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?

We must first solve the number of fiction and nonfiction books
if x is the number of fiction books and
y is the number of nonfinction books

Then,
x + y = 400
x = y + 40

Solving the system of equations:
x = 220
y = 180

Therefore, the probability that Audrey and Ryan will get both nonfiction books is
P = 180/400 + 179/399
P = 0.8986

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facundo3141592 facundo3141592 · Answer 2 · 2020-04-24T02:54:16+02:00

Answer: 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