Question

what is the difference between independent and dependent events?

choose the correct answer below.

a. two events are independent when the occurrence of one event affects the probability of the occurrence of the other event. two events are dependent when the occurrence of one event does not affect the probability of the occurrence of the other event.
b. two events are independent if only one of the two events can occur. two events are dependent if they can occur at the same time.
c. two events are independent when the occurrence of one event does not affect the probability of the occurrence of the other event. two events are dependent when the occurrence of one event affects the probability of the occurrence of the other event.
d. two events are independent if they can occur at the same time. two events are dependent if only one of the two events can occur.

Explanation:

Define independent events

Using the Independent Events Probability knowledge point

$$ P(B|A) = P(B) $$

This means the occurrence of event \(A\) does not affect the probability of event \(B\).

Define dependent events

If the occurrence of one event changes the probability of the other, they are dependent.

$$ P(B|A) eq P(B) $$

Evaluate the given options

• Option A reverses the definitions of independent and dependent events.
• Option B confuses independence with mutually exclusive (disjoint) events.
• Option C correctly states that independent events do not affect each other's probability, while dependent events do.
• Option D also confuses independence with joint occurrences.

Answer:

• A. Two events are independent when the occurrence of one event affects the probability of the occurrence of the other event. Two events are dependent when the occurrence of one event does not affect the probability of the occurrence of the other event.
• B. Two events are independent if only one of the two events can occur. Two events are dependent if they can occur at the same time.
• C. Two events are independent when the occurrence of one event does not affect the probability of the occurrence of the other event. Two events are dependent when the occurrence of one event affects the probability of the occurrence of the other event. (Correct answer)
• D. Two events are independent if they can occur at the same time. Two events are dependent if only one of the two events can occur.