Determine whether the events E and F are independent or dependent. Justify your answer. (a) E: A person attaining a position as a professor attaining a position as a professor. F: The same person...

Determine whether the events E and F are independent or dependent. Justify your answer. (a) E: A person attaining a position as a professor attaining a position as a professor. F: The same person attaining a PhD attaining a PhD. A. E and F are dependent because attaining a position as a professor attaining a position as a professor has no effect on the probability of a person attaining a PhD attaining a PhD. B. E and F are dependent because attaining a PhD attaining a PhD can affect the probability of a person attaining a position as a professor attaining a position as a professor. C. E and F are independent because attaining a position as a professor attaining a position as a professor has no effect on the probability of a person attaining a PhD attaining a PhD. D. E and F are independent because attaining a PhD attaining a PhD has no effect on the probability of a person attaining a position as a professor attaining a position as a professor. (b) E: A randomly selected person accidentally killing a spider accidentally killing a spider. F: Another randomly selected person accidentally swallowing a spider accidentally swallowing a spider. A. E cannot affect F because "person 1 accidentally killing a spider accidentally killing a spider" could never occur, so the events are neither dependent nor independent. B. E can affect the probability of F, even if the two people are randomly selected, so the events are dependent. C. E cannot affect F and vice versa because the people were randomly selected, so the events are independent. D. E can affect the probability of F because the people were randomly selected, so the events are dependent. (c) E: The consumer demand for synthetic diamonds consumer demand for synthetic diamonds. F: The amount of research funding for diamond synthesis amount of research funding for diamond synthesis. A. The consumer demand for synthetic diamonds consumer demand for synthetic diamonds could not affect the amount of research funding for diamond synthesis amount of research funding for diamond synthesis, so E and F are independent. B. The consumer demand for synthetic diamonds consumer demand for synthetic diamonds could affect the amount of research funding for diamond synthesis amount of research funding for diamond synthesis, so E and F are dependent. C. The amount of research funding for diamond synthesis amount of research funding for diamond synthesis could affect the consumer demand for synthetic diamonds consumer demand for synthetic diamonds, so E and F are dependent.