I am trying to study the book Reinforcement Learning: An Introduction (Sutton & Barto, 2018). In chapter 3.1 the authors state the following exercise
Exercise 3.5 Give a table analogous to that in Example 3.3, but for $p(s',r|s,a)$. It should have columns for $s$, $a$, $s'$, $r$, and $p(s',r|s,a)$, and a row for every 4-tupel for which $p(s',r|s,a)>0$.
The following table and graphical representation of the Markov Decision Process is given on the next page.
I tried to use $p(s'\cup r|s,a)=p(s'|s,a)+p(r|s,a)-p(s' \cap r|s,a)$ but without a significant progress because I think this formula does not make any sense as $s'$ and $r$ are not from the same set. How is this exercise supposed to be solved?
Maybe this exercise intends to be solved by using
the resulting system is a linear system of 30 equation with 48 unknowns. I think I am missing some equations...