*probable*) it is an event will happen. For example, it tells us that when a die is rolled, the probability of rolling a

**1**is

**. It tells us that when a die is rolled, the probability of rolling a**

^{1}⁄_{6}**6**is

**. Imagine we wanted to find the probability of rolling a**

^{1}⁄_{6}*1*

**or**rolling a

*6*.

## The Addition Rule

To find a probability of one event**or**another event...

Probability of 1

...replace the **or**Probability of 6**or**with a

**+**...

Probability of 1

This is the addition rule.
**+**Probability of 6## How to Find the Probability of an Event __or__ Another Event

## Question

What is the probability of rolling a**1**or rolling a

**6**on a die?

## Step-by-Step:

## 1

Write down what we are trying to find out.

Probability of rolling a 1

**or**Probability of rolling a 6## 2

Replace

**or**with**+**.
Probability of rolling a 1

**+**Probability of rolling a 6## 3

## 4

Find the probability of rolling a

**6**. The probability of rolling a**6**is**.**^{1}⁄_{6}## 5

Substitute the probability of rolling a 1 (

^{1}⁄_{6}) and rolling a 6 (^{1}⁄_{6}) into the formula.^{1}⁄

_{6}

**+**

^{1}⁄

_{6}=

^{2}⁄

_{6}

## Answer:

The probability of rolling a**1**and rolling a

**6**is

^{2}⁄

_{6}.

## A Formula for the Addition Rule of Probability

The formula for finding the probability of event**A**event

__or__**B**is shown below:

Let's use the formula in an example.

## Question

A spinner will spin and come to rest pointing at a colour.What is the probability of the spinner pointing at red or blue?

## Step-by-Step:

## 1

Start with the formula.

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

## 2

Define the events in our example.

- Let
**R**be the event of the spinner coming to rest at Red.**P(R)**is the probability of spinning Red. - Let
**B**be the event of the spinner coming to rest at Blue.**P(B)**is the probability of spinning Blue.

P(R and B) = P(R) + P(B)

## 3

Find the probability of the spinner coming to rest at Red.
There are

...out of

**2**ways of the spinner stopping at**Red**......out of

**8**equally probable outomes. The probability of the spinner stopping at**Red**is**.**^{2}⁄_{8}**P(R) =**.^{2}⁄_{8}## 4

Find the probability of the spinner stopping at

**Blue**. There are**3**ways of the spinner stopping at**Blue**our of**8**equally probably outcomes. The probability of the spinner stopping at**Blue**is**.**^{3}⁄_{8}**P(B) =**.^{3}⁄_{8}## 5

Substitute the probability of spinning a Red and the probability of spinning a Blue into the formula.

P(R or B) = ^{2}⁄_{8} + ^{3}⁄_{8}

P(R or B) = ^{5}⁄_{8}

## 6

Simplify the fraction if possible. (The fraction in our example is already as simple as possible).

## Answer:

The probability of spinning a**Red**or a

**Blue**is

^{5}⁄

_{8}. We have expressed the probability as a fraction. We can also express this as a number (0.625) or a percentage (62.5%).

## Top Tip

## Or = +

*P(A*=

**or**B)*P(A)*

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

**+**

## Beware

## The Addition Rule Is for Mutually Exclusive Events

The addition rule works for mutually exclusive events.## Note

## A Note on Notation

The probability of an event can be written as:*P(Event)*

**H**be the event that a coin lands on

**H**eads when it has been tossed. We can denote the probability of getting heads as:

*P(H)*

## You might also like...

probabilityunderstanding mutually exclusive eventsunderstanding complementary eventsunderstanding tree diagrams

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