Determine whether the events e and f are independent or dependent. justify your answer.

(a) e: a person having an at dash fault accidenthaving an at-fault accident. f: the same person being prone to road ragebeing prone to road rage.

a. e and f are dependent because being prone to road ragebeing prone to road rage can affect the probability of a person having an at dash fault accidenthaving an at-fault accident.
b. e and f are dependent because having an at dash fault accidenthaving an at-fault accident has no effect on the probability of a person being prone to road ragebeing prone to road rage.
c. e and f are independent because having an at dash fault accidenthaving an at-fault accident has no effect on the probability of a person being prone to road ragebeing prone to road rage.
d. e and f are independent because being prone to road ragebeing prone to road rage has no effect on the probability of a person having an at dash fault accidenthaving an at-fault accident.

(b) e: a randomly selected person accidentally killing a spideraccidentally killing a spider. f: another randomly selected person accidentally swallowing a spideraccidentally swallowing a spider.

a. e cannot affect f because "person 1 accidentally killing a spideraccidentally 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 randomlyselected, 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 consumer demand for synthetic diamondsconsumer demand for synthetic diamonds. f: the amount of research funding for diamond synthesisamount of research funding for diamond synthesis.

a. the consumer demand for synthetic diamondsconsumer demand for synthetic diamonds could affect the amount of research funding for diamond synthesisamount of research funding for diamond synthesis, so e and f are dependent.
b. the consumer demand for synthetic diamondsconsumer demand for synthetic diamonds could not affect the amount of research funding for diamond synthesisamount of research funding for diamond synthesis, so e and f are independent.
c. the amount of research funding for diamond synthesisamount of research funding for diamond synthesis could affect the consumer demand for synthetic diamondsconsumer demand for synthetic diamonds, so e and f are dependent.