Given a decision network, compute the EU of buying a book

44 Views Asked by Bumbble Comm At 26 Mar 2026 - 2:51

I am given this homework:

And this is what I have done up to now:

(a) This is the decision network for that problem

While I think the decision network is correct, I am having struggles with part (b).

Firstly I have computed the utilities based on the action $b$ (buy/not buy the book) and the (values of) random variable $p$ (Passes) this way:

If the student buys the book and passes the course, then the utility is $-100+2000 = 1900$ (i.e., $u(b,p) = 1900$)
If the student buys the book but does not pass the course, then the utility is $-100+0 = -100$ (i.e., $u(b,\neg p) = -100$)
If the student does not buy the book but passes the course, then the utility is $0+2000 = 2000$ (i.e., $u(\neg b,p) = 2000$)
If the student does not buy the book and does not pass the course, then the utility is $0+0 = 0$ (i.e., $u(\neg b,\neg p) = 0$)

Now I have to compute the expected utility of buying the book (and of not buying it), that is:

\begin{align} EU(b) & = \sum_p P(p|b) u(b,p) \\ & = 1900 \times \sum_p P(p|b) \end{align}