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Summary 89
of the two monetary values taking into account their probabilities of
occurrence. The practical use of such a figure is that it allows a decision
maker to evaluate the attractiveness of different options in decision
problems which involve uncertainty, the topic of the next chapter.
The axioms of probability theory
If you use subjective probabilities to express your degree of belief that
events will occur then your thinking must conform to the axioms of
probability theory. These axioms have been implied by the preceding
discussion, but we will formally state them below.
Axiom 1: Positiveness
The probability of an event occurring must be non-negative.
Axiom 2: Certainty
The probability of an event which is certain to occur is 1. Thus axioms 1
and 2 imply that the probability of an event occurring must be at least
zero and no greater than 1.
Axiom 3: Unions
If events A and B are mutually exclusive then:
p(A orB) = p(A) + p(B)
It can be shown that all the laws of probability that we have considered
in this chapter can be derived from these three axioms. Note that they
are generally referred to as Kolmogoroff’s axioms and, as stated above,
they relate to situations where the number of possible outcomes is finite.
In the next few chapters we will use subjective probability assessments
in our calculations without attempting to evaluate the quality of these
judgmental inputs to our analyses. In Chapters 9 and 10 we will consider
the degree to which probability judgments comply with the axioms and
have validity as predictions of future events.
Summary
As we shall see in the next chapter, probability assessments are a
key element of decision models when a decision maker faces risk and
uncertainty. In most practical problems the probabilities used will be