probability priority of comma and bar In probability does , have priority over |?
I am asking because of below question.
Is below X and (Y given by Z)?
P(X,Y|Z)
or is it (X and Y) given by Z?

The sign | denote the conditional probability. It is not an operation on the events. This sign does not refer to events, but to probability. And if $X,Y,Z$ are some events, then $P(X,Y \mid Z)$ is the conditional probability of the event $X\cap Y$, conditioning on the event $Z$. 
