What are the addition rule for events?

Answer»

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
= \(\frac{13}{52}+\frac{4}{52}-\frac{1}{52}\) = \(\frac{16}{52}\) = \(\frac{4}{13}\)

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