CSIT 5220
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L09: Car Buyer Example
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Joe is going to buy a used car, which could be good with probability 0.8 or a
lemon with probability 0.2.

Joe's profit will be $60 if the car is good, and $-100 if it is bad.
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Before buying the car he has the option of having one test or two tests done on
it.
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The first test costs $9, and both together cost $13.
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The first test has a 90% chance of returning positive if the car is good, and
a 40% chance if it's a lemon.
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If the first test returns positive, then the second test has a 88.89% chance
of returning positive if the car is good, and a 33.33% chance if it's a lemon.
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If the first test returns negative, then the second test has a 100% chance of
returning positive if the car is good, and a 44.44% chance if it's a lemon.
How to make the decisions: whether to do the tests, and whether to buy the
car.
CSIT 5220
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The Model: Decision Graph
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Random nodes
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Condition (C): {good, lemon};
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First Test (F); Second Test (S): {not done, positive, negative}
Decision Nodes
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Do Tests (T): {none, first, both}; Buy It (B): {buy don’t buy}
Utility Nodes
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U: costs of tests; V: Profits
CSIT 5220
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The Model: Decision Graph
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Probability Distributions for random variables
P(C):
P(F|C, T)
P(S|F, C, T)
CSIT 5220
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The Model: Decision Graph
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Utility functions for utility nodes
U(T)
V(C, B)
CSIT 5220
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Analysis with Netica
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Finding optimal polices with Netica: Compile network and check “table” of
decision nodes
Best decision regarding Tests: none
CSIT 5220
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Best decision regarding Buy:
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No test: Buy
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First test: Buy if positive
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Both test: Buy if both positive
Impossible scenarios crossed out
CSIT 5220
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Analysis with Netica
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Netica can also compute expected values for different scenario: Just set the
node values, and let Netica do the rest.
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T=none
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B=buy:
Expected Value: 28

B=don’t buy
Expected Value: 0
CSIT 5220
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Analysis with Netica
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T=first
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F=positive (0.8)
 B=buy
35 (best second decision)
 B=don’t buy
-9
F=negative (0.2)
 B=buy
-45
 B=don’t buy
-9 (best second decision)