Question

multiple choice 1 point
classify the two events as independent or dependent and explain your reasoning.
selecting a king from a standard deck, replacing it, and then selecting a queen.
independent because the probability of one event does not affect the probability of the other.
independent because the probability of one event does affect the probability of the other.
dependent because the probability of one event does not affect the probability of the other.
dependent because the probability of one event does affect the probability of the other.
35 multiple choice 1 point
classify the two events as independent or dependent and explain your reasoning.
your car wont start. your car door does not open.
independent because the probability of one event does not affect the probability of the other.
independent because the probability of one event does affect the probability of the other.
dependent because the probability of one event does not affect the probability of the other.
dependent because the probability of one event does affect the probability of the other.

Explanation:

For the first problem, when we replace the king back into the deck, the total number of cards remains the same (\(52\)) for the second draw (selecting a queen). So the outcome of the first event (selecting a king) does not influence the probability of the second event (selecting a queen). For the second problem, a car not starting and a car door not opening are two separate mechanical issues. The failure of one (car not starting) has no impact on the probability of the other (car door not opening).

Answer:

First problem: Independent because the probability of one event does not affect the probability of the other. Second problem: Independent because the probability of one event does not affect the probability of the other.