# Exhaustive Events

# Definitions

When a sample space is distributed down into some mutually exclusive events such that their union forms the sample space itself, then such events are called exhaustive events.

OR

When two or more events form the sample space collectively than it is known as collectively exhaustive events.

OR

When atleast one of the events occur compulsorily from the list of events, then it is also known as exhaustive events.

## Solved Examples of Exhaustive Events

Let explain it with very simple example. After looking at these examples, reader will also get a very clear cut idea about mutually exclusive events.

### Example 1:

A sample space is given

**Sample space = S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}**

To understand what exhaustive events are?

Let an event **x = {1, 2, 3}**

** Event y = {4, 5, 6}**

** Event z = {7, 8, 9, 10}**

**Solution:**

Event x, y, z are mutually exclusive events because;

X n y n z =øNow check whether the events are exhaustive events or not?

For this, take the union of all events;

x u y u z = {1, 2, 3} u {4, 5, 6} u {7, 8, 9, 10} = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} = SEvent x, y & z are exhaustive events, because they form a complete sample space itself.

### Example 2:

A coin is tossed. Tell whether the events are exhaustive events or not?

Where;

Event X = If Head will appear

Event y = If tail will appear

**Solution:**

Both events together are exhaustive events, because one will occur during the conduct of an experiment.