I am given two events, A and B, and a new event C occurs, if and only if exactly one of A or B occurs. I need to prove;

$\displaystyle Pr(C) = Pr(A) + Pr(B) - 2Pr(A\cap B) $

So from the question, i got:

$\displaystyle Pr(C) = Pr (A \cap \bar {B}) \cup Pr(\bar{A} \cap B) $

Is that correct and a good starting point? Or am i missing something out?