# The Addition Rule of Probability(KS3, Year 7)

Probability tells us how likely (how 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 16. It tells us that when a die is rolled, the probability of rolling a 6 is 16. Imagine we wanted to find the probability of rolling a 1 or rolling a 6.

To find a probability of one event or another event...
Probability of 1 or Probability of 6
...replace the or with a +...
Probability of 1 + Probability of 6

## Question

What is the probability of rolling a 1 or rolling a 6 on a die?

## 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

Find the probability of rolling a 1. The probability of rolling a 1 is 16.

## 4

Find the probability of rolling a 6. The probability of rolling a 6 is 16.

## 5

Substitute the probability of rolling a 1 (16) and rolling a 6 (16) into the formula.
16 + 16 = 26

The probability of rolling a 1 and rolling a 6 is 26.

## A Formula for the Addition Rule of Probability

The formula for finding the probability of event A or event 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?

## 1

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.
We can rewrite the addition rule:
P(R and B) = P(R) + P(B)

## 3

Find the probability of the spinner coming to rest at Red. There are 2 ways of the spinner stopping at Red...

...out of 8 equally probable outomes. The probability of the spinner stopping at Red is 28. P(R) = 28.

## 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 38. P(B) = 38.

## 5

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

P(R or B) = 28 + 38

P(R or B) = 58

## 6

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

The probability of spinning a Red or a Blue is 58. We have expressed the probability as a fraction. We can also express this as a number (0.625) or a percentage (62.5%).

## Lesson Slides

The slider below another real example of using the addition rule of probability. In this example, the probability of three events is found using the addition rule.

## Or = +

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

## The Addition Rule Is for Mutually Exclusive Events

The addition rule works for mutually exclusive events.

## A Note on Notation

The probability of an event can be written as:
P(Event)
A letter or symbol can be used to represent an event. For example, let H be the event that a coin lands on Heads when it has been tossed. We can denote the probability of getting heads as:
P(H)

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