Probability · Venn diagrams & set notation
Chapter 1 · 3
The idea
Probability from Venn diagrams
Why the denominator is always the total in the universal set — outsiders included — where P(A ∪ B) = P(A) + P(B) − P(A ∩ B) comes from in the picture, and how a "given that" condition shrinks the denominator to one circle.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
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Probability · Venn diagrams & set notation
Probability from Venn diagrams
Why the denominator is always the total in the universal set — outsiders included — where P(A ∪ B) = P(A) + P(B) − P(A ∩ B) comes from in the picture, and how a "given that" condition shrinks the denominator to one circle.
Why it works
A picture of the sample space
A completed Venn diagram is a picture of the whole sample space. Every member of the group sits in exactly one region of it — inside both circles, inside just one, or outside both — and nobody is counted twice or left out. That is why probabilities read straight off it: the regions cannot overlap, and between them they cover everything.Here are students, asked whether they play football () or tennis ().
Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
Start freeTakes a minute — no card.