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. O A. E and F are dependent because having a credit card can affect the probability of a person going into debt. O B. E and F are independent because going into debt has no effect on the probability of a person having a credit card. O C. E and F are independent because having a credit card has no effect on the probability of a person going into debt. O D. E and F are dependent because going into debt has no effect on the probability of a person having a credit card. (b) E: A randomly selected person finding cheese revolting. F: A different randomly selected person finding cheese delicious. O A. E can affect the probability of F, even if the two people are randomly selected, so the events are dependent. O B. E cannot affect F and vice versa because the people were randomly selected, so the events are independent. O C. E cannot affect F because "person 1 finding cheese revolting" could never occur, so the events are neither dependent nor independent. O D. E can affect the probability of F because the people were randomly selected, so the events are dependent. (c) E: The unusually foggy weather in London on May 8. F: The number of car accidents in London on May 8. O A. The unusually foggy weather in London on May 8 could affect the number of car accidents in London on May 8, so E and F are dependent. O B. The unusually foggy weather in London on May 8 could not affect the number of car accidents in London on May 8, so E and F are independent. O c. The number of car accidents in London on May 8 could affect the unusually foggy weather in London on May 8, so E and F are dependent.

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**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 dependent because having a credit card can affect the probability of a person going into debt.
- **B.** E and F are independent 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 going into debt has no effect on the probability of a person having a credit card.

---

**(b)**  
E: A randomly selected person finding cheese revolting.  
F: A different randomly selected person finding cheese delicious.

- **A.** E can affect the probability of F, even if the two people are randomly selected, so the events are dependent.
- **B.** E cannot affect F and vice versa because the people were randomly selected, so the events are independent.
- **C.** E cannot affect F because "person 1 finding cheese revolting" could never occur, so the events are neither dependent nor independent.
- **D.** E can affect the probability of F because the people were randomly selected, so the events are dependent.

---

**(c)**  
E: The unusually foggy weather in London on May 8.  
F: The number of car accidents in London on May 8.

- **A.** The unusually foggy weather in London on May 8 could affect the number of car accidents in London on May 8, so E and F are dependent.
- **B.** The unusually foggy weather in London on May 8 could not affect the number of car accidents in London on May 8, so E and F are independent.
- **C.** The number of car accidents in London on May 8 could affect the unusually foggy weather in London on May 8, so E and F are dependent.
Transcribed Image Text:**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 dependent because having a credit card can affect the probability of a person going into debt. - **B.** E and F are independent 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 going into debt has no effect on the probability of a person having a credit card. --- **(b)** E: A randomly selected person finding cheese revolting. F: A different randomly selected person finding cheese delicious. - **A.** E can affect the probability of F, even if the two people are randomly selected, so the events are dependent. - **B.** E cannot affect F and vice versa because the people were randomly selected, so the events are independent. - **C.** E cannot affect F because "person 1 finding cheese revolting" could never occur, so the events are neither dependent nor independent. - **D.** E can affect the probability of F because the people were randomly selected, so the events are dependent. --- **(c)** E: The unusually foggy weather in London on May 8. F: The number of car accidents in London on May 8. - **A.** The unusually foggy weather in London on May 8 could affect the number of car accidents in London on May 8, so E and F are dependent. - **B.** The unusually foggy weather in London on May 8 could not affect the number of car accidents in London on May 8, so E and F are independent. - **C.** The number of car accidents in London on May 8 could affect the unusually foggy weather in London on May 8, so E and F are dependent.
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