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Revision notes
Combine conditional probability with restricted, repeated and circular arrangements under an explicit sampling convention.
Key ideas
- Counting and conditional probability
Choose counting structures, interpret event regions and conditional trees, and use the observed condition as the reference set.
- Restricted line arrangements
Count lines of distinct objects with together, apart, position and order restrictions, then turn the counts into probabilities.
- Repeated and circular arrangements
Count restricted repeated and circular outcomes, then condition probabilities on the actual selection and seating experiment.
From the GCE A-Level H2 Mathematics 2027 syllabus
- Include: addition and multiplication principles for counting; permutations nPr and combinations nCr; arrangements of objects in a line or circle, including repetition and restrictions; addition and multiplication of probabilities; mutually exclusive and independent events; tables of outcomes, Venn diagrams, tree diagrams, permutations and combinations to calculate probabilities; conditional probabilities in simple cases; P(A′) = 1 − P(A); P(A ∪ B) = P(A) + P(B) − P(A ∩ B); P(A|B) = P(A ∩ B)/P(B).