Question

34 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 doesnt 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:

When we replace the king after selecting it from the deck, the composition of the deck remains the same for the second draw (selecting a queen). So, the probability of selecting a queen is not affected by the previous event of selecting a king (and replacing it). In probability, two events \(A\) and \(B\) are independent if \(P(B|A)=P(B)\), which means that the occurrence (or non - occurrence) of event \(A\) does not change the probability of event \(B\). Here, let event \(A\) be "selecting a king" and event \(B\) be "selecting a queen". Since we replace the king, \(P(B|A)=\frac{4}{52}\) (because there are 4 queens in a standard deck of 52 cards) and \(P(B)=\frac{4}{52}\).

Answer:

Independent because the probability of one event does not affect the probability of the other.