The books in a private library are classified as fiction and nonfiction. there are 400 books in the library. there are 40 more fiction that 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?

Question

anonymous · Answer

First let's find how many of each type of book there are.

f = Fiction books
nf = Non-Fiction book

f = nf+40
f+nf=400

- Substitute "f" for (nf+40) -

nf+40+nf = 400

To solve for "nf" we have to get rid of any other distractions, to do that we subtract 40 from both sides

2nf = 360
nf = 180
f = 220
Now we know how many of each type of books there are

180 Non-Fiction books
220 Fiction books

First pick (Total Non-Fiction books/Total books)
= 180/400

Second pick (Total Non-Fiction books remaining/Total books remaining)
= 179/399

Since the question asks for Ryan *and* Audrey, we take the 2 probabilities and times them together. 

This gets us 32220/159600

anonymous · Answer

You can simplify the fraction further...