Events of a random experiment — A/L Combined Mathematics

A random experiment is an observational procedure whose outcome cannot be predicted with certainty, but whose set of all possible outcomes—the sample space S—is known beforehand. An event A is a subset of the sample space (A ⊆ S). Elementary events contain a single outcome, while compound events contain multiple outcomes. Key set-theoretic operations define event relationships: (1) Complement A': event that A does not occur; (2) Union A ∪ B: event that at least one of A or B occurs; (3) Intersection A ∩ B: event that both A and B occur simultaneously; (4) Mutually Exclusive Events: A and B cannot occur together (A ∩ B = ∅); (5) Exhaustive Events: their union spans the entire sample space (A ∪ B = S).

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

1. Sample Space Specification: Listing or describing all elements of the sample space S with proper set bracket notation.
2. Venn Diagram Representation: Correctly drawing and shading event regions (A ∩ B, A ∪ B, A ∩ B') on a standard universal rectangle.
3. Mutually Exclusive vs Independent: Distinguishing clearly between mutually exclusive events (A ∩ B = ∅, cannot happen together) and independent events (occurrence of one does not affect the other).