# Mutually Exclusive Events

Mutually exclusive events or disjoint events are the two events that don’t have anything in common. Or it can also be defined as; mutually exclusive events are the two or more than two events that cannot occur at once on a single test of an experiment.

## Mutually Exclusive Events Finding Method:

Method of intersection is used in order to find either the events are mutually exclusive or mutually inclusive events. simply find the intersection of two methods. If there is something that lies in the other events too, then it is mutually inclusive event. In case if the intersection of two or more events is a null set, then it is mutually exclusive events.

For the case, if A & B are mutually exclusive events then A n B = ø

For the case, if three events are mutually exclusive then A, B & C can be written as A n B n C = ø

## Mutually Exclusive Events Examples:

### Example 1:

Suppose a sample consists of first ten natural numbers i.e.,

Sample space = S = {1, 2, 3, 4, 5…….9, 10}

Let A be an event that is multiple of 2 = A = {2, 4, 6, 8, 10}

And B be the event of odd numbers = B = {1, 3, 5, 7, 9}

Now find the intersection of event A with B

A n B = {2, 4, 6, 8, 10} n {1, 3, 5, 7, 9} = {ø}

Result : As both events have nothing in common therefore, the two events are mutually exclusive events.

### Example 2:

A digit is selected at random from the list of first 30 digits.

Let A be the event that the randomly selected digit is multiple of 5

A = {5, 10, 15, 20, 25, 30}

And B be the event that the randomly selected digit is multiple of 9

B = {9, 18, 27}

Find either the two events are mutually exclusive events or mutually inclusive events?

Solution:

A n B = {5, 10, 15, 20, 25, 30} n {9, 18, 27} = {ø}

Result: As both events have nothing in common therefore,therefore two events A & B are mutually exclusive events.