Determine whether the events E and Fare independent or dependent. Justify your a

Question

Determine whether the events E and Fare independent or dependent. Justify your answer. (a) E: A person attaining a position as a professor. F: The same person attaining a PhD. A. E and F are dependent because attaining a PhD can affect the probability of a person attaining a position as a professor. B. E and F are independent because attaining a PhD has no effect on the probability of a person attaining a position as a professor. C. E and Fare independent because attaining a position as a professor has no effect on the probability of a person attaining a PhD. D. E and Fare dependent because attaining a position as a professor has no effect on the probability of a person attaining a PhD. (b) E: A randomly selected person accidentally killing a spider. F: Another randomly selected person accidentally swallowing a spider. A. E cannot affect F because "person accidentally killing a spider" could never occur, so the events are neither dependent nor independent. B. E can affect the probability of F because the people were randomly selected, so the events are dependent. C E can affect the probability of F even if the two people are randomly selected, so the events are dependent. D. E cannot affect F and vice versa because the people were randomly selected, so the events are independent. (c) E: The war in a major oil-exporting country. F: The price of gasoline. A. The price of gasoline could affect the war in a major oil-exporting country, so E and F are dependent. B. The war in a major oil-exporting country could affect the price of gasoline, so E and F are dependent. C. The war in a major oil-exporting country could not affect the price of gasoline, so E and Fare independent.

Explanation / Answer

(a) Correct option:

A: E and F are dependent because attaining a Ph D can affect the probability of a person attaining a position asa professor

EXPLANATION: Events E and F are dependent if the probability of occurrence of E affects the probability of occurrence of F. here, the event E = attaining the position of a professor and event F = The same person attaining a Ph D are dependent evets because getting Ph D will increase his probability of getting professor's post.

(b) Correct option:

D: E cannot affect F and vice versa because the people were randonly selected , so the events are independent.

EXPLANATION:

E = person kiing a spider and F = person swallowing a spider are independent events, because the persons concerned are independent ( because randomly selected)

(c) Correct option:

B: The war in major oil exploring country could affect the price of gasoline, so E and F are dependent.

EXPLANATION: Here, the independent variable: war in major oil exploring country. the dependent variable: price of gasoline

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