Pairwise versus mutual independence

Pairwise independence versus mutual independence in probability

This is an easy probability question that tests whether you can distinguish between two related but different concepts: pairwise independence and mutual independence. It is a common source of confusion even among candidates with solid probability foundations, and firms use it to check conceptual clarity rather than computational skill.

Pairwise independence means that any two events in a set are independent of each other. Mutual independence is stronger: it requires that all events are independent of each other, and moreover that any subset of events remains independent. A set of events can satisfy pairwise independence without satisfying mutual independence. Working through this question requires you to verify independence by checking whether conditional probabilities match unconditional ones, and to recognize when one condition holds but the other does not.

• Definition of independence: P(A ∩ B) = P(A) × P(B)
• Checking independence across pairs versus all combinations
• The distinction between joint and marginal independence