# 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 collective 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, the three events and are exhaustive.

__Complementary Events__

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

Thus,

or

The figure shows the event and the complement of .