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72 Introduction to probability
Because of this, we will be using the concept of probability in our
decision models. Probabilities are measured on a scale which runs from
0 to 1. If the probability of an outcome occurring is zero then this implies
that the outcome is impossible. At the opposite extreme, if it is considered
that an outcome is certain to occur then this will be represented by a
probability of 1 and the greater the chances of the event occurring, the
closer its probability will be to 1. It is worth pointing out that odds
can be converted to probabilities. For example, odds of 50 to 1 against
imply that there are 50 ‘chances’ that the outcome will not occur and
one chance that it will: a total of 51 ‘chances’. Thus the chances of the
event occurring are, in probability terms, 1 in 51 (or 0.0196). ‘Evens’ is,
of course, represented by the probability of 1/2.
In this chapter we will introduce the main ideas and rules which are
used in probability calculations. The ways in which decision analysts
elicit subjective probabilities from decision makers will be described
and evaluated in Chapter 10. Throughout the book we will be using the
notation p() to mean ‘the probability of ...’. For example, we will write
‘the probability of rain’ as p(rain).
Outcomes and events
Before proceeding, we need to be clear in our definitions of outcomes and
events. Suppose that a company is thinking of simultaneously launching
two new products, A and B. The company’s marketing manager decides
to list all the possible things that can happen if the simultaneous launch
goes ahead. His list is shown below:
Both products fail.
Product A succeeds but B fails.
Product A fails but B succeeds.
Both products succeed.
Each of the four possible things that can happen is called an outcome.An
event consists of one or more possible outcomes. For example, the event
‘just one product succeeds’ consists of the two outcomes: ‘A succeeds
but B fails’ and ‘A fails but B succeeds’. The event ‘at least one product
succeeds’ consists of the last three outcomes in the list. However, the
event ‘both products fail’ clearly consists of only one outcome.