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 1⁄6. die_1 It tells us that when a die is rolled, the probability of rolling a 6 is 1⁄6. die_6 Imagine we wanted to find the probability of rolling a 1 or rolling a 6.

The Addition Rule

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
This is the addition rule.

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?
1 and 6

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

Find the probability of rolling a 1. die_1 The probability of rolling a 1 is 1⁄6.

4

Find the probability of rolling a 6. die_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 or event B is shown below:

P(A_or_B)_formula 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?
addition rule example

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.
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...

addition rule step 3 1...out of 8 equally probable outomes. addition_rule_step_3_2 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. addition_rule_step_4 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. addition_rule_answer 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.

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)
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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This page was written by Stephen Clarke.