Introduction; concept of probability

Probability theory finds application in almost every area of human endeavour. Most practical applications, however, require a lengthy description of the mathematical model of the process being studied. Games of chance, on the other hand, are usually easy to describe and readily understood. They are convenient, therefore, for introducing and demonstrating the basic concepts of probability, and we shall make use of them for this purpose in this chapter. Intuitively, at least, there is great similarity between insurance and a game of chance!

A gambler tosses a coin four times. This process may be referred to as an experiment or random experiment (to emphasise the fact that the outcome is uncertain). At each toss, the gambler will obtain either a ‘head’ (H) or a ‘tail’ (T). The particular sequence of ‘heads’ and ‘tails’ obtained is called the outcome of the experiment, and it is clear that the experiment we have described has 24 = 16 possible outcomes. The sequence H H T H is one possible outcome. The performance of an experiment is called a trial.

The gambler may count the number of ‘heads’ he or she obtains in a trial. This number is a random variable which may take any one of the non-negative integer values 0, 1, 2, 3, 4.