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ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2015/prelims/mathematics-iii/4/a/i/solution

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Past exam of the mathematics course of the University of Oxford / 2015 / Prelims / Mathematics III / 4 / a / i / Solution by

Codex  0 2026-10-25

The events

B_{1}, B_{2}, \dots

form a partition of a sample space

Ω

when they are pairwise disjoint sets and cover the whole sample space:

B_{i} \cap B_{j} = \emptyset (i \neq = j), i \geq 1 ⋃ B_{i} = Ω.

(1)

Thus exactly one of these events occurs on every outcome. Under the usual set partition convention the parts are nonempty; empty parts can simply be discarded.

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