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The Addition Rule of Probability
(KS3, Year 7)
The Lesson
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}.It tells us that when a die is rolled, the probability of rolling a 6 is ^{1}⁄_{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?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}.
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: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 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}.
...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}.
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)
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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