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Conditional Probability (Cambridge (CIE) IGCSE Maths) : Revision Note

Roger B

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Roger B

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Cambridge (CIE) Maths: ExtendedEdexcel Maths A (Modular): Higher Unit 1Edexcel Maths A: HigherCambridge (CIE) International Maths: Extended

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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)

Examiner Tips and Tricks

Conditional probability can be written using formal notation.

The notation straight P open parentheses A vertical line B close parentheses describes the probability of event A occurring, given that event B has already occurred.

Note that you are not expected to know this notation for the exam, but you are expected to be able to calculate conditional probabilities using Venn diagrams, tree diagrams or tables.

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 selects a multiple of three) = 3 over 9

      • 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 fourth

      • 1 possibility (6) out of only 4 possibilities (2, 4, 6, 8)

      • This is a conditional probability

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.

Find the probability that event A will occur given that event B has already occurred. Simplify your answer.

Two sets, A and B, represented on a Venn diagram

Given that B has already happened, your probability will be out of the total number in B

Find the total number in B

14 + 28 + 7 + 35 + 21 = 105

Out of this total number in B, find how many are in A

14 + 28 = 42

Form a probability by dividing 42 by 105

42 over 105

Simplify your answer

straight P open parentheses event space A space occurs space given space that space event italic space B space has space already space occured close parentheses equals 2 over 5

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    Roger B

    Author: Roger B

    Expertise: Maths Content Creator

    Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.