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?

Answer 1

Start first by determining the number of books of each category. if x is the nbr. of nonfiction then x+40 is the nbr of fiction. x+x+40=400
so x=180 is the nbr. of nonfiction and 220 is the nbr of fiction.the probability would be 180/400×179/399 so 2nd option

Answer 2

Answer:  Second option is correct.

Step-by-step explanation:

Let the number of fiction book be 'x'.

Let the number of non fiction book be 'y'.

Total number of books = 400

So, equation would be

$x+y=400------------(1)$

Since there are 40 more fiction books than non fiction books.

So, equation would be

$x-y=40-------------(2)$

From Eq(1) and Eq(2), we have

$x+y=400\\\\x-y=40\\\\-----------------------------------\\\\2x=440\\\\x=\dfrac{440}{2}\\\\x=220$

And we will find the value of y:

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

As we have given that Ryan randomly picks one book without replacing it he picks the another book.

Probability that both pick non fiction books would be

$\dfrac{180}{400}\times \dfrac{179}{399}\\\\=0.20$

Hence, Second option is correct.