### Introduction

Probability is about the study of uncertainty. Engineers are expected to design and produce systems which are both useful and reliable. Essentially we are dealing with situations where ‘chance’ is at work and probability theory gives us the theoretical underpinning necessary for a full understanding of any experimental results we observe in practice. Probability theory also gives us the tools to set up mathematical models of systems and processes which are affected by random occurrences or ‘chance’. In fact the study of probability enables engineers to discuss the reliability of the processes they use and the systems they produce in terms that other engineers, scientists and designers can understand. It is worth noting that ‘chance’ is taken to be responsible for variations in simple manufactured products such as screws, bolts, and light bulbs as well as complex products such as cars, ships and aircraft. In each of these products, small chance variations in raw materials and production processes may have a substantial effect on a product.

#### Prerequisites

- understand the ideas of sets and subsets

#### Learning Outcomes

- explain the terms ‘random experiment’ and ‘event’
- calculate the probability of an event occurring
- calculate the probability that an event does not occur

#### Contents

1 Introductory probability1.1 Terminology

1.2 Events

1.3 Complement

2 Definitions of probability

2.1 Relative frequency applied to probability

2.2 Equi-probable spaces and the principle of equally likely outcomes

2.3 Definition