5.3.3—Exclusive and independent events
- Syllabus
- 9709–2028–2029
- Objective
- 5.3.3
- Level
- AS
Mutual exclusivity and independence describe different relationships
Events are mutually exclusive when A∩B=∅. They are independent when P(A∩B)=P(A)P(B), equivalently P(A|B)=P(A) when defined.
Disjoint non-zero events cannot be independent: learning that one occurred makes the other impossible. Test the stated relationship with the correct equation.
A single die roll being even and odd is mutually exclusive; two independent coin tosses are not mutually exclusive across different tosses.
“Independent” does not mean unrelated in everyday language, and mutually exclusive events are not independent unless one has probability zero.
ConceptA-Level CAIE Mathematics AS