Determine whether the events E and F are independent or dependent. Justify your answer. (a) E: A person going into debt. F: The same person having a credit card. A. E and F are independent because going into debt has no effect on the probability of a person having a credit card. B. E and F are dependent because going into debt has no effect on the probability of a person having a credit card. C. E and F are independent because having a credit card has no effect on the probability of a person going into debt. D. E and F are dependent because having a credit card can affect the probability of a person going into debt.

We say that two events A and B are independent when the probability that event A occurs has no effect on the probability that event B occurs. On the other side, A and B are dependent when the outcome of A actually affects the probability of the occurrence of B.

In this problem the events are:

E: A person going into debt.

F: The same person having a credit card.

In this case, we know that when one person has a debt, the probability that the person gets a credit card approved is affected (it is less probable). Also, a person that has a credit card has more probability of going into debt because of it.

Therefore, these 2 events are dependent because having a credit card can affect the probability of a person going into debt.