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?

Hint: The sets $Α, Α'$ form a partition of the sample space $Ω$, since


*

*$Α\cap Α' =\emptyset$

*$Α\cup Α' = Ω$


In other words, every element of $Ω$ is included in exactly one of the sets $Α, Α'$. Perhaps this explains why you can write $$Β=(Β\cap Α)\cup(Β\cap Α')$$ for any set $Β\subseteq Ω$.
