Final answer:
Events are not independent when selections are made without replacement; in this case, the probability of the second event is affected by the outcome of the first event.
Step-by-step explanation:
The question revolves around the concept of independence in probability and whether or not events are independent when selections are made without replacement. The answer is that in the context of this question, the events are not independent because the outcome of one event affects the probabilities of subsequent events. This is because without replacement, once an item is selected, it cannot be chosen again, and this changes the total number of outcomes and the individual probabilities of each remaining event. For instance, if you have a deck of cards and you pick one without putting it back (sampling without replacement), the probability of picking any other specific card changes because there is now one less card in the deck.
To further define this concept, two events A and B are independent if the occurrence of A does not affect the probability of B occuring, and vice versa. This is not the case when sampling without replacement. The probability of event B given that event A has occurred (P(B|A)) is not equal to just the probability of event B (P(B)), which shows the dependence of these events.