Now you, the customer, have just bought a Surprise candy at the store but have not yet opened the box. Consider the three Bayes nets in FigureĀ 3candy-figure.

1. Which network(s) can correctly represent ${\textbf{P}}(Flavor,Wrapper,Shape)$?

2. Which network is the best representation for this problem?

3. Does network (i) assert that ${\textbf{P}}(Wrapper|Shape){\textbf{P}}(Wrapper)$?

4. What is the probability that your candy has a red wrapper?

5. In the box is a round candy with a red wrapper. What is the probability that its flavor is strawberry?

6. A unwrapped strawberry candy is worth $s$ on the open market and an unwrapped anchovy candy is worth $a$. Write an expression for the value of an unopened candy box.

7. A new law prohibits trading of unwrapped candies, but it is still legal to trade wrapped candies (out of the box). Is an unopened candy box now worth more than less than, or the same as before?

The Surprise Candy Company makes candy in
two flavors: 75% are strawberry flavor and 25% are anchovy flavor. Each
new piece of candy starts out with a round shape; as it moves along the
production line, a machine randomly selects a certain percentage to be
trimmed into a square; then, each piece is wrapped in a wrapper whose
color is chosen randomly to be red or brown. 70% of the strawberry
candies are round and 70% have a red wrapper, while 90% of the anchovy
candies are square and 90% have a brown wrapper. All candies are sold
individually in sealed, identical, black boxes.

Now you, the customer, have just bought a Surprise candy at the store
but have not yet opened the box. Consider the three Bayes nets in
FigureĀ 3candy-figure.

1. Which network(s) can correctly represent
${\textbf{P}}(Flavor,Wrapper,Shape)$?

2. Which network is the best representation for this problem?

3. Does network (i) assert that
${\textbf{P}}(Wrapper|Shape){\textbf{P}}(Wrapper)$?

4. What is the probability that your candy has a red wrapper?

5. In the box is a round candy with a red wrapper. What is the
probability that its flavor is strawberry?

6. A unwrapped strawberry candy is worth $s$ on the open market and an
unwrapped anchovy candy is worth $a$. Write an expression for the
value of an unopened candy box.

7. A new law prohibits trading of unwrapped candies, but it is still
legal to trade wrapped candies (out of the box). Is an unopened
candy box now worth more than less than, or the same as before?