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
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