Events of a random experiment — A/L Combined Mathematics

What must I remember about Events of a random experiment?

• Random Experiment: An experiment whose outcome cannot be predicted with certainty in advance, but whose set of all possible outcomes is completely known beforehand.
• Sample Space S: The set of all possible fundamental outcomes of a random experiment; discrete (finite or countably infinite) or continuous.
• Event: Any subset E of the sample space S (E ⊆ S); occurs if the actual experiment outcome belongs to E; Simple / Elementary event contains a single outcome; Compound event contains two or more outcomes.
• Special Events: Null / Impossible Event ∅ (can never occur, P(∅) = 0); Sure / Certain Event S (always occurs, P(S) = 1); Complementary Event E' (event 'E does not occur', E ∩ E' = ∅ and E ∪ E' = S).
• Set Operations on Events: Union A ∪ B ('A or B or both'); Intersection A ∩ B ('both A and B occur'); Mutually Exclusive (disjoint) events cannot occur simultaneously: A ∩ B = ∅; Exhaustive events cover entire sample space: A ∪ B = S.

Test yourself (1 minute)

1. De Morgan's Laws for Events

   (A ∪ B)' = A' ∩ B' (neither A nor B occurs); (A ∩ B)' = A' ∪ B' (at least one does not occur).

2. Relative complement (Difference of events)

   A - B = A ∩ B' (event A occurs but B does not); P(A ∩ B') = P(A) - P(A ∩ B).

3. Venn diagram visualization

   Always sketch overlapping Venn circles for events A and B to partition sample space into four disjoint subsets: A ∩ B', A ∩ B, A' ∩ B, and A' ∩ B'.

Practise Events of a random experiment questions today

Source: NIE G.C.E. (A/L) Combined Mathematics Resource Book - Applied Mathematics, Unit 7

What should I study first?

What comes next?

Next in the syllabus

Where does Events of a random experiment fit in the syllabus?

Year 2 · Term 3