Describe events as subsets of a sample space using unions, intersections, and complements.
Sort a sample space into the four regions of a two-event Venn diagram
Problem
Using the Venn diagram, place every outcome from \(S={1,2,3,4,5,6}\) into \(A\) only, \(A\cap{}B\), \(B\) only, or \(\text{outside}~\text{both}\) when \(A={1,2,3}\) and \(B={3,4}\).
The four Venn regions form a disjoint partition of the sample space. We’ll find the overlap first, remove it to obtain each event-only region, subtract the union from the sample space for outside both, and audit that every outcome appears exactly once.
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