AQA · Mathematics · 8300
GCSE Maths: Venn Diagrams
Probability · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Venn Diagrams (Corbettmaths Video 380), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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What does the symbol ξ represent in a Venn diagram?
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The universal set — every element under consideration (everything inside the rectangle).
What does A ∩ B mean?
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The intersection of A and B — elements that are in both A and B (the overlap region).
What does A ∪ B mean?
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The union of A and B — elements that are in A, in B, or in both.
A' denotes the ? of set A — every element of ξ that is not in A.
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complement
If ξ = ?, A = multiples of 3, B = multiples of 5, what is P(A ∩ B)?
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1/16 — only 15 is a multiple of both 3 and 5.
Formula for the number of elements in A ∪ B?
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n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Subtract the overlap so it is not counted twice.
110 workers: 90 like tea, 41 like coffee, 25 like both. How many like neither?
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4. Tea or coffee = 90 + 41 − 25 = 106, so 110 − 106 = 4.
38% visited Canada, 80% France, 11% neither. What percentage visited both?
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29%. At least one = 89%, so both = 38 + 80 − 89 = 29%.
How do you fill in the 'only A' region of a Venn diagram from n(A) and n(A ∩ B)?
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Only A = n(A) − n(A ∩ B). Always fill the intersection first, then subtract it from each set total.
How is the conditional probability P(B | A) read from a Venn diagram?
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P(B | A) = n(A ∩ B) ÷ n(A): restrict to the A circle and take the fraction of it that lies in B.
Which Venn region does A ∩ B' represent?
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The part of A outside B — elements in A only.
100 gym visitors: 18 spinning, 10 both classes, 56 neither. P(attended only circuits)?
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26/100 = 13/50. Only spinning = 8; circuits total = 100 − 56 − 8 = 36; only circuits = 36 − 10 = 26.
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