Venn Diagrams with Conditional Probability (Edexcel International A Level (IAL) Maths): Revision Note

Exam code: YMA01

Author

Paul

Last updated

24 June 2025

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Venn diagrams with conditional probability

How do I find conditional probabilities from a Venn diagram?

Interpreting questions in terms of OR ( $\cup$ ), AND ( $\cap$ ), complement ( ‘ ) and “given that” ( | )
Conditional probability may now be involved too
Use mini-Venn diagrams to sketch and shade the regions you are dealing with – use different colours if available or different styles of shading if not
- Shading can help you see the answer
since $P (A | B) = \frac{P (A \cap B)}{P (B)}$ shade B first, then shade $A \cap B$
- the answer will then be $\frac{" double shading "}{" all shading "}$

Worked Example

Three events, $A, B$ and $C$ are such that

events $A$ and $C$ are mutually exclusive

$P (A \cap B) = 0.2 P (B \cap C) = 0.3 P ((A \cup B \cup C)') = 0.1 P (B) = 0.7 P (A') = 0.75 .$

(a) Draw a complete Venn diagram to show the probabilities connecting the three events.

(b) Find

(i) $P (A | B)$

(ii) $P (A' | C')$

(iii) $P (C | (A \cup B)')$

3-2-2-fig2-we-solution-part-2-luggage-removed

Examiner Tips and Tricks

Always draw the box in a Venn diagram; it represents all possible outcomes of the experiment so is a crucial part of the diagram, the bubbles merely represent the events we are particularly interested in
You may be able to answer some questions by applying formulae or you may prefer to use shaded mini-Venn diagrams; complicated questions tend to be easier with mini-Venn diagrams

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Venn Diagrams with Conditional Probability (Edexcel International A Level (IAL) Maths): Revision Note

Venn diagrams with conditional probability

How do I find conditional probabilities from a Venn diagram?

Ready to test your students on this topic?

Data Presentation & Interpretation

Statistical Measures

Basic Statistical Measures

Frequency Tables

Standard Deviation & Variance

Coding Data

Statistical Modelling

Working with Data

Data Presentation

Stem & Leaf Diagrams

Box Plots

Histograms

Outliers

Interpreting Data

Skewness

Correlation & Regression

Scatter Diagrams

Correlation & Regression

Coding Bivariate Data

Probability

Basic Probability

Calculating Probabilities & Events

Venn Diagrams

Tree Diagrams

Further Probability

Conditional Probability

Venn Diagrams with Conditional Probability

Tree Diagrams with Conditional Probability

Probability Formulae

Statistical Distributions

Discrete Random Variables

Discrete Probability Distributions

E(X) & Var(X) (Discrete)

aX+b

Discrete Uniform Distribution

Normal Distribution

The Normal Distribution

Standard Normal Distribution

Calculations with Normal Distributions

Finding the Parameters of a Normal Distribution

Author: Paul