Question

which statement is correct regarding independent events?
two events are independent if they have no outcomes in common and cannot occur at the same time.
two events are independent if they have outcomes in common and can occur at the same time.
two events are independent if the outcome of the first event does not affect the outcome of the second event.
two events are independent if the outcome of the first event affects the outcome of the second event.

Explanation:

• First option: Events with no common outcomes and cannot occur simultaneously are mutually - exclusive events, not independent events.
• Second option: Having common outcomes and being able to occur at the same time is not the definition of independent events.
• Third option: By the definition of independent events, if the outcome of the first event does not affect the outcome of the second event, the two events are independent.
• Fourth option: If the outcome of the first event affects the outcome of the second event, the events are dependent, not independent.

Answer:

Two events are independent if the outcome of the first event does not affect the outcome of the second event.