Ear Fare in dep (a) E: A person attaining a position as a professor. F: The same person attaining a PhD. A. E and F are independent because attaining a PhD has no effect on the probability of a person attaining a position as a professor. OB. E and F are independent because attaining a position as a professor has no effect on the probability of a person attaining a PhD. OC. E and F are dependent because attaining a position as a professor has no effect on the probability of a person attaining a PhD. OD. E and F are dependent because attaining a PhD can affect the probability of a person attaining a position as a professor. (b) E A randomly selected person at school A having a high GPA. F: A randomly selected person at school B having a low GPA. OA. E can affect the probability of F, even if the two people are randomly selected, so the events are dependent. OB. E can affect the probability of F because the people were 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. OD. E cannot affect F because "person 1 at school A having a high GPA" could never occur, so the events are neither dependent nor independent. (c) E: The consumer demand for synthetic diamonds. F: The amount of research funding for diamond synthesis. OA. The consumer demand for synthetic diamonds could affect the amount of research funding for diamond synthesis, so E and F are dependent. OB. The amount of research funding for diamond synthesis could affect the consumer demand for synthetic diamonds, so E and F are dependent. OC. The consumer demand for synthetic diamonds could not affect the amount of research funding for diamond synthesis, so E and F are independen