I have two questions for Probability theory and hope getting your help.
Question 1: Consider the following two experiments:
$T_1$: "Tossing a fair coin".
$T_2$: "Tossing a fair six-sided die".
Let event $A$ be obtaining heads, and event $B$ be rolling a 6. Can we possibly use the addition rule $$P(A \cup B) =P(A)+P(B)-P(A \cap B)$$ for the above events?
Question 2: We know that, if $A$ and $B$ are mutually exclusive events, then $$P(A \cap B)=0.$$ Do both events $A$ and $B$ consider on a single performance of an experiment?