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?

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

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RenatoMattice RenatoMattice · Answer 2 · 2019-06-06T08:18:40+02:00

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

[tex]x+y=400------------(1)[/tex]

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

So, equation would be

[tex]x-y=40-------------(2)[/tex]

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

[tex]x+y=400\\\\x-y=40\\\\-----------------------------------\\\\2x=440\\\\x=\dfrac{440}{2}\\\\x=220[/tex]

And we will find the value of y:

[tex]220+y=400\\\\y=400-220\\\\y=180[/tex]

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

[tex]\dfrac{180}{400}\times \dfrac{179}{399}\\\\=0.20[/tex]

Hence, Second option is correct.