Probability of A or B (1 of 3)

---

If events A and B are mutually exclusive, then the probability of A or B is simply:

p(A or B) = p(A) + p(B).

What is the probability of rolling a die and getting either a 1 or a 6? Since it is impossible to get both a 1 and a 6, these two events are mutually exclusive. Therefore,

p(1 or 6) = p(1) + p(6) = 1/6 + 1/6 = 1/3

If the events A and B are not mutually exclusive, then

p(A or B) = p(A) + p(B) - p(A and B).

The logic behind this formula is that when p(A) and p(B) are added, the occasions on which A and B both occur are counted twice. To adjust for this, p(A and B) is subtracted. What is the probability that a card selected from a deck will be either an ace or a spade? The relevant probabilities are:

p(ace) = 4/52
p(spade) = 13/52