Probability models for random events — A/L Combined Mathematics

Classical probability models define the likelihood of an event A in an equiprobable sample space S as P(A) = n(A) / n(S), satisfying Kolmogorov's axioms: (1) 0 ≤ P(A) ≤ 1 for all A; (2) P(S) = 1 and P(∅) = 0; (3) Complement Rule: P(A') = 1 - P(A); (4) The Addition Theorem: For any two events A and B: P(A ∪ B) = P(A) + P(B) - P(A ∩ B). If A and B are mutually exclusive, P(A ∩ B) = 0 and P(A ∪ B) = P(A) + P(B). Tree diagrams model multi-stage sequential experiments with branches weighted by branch probabilities, multiplying probabilities along paths and adding disjoint branch paths.

Check before you answer (A/L Applied Maths Paper 2)

1. Addition Rule Verification: Applying P(A ∪ B) = P(A) + P(B) - P(A ∩ B) without omitting the intersection term for non-exclusive events.
2. Probability Tree Diagram: Drawing fully labeled probability trees with branch probabilities summing strictly to 1 at every fork.
3. De Morgan's Laws in Probability: Applying P(A' ∩ B') = P((A ∪ B)') = 1 - P(A ∪ B) in set-theoretic probability questions.