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 recall the definition of independent events: Two events are independent if the occurrence (or outcome) of one event does not affect the probability or outcome of the other event.

• The first option describes mutually exclusive events (no common outcomes, can't occur together), not independent events.
• The second option is incorrect because sharing common outcomes doesn't define independence; independence is about the effect of one event on the other, not overlapping outcomes.
• The third option matches the definition of independent events: the outcome of the first event does not affect the outcome of the second event.
• The fourth option describes dependent events, where one event's outcome affects the other.

Answer:

The correct statement is: "Two events are independent if the outcome of the first event does not affect the outcome of the second event." (corresponding to the third option among the given choices, though the exact option label isn't visible, the description is as above)