Theory of Probability

7A Preliminary Survey

7.1 Why a Survey at this Stage?

7.1.1. Our discussion of the requirements of the conceptual formulation of the theory of probability has already revealed its wide range of application. It applies, in fact, whenever the factor of uncertainty is present. The range of problems encountered is also extensive. Diverse in nature and in complexity, these problems require a corresponding range of mathematical techniques for their formulation and analysis, techniques which are provided by the calculus of probability. For a number of reasons, it is useful to give a preliminary survey, illustrating these various aspects. In setting out our reasons, and by inviting the reader to take note of certain things, we shall be able to draw attention to those points which merit and require the greatest emphasis.

First of all, we note that individual topics acquire their true status and meaning only in relation to the subject as a whole. This is probably true of every subject, but it is particularly important in the case of probability theory. In order to explore a particular area, it pays to get to know it in outline before starting to cover it in great detail (although this will be necessary eventually), so that the information from the detailed study can be slotted into its rightful place. If we were to proceed in a linear fashion, we would not only give an incomplete treatment but also a misleading one, in that it would be difficult to see the connections between the various ...