I have a following question from a GRE test prep book:
In a probability experiment, $G$ and $H$ are independent events. The probability that $G$ will occur is $r$, and the probability that $H$ will occur is $s$, where both $r$ and $s$ are greater than $0$.
In the answer, the probability that either $G$ will occur or $H$ will occur, but not both is defined as: $r + s - 2rs$.
I thought the union of two events A and B is given as $P(A \cup B)=P(A)+P(B)-P(A \cap B)$ which in this question equates to $r+s-rs$. My questions are: Which one is correct? Does the definition of union include the probability that both events will occur?