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226 Revising judgments in the light of new information
Events
Prior probabilities Conditional probabilities
Low sales
High sales
0.6
0.4
Expected utility = 0.68
Hold small stocks
Hold large stocks
Expected utility = 0.6
New information
0.2
Forecast of high sales
0.75
Forecast of high sales
Expected utility = 0.755
Hold small stocks
Hold large stocks
Expected utility = 0.85
Low sales
High sales
Low sales
High sales
(a)
Joint probabilities
0.4 × 0.2 = 0.08
0.6 × 0.75 = 0.45
p(forecast of high sales) = 0.53
(b)
0.15
Low sales
High sales
0.85
0.15
Low sales
High sales
(c)
0.4
0.6
0.4
0.6
0.85
Profit
$80000
$140000
$20000
$220000
Profit
$80000
$140000
$20000
$220000
Utility
Posterior probabilities
0.08
= 0.15
0.53
0.45
= 0.85
0.53
Utility
Figure 8.7 – (a) A decision tree for the retailer’s problem based on prior probabilities;
(b) applying Bayes’ theorem to the retailer’s problem; (c) a decision tree for the retailer’s
problem using posterior probabilities
0.5
0.8
0
1.0
0.5
0.8
0
1.0