Events
Complement of an Event of an Experiment
The dictionary definition of "complement" is something that completes to make a perfect whole. The complement of an event E consists of all the outcomes in the associated experiment that are not in E. This means the union of E together with its complement comprises the experiment's entire sample space S (the perfect whole in this case).
In this tutorial, we will use EC to denote the complement of an event E.
Probability of the Complement of an Event
The probability of EC, the complement of the event E, is simply the probability that E won't happen. We will use the Addition Rule of Probability to deduce this.
First, we observe that E and EC are mutually exclusive events. There are no outcomes in the sample space S which belong to both E (green area) and its complement (blue
area). The Venn diagram for these events is as follows.
The Addition Rule for mutually exclusive events gives us that:
P(S) = P(E or EC) = P(E) + P(EC) = 1 or P(EC) = 1 - P(E) .
Examples
Example using the Addition Rule
Example using the Marginal Probabilities
Last Updated by SAS October 07, 2026, 16:00:54
