The books in a private library are classified as fiction and nonfiction. There are 400 books in the library. There are 40 more fiction books than nonfiction books. Audrey randomly picks a book. A few minutes later, Ryan randomly picks one of the remaining books. What is the probability that both pick nonfiction books? A. 180 × 189
400 × 400.

B. 180 × 179
400 × 399.

C. 180 × 179
400 × 400.

D. 180 × 189
400 × 399.

Given:
Total number of books = 400
fiction books = x + 40
non fiction books = x

x + x + 40 = 400
2x + 40 = 400
2x = 400 - 40
2x = 360
x = 360/2
x = 180 non fiction books

x + 40 = 180 + 40 = 220 fiction books.

Audrey picks a book: P(non fiction) = 180/400
Ryan picks a book: P(non fiction) = 179/399

Answer Link

JeanaShupp JeanaShupp · Answer 2 · 2019-02-25T10:32:28+01:00

Answer: B. [tex]\frac{180}{400}\times\frac{179}{399}[/tex]

Step-by-step explanation:

Let x be the number of fiction books and y be the number of non-fiction books.

Then according to the question, we have the following system:-

[tex]x+y=400.........(1)\\x-y=40.........(2)[/tex]

Adding (1) and (2), we get

[tex]2x=440\\\Rightarrow\ x=220[/tex]

Substitute value of x in equation (1), we get

[tex]220+y=400\\\Rightarrow\ y=180[/tex]

Also, Audrey randomly picks a book.

Favorable outcomes for drawing a nonfiction book =180

A few minutes later, Ryan randomly picks one of the remaining books .

Remaining books = 400-1=399

Favorable outcomes for drawing a nonfiction book =180-1=179

The probability that both pick nonfiction books is given by :-

[tex]P=\frac{180}{400}\times\frac{179}{399}[/tex]