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:

To determine the correct statement about independent events, we analyze each option:

• The first option describes mutually exclusive events (no common outcomes, can't occur together), not independent events.
• The second option's description (having common outcomes and occurring together) does not define independent events. Independent events are about the lack of influence between outcomes, not about shared outcomes or co - occurrence.
• The third option correctly defines independent events: two events are independent when the outcome of one event does not impact the outcome of the other event.
• The fourth option describes dependent events, where the outcome of one event affects the outcome of the other, which is the opposite of independent events.

Answer:

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