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90 Introduction to probability
subjective, but they must still conform to the underlying axioms of
probability theory. Again, our approach has been normative; probability
calculus is designed to show you what your judgments should look like
if you accept its axioms and think rationally.
In later chapters we will look at methods which are designed to
help the decision maker to generate coherent assessments, and we will
examine in detail how good individuals are at making judgments about
probabilities. Often the receipt of new information, such as market
research results or provisional sales figures, can be used to modify
initial probability assessments, and in Chapter 8 we will show how this
revision of opinion should be carried out.
Above all, the correct application of the rules and concepts which
we have introduced in this chapter requires both practice and clarity
of thought. You are therefore urged to attempt the following exercises
before reading further.
Exercises
(1) Determine the probability of each of the following events occurring.
State the approach to probability which you used and any
assumptions which you needed to make.
(a) A person selected from the payroll of a company is a clerical
worker given that there are 350 people on the payroll of whom
120 are clerical workers.
(b) A light bulb selected from a production line is defective if, out
of 400 bulbs already tested, eight were defective.
(c) A new-born baby is male.
(d) This month’s sales forecast for a product has an error of more
than 10% if the forecast had an error of over 10% in 21 out of
the last 60 months.
(e) A permanently manned space station is established on Mars by
the year 2050.
(2) The following table shows an estimated probability distribution for
the sales of a new product in its first week:
Number of unitssold 0 1 2 3 4 5
Probability 0.05 0.15 0.20 0.35 0.15 0.10