The diagram shows the probability distribution of a two step process. Each branch represents a particular outcome.
I guess it's been solved but I just want to clarify the notation.
p(B'|A') represents the probability of B' given A' happened. Since B' occurs after A' just read the probability branch of B' after A'
(If you needed the probability of (A'|B'), that's a longer process which can be discussed at a later time.)
p(B'∩A') is the probability of both events happening.
Since only one path satisfies both happening and both events are steps in a process we multiply the probability of the separate events to get the probability.
