For any two events $A$ and $B$, the probability that exactly one of th…

Question

For any two events $A$ and $B$, the probability that exactly one of them occurs is

Accepted Answer

A. $P(A)+P(B)-2P(A\cap B)$

Exactly one of $A$ or $B$ means either $A$ occurs without $B$, or $B$ occurs without $A$. So
$$P(	ext{exactly one})=P(A\cup B)-P(A\cap B).$$
Using $P(A\cup B)=P(A)+P(B)-P(A\cap B)$ gives $P(A)+P(B)-2P(A\cap B)$.

Answer

$P(A\cap B)$

Answer

$P(A\cup B)+P(A\cap B)$

Answer

$1-P(A\cup B)$