Consider a student who has the choice to buy or not buy a textbook for a course. We’ll model this as a decision problem with one Boolean decision node, $B$, indicating whether the agent chooses to buy the book, and two Boolean chance nodes, $M$, indicating whether the student has mastered the material in the book, and $P$, indicating whether the student passes the course. Of course, there is also a utility node, $U$. A certain student, Sam, has an additive utility function: 0 for not buying the book and -$100 for buying it; and $2000 for passing the course and 0 for not passing. Sam’s conditional probability estimates are as follows:
You might think that $P$ would be independent of $B$ given $M$, But this course has an open-book final—so having the book helps.
Draw the decision network for this problem.
Compute the expected utility of buying the book and of not buying it.
What should Sam do?