Question

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 (A and B) have no overlap (no shared region). Non - mutually exclusive (B and C) have an overlap (shared region).

Step2: Analyze Each Diagram

• First Diagram: A and B overlap, so A and B not mutually exclusive. Eliminate.
• Second Diagram: A and B overlap (not mutually exclusive), B and C don't overlap (mutually exclusive). Eliminate.
• Third Diagram: A and B don't overlap (good for mutual exclusivity), B and C don't overlap (bad, need non - mutual). Eliminate.
• Fourth Diagram: A and B don't overlap (mutually exclusive), B and C overlap (non - mutually exclusive). Correct.

Answer:

The Fourth Venn Diagram (the right - most one with A, B, C where A and B don't overlap, B and C overlap)