Suppose we have events $A$ and $B$. We want to write the probability that exactly one of the events $A,B$ occurs in terms of $P(A),P(B)$ and $P(A \cap B)$ only
My thought: Since I want only one occurring, $A$ or $B$, we must find $P(A \cup B)$ which equals $P(A) + P(B) - P(A \cap B)$.. However, on my answer sheet it says the answer is $P(A) + P(B) - 2P(A \cap B )$. Am I missing something?