Question

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

Explanation:

Independent events are defined such that the occurrence or outcome of one event has no impact on the occurrence or outcome of the other event. Let’s analyze each option:

• If the outcome of the first event affects the second, the events are dependent (not independent).
• Having outcomes in common and occurring at the same time relates to overlapping events (not independence).
• Having no common outcomes and not occurring simultaneously is about mutually - exclusive events (not independence).
• The correct definition is when the first event’s outcome doesn’t affect the second’s, which aligns with the concept of independent events.

Answer:

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