Question

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.

Answer 1

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 2

Answer: B. $\frac{180}{400}\times\frac{179}{399}$

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:-

$x+y=400.........(1)\\x-y=40.........(2)$

Adding (1) and (2), we get

$2x=440\\\Rightarrow\ x=220$

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

$220+y=400\\\Rightarrow\ y=180$

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 :-

$P=\frac{180}{400}\times\frac{179}{399}$