Introduction

In the next three chapters various methods used to determine the probabilities required for decision making are explored and four broad approaches distinguished:

1. (a) the enumeration (or theoretical) approach;

2. (b) the relative frequency or collective principle;

3. (c) the actuarial approach;

4. (d) the subjective (or personal) approach.

Items (a), (b) and (c) are covered in this chapter, item (d) in Chapter 3. Chapter 4 then looks at questions of bias in assessments, and how these can be ameliorated. Whichever approach is employed to determine probabilities, the basic rules for handling probabilities, summarized briefly in Appendix A, remain the same.

The enumeration approach

A coin is tossed to determine whether you or your opponent should have the choice to serve first in a tennis match. The coin has two sides which look evenly balanced. You consider them equally likely and consequently assign them both a probability of 1/2. The same procedure could be followed in a board game using an ordinary six-sided die, each face appearing equally likely and therefore assigned a probability of 1/6. In taking part in a roulette game it is again assumed without great deliberation that the 36 slots (or 37 including the zero) are all equally likely. In the local village fete, 500 tickets are sold in a raffle for an electric mixer. You hold five tickets and assume unconsciously that your chances of winning are 1 in 100.

In these instances the assessment is made on the grounds that, if there are m different outcomes whose relative likelihood of occurrence seem indistinguishable, and only one outcome is a ‘success’, then its probability is 1/m.