Question

identifying a venn diagram
events a and b are mutually exclusive. events b and c are non - mutually exclusive. which venn diagram could represent this description?

Explanation:

Step1: Recall Mutually Exclusive Definition

Mutually exclusive events have no overlapping (intersection is empty). So A and B should not overlap. Non - mutually exclusive events have an overlapping (intersection is non - empty), so B and C should overlap.

Step2: Analyze Each Diagram

• First diagram: A and B overlap (so A and B are not mutually exclusive) → Eliminate.
• Second diagram: A and B overlap (so A and B are not mutually exclusive) → Eliminate.
• Third diagram: A and B do not overlap (good for mutual exclusivity), but B and C do not overlap (bad for non - mutual exclusivity of B and C) → Eliminate.
• Fourth diagram: A and B do not overlap (satisfies mutual exclusivity of A and B), B and C overlap (satisfies non - mutual exclusivity of B and C) → This is the correct one.

Answer:

The fourth Venn diagram (the one where A and B are separate, and B and C overlap).