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4
Introduction
Introduction to probability
In the previous chapter we discussed the analysis of decisions where
uncertainty was not considered to be a major factor. However, in many
problems the decision maker is not sure what will happen if a particular
course of action is chosen. A company that is considering the purchase
of an expensive new machine will face uncertainty relating to factors
such as the machine’s reliability, life span and resale value. Similarly,
an individual who has to decide whether or not to purchase household
insurance will be uncertain as to whether his home will be burgled,
flooded or damaged by fire. In the next chapter we will be looking at
how to analyze decisions which involve uncertainty, but before this we
need to consider how the concept of probability can be used to provide
a measure of uncertainty.
There are a number of ways in which uncertainty can be measured
and expressed. The simplest method involves the use of words such
as ‘unlikely’, ‘almost impossible’, ‘probable’, ‘doubtful’ and ‘expected’.
Unfortunately, it has been found that different people attach very different
meanings to these expressions, and even individuals are not
consistent over time in their use of them. For example, Moore and
Thomas 1 discuss an experiment at a business school where a large number
of executives were asked to rank 10 words or phrases in decreasing
order of uncertainty. The ranking of the word ‘likely’ ranged from
second to seventh, while the ranking for ‘unlikely’ ranged from third
to tenth.
Numbers offer a much more precise way of measuring uncertainty, and
most people will be familiar with the use of odds. While many decision
makers may be happy to use expressions such as ‘100 to 1 against’ or
‘evens’, odds do have the disadvantage that they are awkward to handle
arithmetically when, for example, we want to determine the chances
that a number of different outcomes will occur.