Mathematics: 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.

The books in a private library are classified as - id4424190, ashlynhenderson0323

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14.01.2022

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 :-

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

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