Addition and Multiplication Rules of Probability

Topic Content:

The addition rule of probability is used to determine the probability of two or more events occurring, either individually or in combination.

There are two forms of the rule:

Mutually Exclusive Events:

Two or more events are said to be mutually exclusive if one outcome prevents another from occurring. If events A and B are mutually exclusive, the probability of A or B occurring is the sum of their individual probabilities.

P(A or B) = P(A) + P(B) = P(A ∪ B)

Note: If a question has the word ‘or’ or ‘either/or’, use the addition rule to solve it.

Since mutually exclusive events cannot happen at the same time, their intersection is an empty set (∅). In other words, if one event occurs, the other cannot. This is often represented in a Venn diagram with no overlapping circles.

Example 7.1.1:

A bag contains three red balls, four blue balls, five white balls and six black balls. A ball is picked at random. What is the probability that it is either:

(a) red or blue
(b) red or white
(c) blue or white
(d) blue or black
(e)