A set of events E1, E2, ..., En represents partition of a sample space S, if
- Ei ∩ Ej = Φ, i ≠ j, i, j = 1, 2, 3, ...........n
- E1 ∪ E2 ∪ E3 ∪ ... ∪ En = S and
- P(Ei) > 0, ∀ i = 1, 2, 3, ..., n
In other words, the events E1, E2, ..., En represent a partition of the sample space S if they are pairwise disjoint, exhaustive and have non-zero probabilities.
Example :
Any non-empty event E and its complement £' form a partition of the sample space S.
∵ E ∩ E'= Φ
and E ∪ E' = S
