Question

select the correct answer.
the top shelf of a bookcase holds 6 fiction and 4 nonfiction books. on the bottom shelf are 3 fiction and 5 nonfiction 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 top 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 bottom 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 changes the probability of the second event (i.e., sampling without replacement from the same group).

Step2: Analyze Option A

First pick: top fiction (6 total top books: 6 fiction, 4 nonfiction). After picking 1 fiction, top shelf has 5 fiction, 4 nonfiction left. But the second pick is nonfiction from top, so total top books decrease by 1. However, we can also check other options.

Step3: Analyze Option B

First pick: top fiction, second pick: bottom fiction. These are separate shelves, so the first pick does not affect the total number of bottom fiction books. Independent events.

Step4: Analyze Option C

First pick: top fiction, second pick: bottom nonfiction. Separate shelves, so the first pick does not change the count of bottom nonfiction books. Independent events.

Step5: Analyze Option D

First pick: bottom nonfiction (5 total bottom nonfiction, 8 total bottom books). After picking 1 nonfiction, bottom shelf has 4 nonfiction, 7 total books left. The probability of picking a second bottom nonfiction changes from $\frac{5}{8}$ to $\frac{4}{7}$, so the events are dependent.

Answer:

D. one of the nonfiction books on the bottom shelf, and a second nonfiction book from the bottom shelf