TITLE: Proof of Probability of Set Difference
QUESTION [6 upvotes]: I've been trying to figure out a rigorous proof for the following identity but I'm getting nowhere:
$P[A\setminus B]=P[A]-P[A \cap B]$
It seems obvious with Venn diagrams but I'm interested in a formal proof for this. Any help and/or hints appreciated!

REPLY [9 votes]: If two sets $E_1$ and $E_2$ are disjoint, then $P(E_1 \cup E_2) = P(E_1) + P(E_2)$. Apply this to $E_1=A \cap B$ and $E_2=A \setminus B$.