Introduction

We may believe that the ‘laws of chance’ that apply when tossing a coin or rolling dice have little to do with experiments carried out in a laboratory. Rolling dice and tossing coins are the stuff of games. Surely, well planned and executed experiments provide precise and reliable data, immune from the laws of chance. Not so. Chance, or what we refer to more formally as probability, has rather a large role to play in every experiment. This is true whether an experiment involves counting the number of beta particles detected by nuclear counting apparatus in one minute, measuring the time a ball takes to fall a distance through a liquid or determining the values of resistance of 100 resistors supplied by a component manufacturer. Because it is not possible to predict with certainty what value will emerge when a measurement is made of a quantity, say of the time for a ball to fall a fixed distance through liquid, we are in a similar position to a person throwing several dice, who cannot know in advance which numbers will appear ‘face up’. If we are not to give up in frustration at our inability to discover the ‘exact’ value of a quantity experimentally, we need to find out more about probability and how it can assist rather than hamper our experimental studies.

In many situations a characteristic pattern or distribution emerges in data gathered when repeat measurements are made of a quantity. A distribution of values indicates that there is a probability associated with the occurrence of any particular value. Related to any distribution of ‘real’ data there is a probability distribution which allows us to calculate the probability of the occurrence of any particular value. Real probability distributions can often be approximated by a ‘theoretical’ probability distribution. Though it is possible to devise many theoretical probability distributions, it is the so called ‘normal’ probability distribution (also referred to as the Gaussian distribution) that is most widely used. This is because histograms of data obtained in many experiments have shapes that are very similar to that of the normal distribution. An attraction of the normal and other distributions is that they provide a way of describing data in a quantitative manner which complements and extends visual representations of data such as the histogram. Using the properties of the normal distribution we are usually able to summarise a whole data set, which may consist of many values, by one or two carefully chosen numbers.