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?

The probability is P =  0.20

Step-by-step explanation:

The data that we have is:

Total books = 400

If the number of non fiction books is Nf and the number of fiction books is F, we have that:

F  = Nf  + 40

So here we have a system of equations:

Nf + F = 400

F = Nf + 40

we can replace the second equation in the first one, and solve it for Nf.

Nf + (Nf + 40) = 400

2*Nf + 40 = 400

2*Nf = 400 - 40 = 360

Nf = 180

So we have 180 non-fiction books.

We want to calculate the probability of picking at random two non-fiction books.

When Audrey picks one, the probabilty is equal to the number of non-fiction books divided the total number of books:

p1 = 180/400

for Ryan we have the same, but the number of books is 399 now (Because Audrey already took one), and the number of non-fiction books is 179.

p2 = 179/399

The probabiliy for both events to happen is:

P = p1*p2 = (180/400)*(179*399) = 0.20