Exhaustive Events

Exhaustive Events

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Exhaustive events

Events \(A\) and \(B\) are exhaustive if their union is the entire sample space: \(A\cup B=S\).

Exhaustive union

\[P(A\cup B)=1\]

The overlapping rectangles represent \(A\) and \(B\). Every point of \(S\) lies in at least one event; the middle strip belongs to both. Exhaustive events need not be mutually exclusive.

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