Statistics · Probability
Chapter 1 · 3
The idea
Venn diagrams
Using a Venn diagram to organise events: the intersection A∩B ("and"), the union A∪B ("or"), and the complement A′ ("not"); filling in the regions from the numbers in a problem (starting with the overlap); reading probabilities off the diagram; and the addition formula P(A∪B) = P(A) + P(B) − P(A∩B).
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Statistics · Probability
Venn diagrams
Using a Venn diagram to organise events: the intersection A∩B ("and"), the union A∪B ("or"), and the complement A′ ("not"); filling in the regions from the numbers in a problem (starting with the overlap); reading probabilities off the diagram; and the addition formula P(A∪B) = P(A) + P(B) − P(A∩B).
Why it works
And, or, not — as regions
A Venn diagram draws each event as a circle inside a rectangle (the universal set , all possible outcomes). Where circles overlap, outcomes belong to both events. This turns "and / or / not" into regions you can simply count.The three set operations:
- Intersection — outcomes in both and (the overlap).
- Union — outcomes in or (or both) — everything inside either circle.
- Complement — outcomes not in — everything outside circle .
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The rest of the explanation, plus 4 worked examples you step through move by move.
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