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Yes, the impossible event (the empty set) is independent of any event. Because its probability is 0, the probability of its intersection with any event is 0, which perfectly satisfies the mathematical definition of independence.

Conditions: Event B is the impossible event ($B = \emptyset$).; Event A is any arbitrary event.

Yes, the impossible event (the empty set) is independent of any event. Because its probability is 0, the probability of its intersection with any event is 0, which perfectly satisfies the mathematical definition of independence.

Conditions: Event B is the impossible event ($B = \emptyset$).; Event A is any arbitrary event.

The correct statement is that if the intersection of two events is nonempty ($AB \neq \emptyset$), then the two events may be independent.

Conditions: A and B are any two events in a random experiment.

The correct statement is that if the intersection of two events is nonempty ($AB \neq \emptyset$), then the two events may be independent.

Conditions: A and B are any two events in a random experiment.

Two events are mutually exclusive if their intersection is the empty set, meaning they cannot occur simultaneously in the same random experiment.

Conditions: Events A and B are two events in the same random experiment.

Two events are mutually exclusive if their intersection is the empty set, meaning they cannot occur simultaneously in the same random experiment.

Conditions: Events A and B are two events in the same random experiment.