Verify an identity in probability Verify the identity:
$$P(A\cup B)=P(A)+P(B\cap A')$$
I could verify using the Venn diagram. Is there another way?

$A\cup B=A\cup(B\cap A^c)$ where $A$ and $B\cap A^c$ are disjoint.
So if we are dealing with measurable sets then $$P(A\cup B)=P(A\cup(B\cap A^c))=P(A)+P(B\cap A^c)$$
