# Exhaustive and Complementary Events

__Exhaustive Events__:

When a sample space is partitioned into some mutually exclusive events such that their union is the sample space itself then the events are called exhaustive events or collectively events.

Suppose a die is tossed and the sample space is

Let

Hence the events and are mutually exclusive because and . As shown in the figure three events and which are exhaustive.

and

__Complementary Events__:

If is an event defined in the sample space , then is denoted by and is called complement of .

Thus,

or

In the figure shown that the event and the complement of .