It is important that the events be disjoint: i.e., that there is no way for \(A\) and \(B\) to both happen at the same time. For example, a standard deck of 52 cards contains \(26\) red cards and \(12\) face cards. However, the number of ways to select a card which is either red or a face card is not \(26 + 12 = 38\text{.}\) This is because there are 6 cards which are both red and face cards.
in-context