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10
6. (18 points)
Bayes’ Nets: The Mind of Pacman
Pacman doesn’t just eat dots. He also enjoys pears, apples, carrots, nuts, eggs and toast. Each morning, he
chooses to eat some subset of these foods. His preferences are modeled by a Bayes’ net with this structure.
A
B
C
D
E
A
E
C
A
E
C
P
C
E
T
N
A
a) (2 pt)
Factor the probability that Pacman chooses to eat only apples and nuts in terms of conditional
probabilities from this Bayes’ net.
P
(
¬
p,a,
¬
c,n,
¬
e,
¬
t
) =
P
(
a
)
·
P
(
¬
p

a
)
·
P
(
¬
c

a
)
·
P
(
n
¬
p,
¬
c
)
·
P
(
¬
t
¬
c
)
·
P
(
¬
e

n,
¬
t
)
b) (4 pt)
For each of the following properties, circle whether they are
true
,
false
or
unknown
of the distribution
P
(
P,A,C,N,E,T
) for this Bayes’ net.
Without the conditional probability tables, we do not know if any two variables are dependent. From the
network topology, we can only conclude
true
or
unknown
for the questions below.
N
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 Spring '08
 Staff
 Artificial Intelligence

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