Problem

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

Answer

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Answer

\(\boxed{\text{Final Answer: C. E and F are dependent because having a credit card can affect the probability of a person going into debt.}}\)

Steps

Step 1 :Determine whether the events E and F are independent or dependent.

Step 2 :Event E is a person going into debt and event F is the same person having a credit card.

Step 3 :Consider whether having a credit card (event F) can affect the probability of a person going into debt (event E).

Step 4 :If a person has a credit card, they might be more likely to go into debt due to the ease of spending money that they do not currently have.

Step 5 :Conversely, if a person does not have a credit card, they might be less likely to go into debt because they can only spend money that they currently possess.

Step 6 :Therefore, it seems that the events E and F are dependent.

Step 7 :\(\boxed{\text{Final Answer: C. E and F are dependent because having a credit card can affect the probability of a person going into debt.}}\)

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