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84 Introduction to probability
decision it is more likely that we will be concerned to identify all the
possible events which could occur, if a particular course of action was
chosen, together with their probabilities of occurrence. This complete
statement of all the possible events and their probabilities is known
as a probability distribution. For example, a consortium of business
people who are considering setting up a new airline might estimate the
following probability distribution for the number of planes they will
be able to have in service by the end of the year (this distribution is
illustrated in Figure 4.2):
No. of planes in service Probability
1 0.3
2 0.4
3 0.2
4 0.1
Note that the probabilities sum to 1, since all the possible events have
been listed. The ‘number of planes in service’ is known as an uncertain
quantity. If we plotted, on a continuous scale, the values which this
quantity could assume then there would be gaps between the points:
it would clearly be impossible for the airline to have 2.32 or 3.2451
planes in service since the number of planes must be a whole number.
This is therefore an example of what is known as a discrete probability
distribution.
Probability
0.4
0.3
0.2
0.1
1.0
0 1 2 3 4
Number of planes in service
Figure 4.2 – Probability distribution for number of planes in service by end of year