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CALCULATING BRANCH PROBABILITIES 567

Market Research
State of Nature Favourable, F Unfavourable, U
P(F|s 1 ) ¼ 0.90 P(U|s 1 ) ¼ 0.10
Strong demand, s 1
P(F|s 2 ) ¼ 0.25 P(U|s 2 ) ¼ 0.75
Weak demand, s 2

Note that the preceding probability assessments provide a reasonable degree of
confidence in the market research study. If the true state of nature is s 1 , the
probability of a favourable market research report is 0.90 and the probability of an
unfavourable market research report is 0.10. If the true state of nature is s 2 ,the
probability of a favourable market research report is 0.25 and the probability of an
unfavourable market research report is 0.75.
The reason for a 0.25 probability of a potentially misleading favourable market
research report for state of nature s 2 is that when some potential buyers first hear
about the new project, their enthusiasm may lead them to overstate their real
interest in it. A potential buyer’s initial favourable response can change quickly to
a ‘no thank you’ when later faced with the reality of signing a purchase contract and
making a down payment.
In the following discussion, we present a tabular approach as a convenient
method for carrying out the probability calculations. The calculations for the
PDC problem based on a favourable market research report (F) are summarized
in Table 13.7. The steps used to develop this table are as follows:

Step 1. In column 1 enter the states of nature. In column 2 enter the prior
probabilities for the states of nature. In column 3 enter the conditional
probabilities of a favourable market research report (F) given each state of
nature.
Step 2. In column 4 calculate the joint probabilities by multiplying the prior
probability values in column 2 by the corresponding conditional
probability values in column 3.
Step 3. Sum the joint probabilities in column 4 to obtain the probability of a
favourable market research report, P(F).
Step 4. Divide each joint probability in column 4 by P(F) ¼ 0.77 to obtain the
revised or posterior probabilities, P(s 1 |F) and P(s 2 |F).
Table 13.7 shows that the probability of obtaining a favourable market research
report is P(F) ¼ 0.77. In addition, P(s 1 |F) ¼ 0.94 and P(s 2 |F) ¼ 0.06. In particular,
note that a favourable market research report will prompt a revised or posterior
probability of 0.94 that the market demand will be strong, s 1 .

Table 13.7 Branch Probabilities for the PDC Project Based on a Favourable
Market Research Report
States of Prior Conditional Joint Posterior
Nature Probabilities Probabilities Probabilities Probabilities
P(s j ) P(F|s j ) P(F \ s j ) P(s j |F)
s j
0.8 0.90 0.72 0.94
s 1
0.2 0.25 0.05 0.06
s 2
1.0 P(F) ¼ 0.77 1.00

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