P4ProbabilityFoundation & Higher

Venn Diagrams

A Venn diagram sorts things into overlapping circles. They make “and”, “or” and “not” probability questions visual — once the diagram is filled in, you just count.

40 min Video by GCSE Maths AQA GCSE Maths

Probability using Venn DiagramsWatch the walkthrough, then read the notes below.

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What you'll learn

Fill in a Venn diagram
Use set notation: ∪, ∩, and complement
Find probabilities from a Venn diagram
Handle the overlap correctly

Filling in the regions

Always start with the $intersection$ (the overlap) and work outwards, so items are not double-counted. The numbers in all regions should add to the total.

1Both = 5 goes in the overlap.

2Only maths

= 12 - 5 = 7

Answer7

Set notation

$A \cup B$ means “A or B” (everything in either circle). $A \cap B$ means “A and B” (the overlap). $A^{'}$ means “not A”. Probabilities come from counting the right region over the total.

A \cup B (or), A \cap B (and), A^{'} (not)

Set notation for Venn diagrams.

Tip — Fill the overlap first to avoid counting people twice.

Remember these

A \cap B = overlap (and)

Intersection.

A \cup B = either circle (or)

Union.

Watch out for these

Putting the full totals in the circles, ignoring the overlap.

Subtract the overlap so each region is counted once.

Confusing ∪ (or) with ∩ (and).

∪ = union (or); ∩ = intersection (and).

Key takeaways

Fill the overlap (intersection) first.
∪ = or, ∩ = and, A′ = not.
Probability = count of a region ÷ total.

Test yourself

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