# Mutually Exclusive Events

How to find the probability of mutually exclusive events: formula, example, and its solution.

## Formula

Mutually exclusive events are the events

that cannot happen together.

This means P(*A* and *B*) = 0.

So, for mutually exclusive events,

use this formula:

P(*A* or *B*) = P(*A*) + P(*B*).

Probability of (*A* or *B*, Union)

## Example 1

A die has 6 sides: from 1 to 6.

So there are 6 ways to get a number.

So n(*S*) = 6.

Set the event *A* as

getting a 1.

So write {1}.

And set the event *B* as

getting an even number.

The even numbers from 1 to 6 are

{2, 4, 6}.

As you can see,

there's no number that is in both *A* and *B*.

Then write [*A* and *B*: *ϕ*].

This means

there's no number that satisfies [*A* and *B*].

So P(*A* and *B*) = 0.

So *A* and *B* are mutually exclusive events.

*A*: {1}

So n(*A*) = 1.*B*: {2, 4, 6}

So n(*B*) = 3.

n(*S*) = 6

n(*A*) = 1

n(*B*) = 3

So P(*A*) = 1/6.

And P(*B*) = 3/6.

Since you're going to add 1/6 and 3/6,

don't reduce 3/6.

Probability

*A* and *B* are mutually exclusive events.

P(*A*) = 1/6

P(*B*) = 1/2

So P(*A* or *B*) = 1/6 + 3/6.

So P(*A* or *B*) = 2/3 is the answer.

## Example 2

Numbers from 1 to 10 are given.

So there are 10 numbers

that can be picked.

So n(*S*) = 10.

Set the event *A* as

picking a number less than or equal to 2.

Those numbers are

{1, 2}.

And set the event *B* as

picking the multiples of 3.

The multiples of 3 from 1 to 10 are

{3, 6, 9}.

As you can see,

there's no number that is in both *A* and *B*.

So *A* and *B*: *ϕ*.

*A*: {1, 2}

So n(*A*) = 2.*B*: {3, 6, 9}

So n(*B*) = 3.

n(*S*) = 10

n(*A*) = 2

n(*B*) = 3

So P(*A*) = 2/10.

And P(*B*) = 3/10.

Since you're going to add 2/10 and 3/10,

don't reduce 2/10.

Probability

*A* and *B* are mutually exclusive events.

P(*A*) = 2/10

P(*B*) = 3/10

So P(*A* or *B*) = 2/10 + 3/10.

So P(*A* or *B*) = 1/2 is the answer.