Mutually Exclusive Events

Two or more events are mutually exclusive if one outcome prevents another outcome from happening. E.g. if you throw a coin, you can only obtain one side at a time i.e. a tail or head. Therefore, throwing a coin is mutually exclusive. 

If events P and Q are mutually exclusive, then the probability of P or Q is: 

P (P or Q) = P (P) + P (Q)

This is called the addition Rule or the OR rule. When you use OR, you add. 

Note: If a question contains the word “or” or “either/or”, use the addition rule to solve it.

Example 10.4.1:

If 7 women, 2 men, 5 girls, and 6 boys have an equal chance of winning a game. What is the probability that:
(a) a boy will win first,
(b) a girl or woman or a man will win first? 

Solution