Conditional Probability (Edexcel GCSE Maths): Revision Note
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Conditional Probability
What is a conditional probability?
A conditional probability is the probability of something happening (A) given that something else has already happened (B)
It is written
Pronounced "the probability of A given B"
How do I calculate conditional probabilities?
Conditional probabilities must be out of a smaller restricted set of outcomes (not out of all possible events)
For example, if a computer randomly selects a digit from 1, 2, 3, 4, 5, 6, 7, 8, 9
P(it select a multiple of three) =
This is not a conditional probability
There are 3 possibilities (3, 6, 9) out of all 9 possibilities
However, if you program the computer to only select from even numbers, then
P(it selects a multiple of three given that it selects an even number) =
1 possibility (6) out of only 4 possibilities (2, 4, 6, 8)
This is a conditional probability, written P(multiple of 3 | even) =
Examiner Tips and Tricks
Look out for conditional probability questions within larger questions on two-way tables, Venn diagrams or tree diagrams
They often use the phrase given that
Worked Example
A Venn diagram is shown below. The numbers represent numbers of people.
When 1 random person is selected, find , simplifying your answer.

means the probability that A is true, given that B is true
Given that B is true, your probability will be out of the total number in B
Find the total number in B
63 + 42 = 105
Out of this total number in B, find how many are in A
42
Form a probability by dividing 42 by 105
Simplify your answer
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