Question

select the correct answer. the top shelf of a bookcase holds 6 fiction and 4 non - fiction books. on the bottom shelf are 3 fiction and 5 non - fiction books. choosing which 2 books describes a pair of dependent events? a. one of the fiction books on the top shelf, and then one of the nonfiction books on the bottom shelf b. one of the fiction books on the top shelf, and then a second fiction book from the bottom shelf c. one of the fiction books on the top shelf, and then one of the nonfiction books on the top shelf d. one of the nonfiction books on the bottom shelf, and a second nonfiction book from the bottom shelf

Explanation:

Step1: Define dependent events

Dependent events are events where the outcome of the first event affects the outcome of the second event.

Step2: Analyze option A

When we first choose a fiction book from the top - shelf, the number of available non - fiction books on the bottom shelf for the second choice is affected if we do not replace the first - chosen book. So these two events are dependent.

Step3: Analyze option B

Choosing two fiction books from different shelves is not a typical case of dependent events as the choice of the first fiction book does not directly impact the choice of the second fiction book in a way that the sample space of the second choice is affected by the first choice in a non - replaceable sense relevant to the problem context.

Step4: Analyze option C

Choosing two books from the top shelf where one is fiction and one is non - fiction (assuming we are not replacing the first - chosen book) is not the most straightforward example of dependent events as the focus of dependent events here should be across different shelves and how the first choice affects the second choice in terms of overall available books.

Step5: Analyze option D

Choosing two non - fiction books from the bottom shelf is not a case of dependent events in the context of the problem as the choice of the first non - fiction book does not have a significant impact on the nature of the second non - fiction book choice in terms of the overall problem setup which is about cross - shelf dependent choices.

Answer:

A. one of the fiction books on the top shelf, and then one of the non - fiction books on the bottom shelf