# 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.