I have this:
$$X_1 = \left \{ \begin{matrix} 0 & \overline{E_2} \\ 1 & E_2 \end{matrix}\right.$$$$ X_2 = \left \{ \begin{matrix} 1 & \overline{E_2} \cap \overline{E_3} \\ 2 & \overline{E_2} \cap E_3 \\ 3 & otherwise\end{matrix}\right. $$
And I'm asked to calculate the probabilities $P(X_2,X_1)$ and $P(X_2|X_1)$
But I don't know what the comma or the | mean here.
Is the comma something like all possible combinations, for example $P(X_2=1, X_1=0), ... , P(X_2=3, X_1=1)$? As fot the bar I don't have a guess.
Yes, your guess for the first part is correct. For the second part you have to find $P(X_2=1|X_1=0)=\frac {P(X_2=1,X_1=0)} {P(X_1=0)}$ etc.