Final answer:
The probability of selections without replacement in a sample space are considered dependent events because the occurrence of one event affects the likelihood of subsequent events.
Step-by-step explanation:
When considering if events are dependent or independent, the key factor is whether the occurrence of one event affects the probability of the other event occurring. Sampling without replacement means that each element can only be selected once, which alters the probabilities of subsequent selections, making the events dependent. In contrast, with replacement, the selection of one element has no impact on the probability of selecting another, thus the events are independent.
For example, if we pick a card from a deck and do not put it back, the probability of picking another specific card changes, showing that the events are dependent. If the card is returned to the deck, the probability doesn't change, signifying that the events are independent. If two events cannot happen at the same time, they are mutually exclusive; if they can occur together, it's a case of joint probability.