P(A or B) = P(A) + P(B) if A and B are mutually exclusive!
What is the probability of getting a Queen + the probability of getting a 7?
P(Queen) = ^{4} / _{52} and P(7) = ^{4} / _{52}.
Adding P(Queen) and P(7), ^{4} / _{52} + ^{4} / _{52} = ^{8} / _{52}, which is the probability of P(Queen or 7)!!! You might be wondering, "Does this work all the time?" It works when the two events are mutually exclusive.
If two events (call them A and B) are mutually exclusive, then the probability of A or B occuring is...
P(A or B) = P(A) + P(B)
WARNING: This only works when the two events are mutually exclusive. We will see why in this next example:
Find the probability that a card selected from a standard deck is an Ace or a heart.
P(Ace) = ^{4} / _{52}
P(heart) = ^{13} / _{52}
Note that P(Ace) and P(heart) are not mutually exclusive since they share a common card - the Ace of Hearts (colored purple above). If we add P(Ace) and P(heart) to get P(Ace or heart), we will count any card that is both an Ace and a heart twice. Therefore, we must subtract out the number of cards that are both Aces and hearts.