Probability

Venn Diagrams and Set Notation

Represent sets visually and calculate probabilities from regions.

Probability overviewTree diagramsConditional probability

Key notation

Intersection\[A\cap B\]
Union\[A\cup B\]
Complement\[A'\]
Neither\[(A\cup B)'\]
ABA∩BUniversal set U
The overlap represents outcomes that are in both sets.

Worked example

In a class of 30 students, 18 study French, 14 study Spanish and 8 study both. Find how many study neither language.

  1. Use inclusion-exclusion: \(n(F\cup S)=n(F)+n(S)-n(F\cap S)\).
  2. So \(n(F\cup S)=18+14-8=24\).
  3. Therefore \(30-24=6\) students study neither.
Common mistake: do not add the overlap twice.

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