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If the intersection of two events is nonempty, it means they can occur simultaneously. However, this only means they might possibly be independent; it does not guarantee independence, as strong dependencies like subset relationships can still exist.

Conditions: Events A and B have a non-empty intersection ($AB \neq \emptyset$).

If the intersection of two events is nonempty, it means they can occur simultaneously. However, this only means they might possibly be independent; it does not guarantee independence, as strong dependencies like subset relationships can still exist.

Conditions: Events A and B have a non-empty intersection ($AB \neq \emptyset$).

A non-empty intersection means the events can occur simultaneously, but it does not guarantee independence. If one event is a subset of the other, the occurrence of the first strictly dictates the occurrence of the second, creating strong dependence despite the non-empty intersection.

Conditions: Events A and B have a non-empty intersection ($AB \neq \emptyset$).; Event A is a subset of event B ($A \subset B$).

A non-empty intersection means the events can occur simultaneously, but it does not guarantee independence. If one event is a subset of the other, the occurrence of the first strictly dictates the occurrence of the second, creating strong dependence despite the non-empty intersection.

Conditions: Events A and B have a non-empty intersection ($AB \neq \emptyset$).; Event A is a subset of event B ($A \subset B$).