When two events are mutually exclusive, we can find the probability of either of them occurring by adding together the separate probabilities.
Ex. The probability of throwing a 3 or a 5 with a dice is
P(3) + P(5) = \(\frac{1}{6}+\frac{1}{6}\) = \(\frac{2}{6}\) = \(\frac{1}{3}\).
Note. Addition rule in case of events which are not mutually exclusive.
Ex. From a well shuffled pack of 52 cards, a card is drawn at random. Find the probability that it is either a spade or a queen.
Sol. Let A be the event of getting a spade and B be the event of getting a queen.
A and B are not mutually exclusive as there is a queen of spades also, so P(either a spade or a queen) = P(spade) + P( queen) – P( queen of spade
= \(\frac{13}{52}+\frac{4}{52}-\frac{1}{52}\) = \(\frac{16}{52}\) = \(\frac{4}{13}\) |
