualifications in England, Northern Ireland and Wales (FHEQ) and the Scottish Credit and Qualifications Framework (SCQF). These define a hierarchy of levels and describe the achievement expected at each level. The information provided shows how OU module levels correspond to these frameworks.
Level of Study
OU SCQF FHEQ
3 10 6

## 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.

## Teaching and assessment

• Marking your assignments (TMAs) and providing detailed feedback for you to improve.
• Guiding you to additional learning resources.
• Providing individual guidance, whether that’s for general study skills or specific module content.
• Facilitating online discussions between your fellow students, in the dedicated module and tutor group forums.

Module tutors also run online tutorials throughout the module. Where possible, recordings of online tutorials will be made available to students. While these tutorials won’t be compulsory for you to complete the module, you’re strongly encouraged to take part.

### Assessment

The assessment details for this module can be found in the facts box.

Although your scores on the TMAs will not contribute directly to your final grade, you will need to successfully complete at least 2 of the 3 TMAs. You will be given more information when you begin the module.

## Future availability

Applications of probability (M343) starts once a year – in October.

We expect it to start for the last time in October 2026.

## Regulations

As a student of The Open University, you should be aware of the content of the academic regulations which are available on our Student Policies and Regulations website.

### Course work includes:

3 Tutor-marked assignments (TMAs)
Examination
No residential school

## Entry requirements

There is no formal pre-requisite study, but you must have the required mathematical skills.

## 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.

## Register

Start End England fee Register
07 Oct 2023 Jun 2024 £1731.00

Registration closes 07/09/23 (places subject to availability)

This module is expected to start for the last time in October 2026.

### Study costs

There may be extra costs on top of the tuition fee, such as set books, a computer and internet access.

If your income is not more than £25,000 or you are in receipt of a qualifying benefit, you might be eligible for help with some of these costs after your module has started.

## Ways to pay for this module

### Open University Student Budget Account

The Open University Student Budget Accounts Ltd (OUSBA) offers a convenient 'pay as you go' option to pay your OU fees, which is a secure, quick and easy way to pay. Please note that The Open University works exclusively with OUSBA and is not able to offer you credit facilities from any other provider. All credit is subject to status and proof that you can afford the repayments.

You pay the OU through OUSBA in one of the following ways:

• Register now, pay later – OUSBA pays your module fee direct to the OU. You then repay OUSBA interest-free and in full just before your module starts. 0% APR representative. This option could give you the extra time you may need to secure the funding to repay OUSBA.
• Pay by instalments – OUSBA calculates your monthly fee and number of instalments based on the cost of the module you are studying. APR 5.1% representative.

#### Joint loan applications

If you feel you would be unable to obtain an OUSBA loan on your own due to credit history or affordability issues, OUSBA offers the option to apply for a joint loan application with a third party. For example, your husband, wife, partner, parent, sibling or friend. In such cases, OUSBA will be required to carry out additional affordability checks separately and/or collectively for both joint applicants who will be jointly and severally liable for loan repayments.

As additional affordability checks are required when processing joint loan applications, unfortunately, an instant decision cannot be given. On average the processing time for a joint loan application is five working days from receipt of the required documentation.

Studying with The Open University can boost your employability. OU courses are recognised and respected by employers for their excellence and the commitment they take to complete. They also value the skills that students learn and can apply in the workplace.

More than one in ten OU students are sponsored by their employer, and over 30,000 employers have used the OU to develop staff so far. If the module you’ve chosen is geared towards your job or developing your career, you could approach your employer to see if they will sponsor you by paying some or all of the fees.

• Your employer just needs to complete a simple form to confirm how much they will be paying and we will invoice them.
• You won’t need to get your employer to complete the form until after you’ve chosen your module.

### Credit/debit card

You can pay part or all of your tuition fees upfront with a debit or credit card when you register for each module.

We accept American Express, Mastercard, Visa and Visa Electron.

### Mixed payments

We know that sometimes you may want to combine payment options. For example, you may wish to pay part of your tuition fee with a debit card and pay the remainder in instalments through an Open University Student Budget Account (OUSBA).

Please note: your permanent address/domicile will affect your fee status and therefore the fees you are charged and any financial support available to you. The fee information provided here is valid for modules starting before 31 July 2024. Fees normally increase annually. For further information about the University's fee policy, visit our Fee Rules

This information was provided on 10/06/2023.

In order to qualify, you must:

1. be resident in England
2. have a personal income of less than £25,000 (or receive qualifying benefits)
3. have not completed one year or more on any full-time undergraduate programme at FHEQ level 4 or above, or completed 30 credits or more of OU study

Once you've started the registration process, either online or over the phone, we'll contact you about your payment options. This will include instructions on how you can apply to study for free if you are eligible.

If you're unsure if you meet the criteria to study for free, you can check with one of our friendly advisers on +44 (0)300 303 0069 or you can request a call back.

Don't worry! We offer a choice of flexible ways to help spread the cost of your Access module. The most popular options include:

• monthly payments through OUSBA
• part-time tuition fee loan (you'll need to be registered on a qualification for this option)

To explore all the options available to you, visit Fees and Funding.

## What's included

• a week-by-week study planner
• course-specific module materials
• audio and video content
• assessment details, instructions and guidance
• online tutorial access

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

You’ll need broadband internet access and a desktop or laptop computer with an up-to-date version of Windows (10 or 11), or macOS (11 'Big Sur' or higher).

Any additional software will be provided or is generally freely available.

To join in spoken conversations in tutorials, we recommend a wired headset (headphones/earphones with a built-in microphone).

Our module websites comply with web standards, and any modern browser is suitable for most activities.

Our OU Study mobile app will operate on all current, supported versions of Android and iOS. It’s not available on Kindle.

It’s also possible to access some module materials on a mobile phone, tablet device or Chromebook. However, as you may be asked to install additional software or use certain applications, you’ll also require a desktop or laptop as described above.

## If you have a disability

The OU strives to make all aspects of study accessible to everyone and this Accessibility Statement outlines what studying M343 involves. You should use this information to inform your study preparations and any discussions with us about how we can meet your needs.