Partition of a Sample Space

Topics: Probability - Sample Space - Partition of a Set

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(definition)

We say that a collection of sets $(B_i{)}_{i\in \mathbb{N}}$ forms a partition of a sample space $\Omega$ if:

1. ${\bigcup }_{i\in \mathbb{N}}{B}_i=\Omega$

2. $B_i\cap B_j=\varnothing \forall i\ne j$ (disjoint)

From this definition, we get the total probability formula and Bayes’ formula.