Answer: B. \(\frac{180}{400}\times\frac{179}{399}\)
Step-by-step explanation:
Let x be the number of fiction books and y be the number of non-fiction books.
Then according to the question, we have the following system:-
\(x+y=400.........(1)\\x-y=40.........(2)\)
Adding (1) and (2), we get
\(2x=440\\\Rightarrow\ x=220\)
Substitute value of x in equation (1), we get
\(220+y=400\\\Rightarrow\ y=180\)
Also, Audrey randomly picks a book.
Favorable outcomes for drawing a nonfiction book =180
A few minutes later, Ryan randomly picks one of the remaining books .
Remaining books = 400-1=399
Favorable outcomes for drawing a nonfiction book =180-1=179
The probability that both pick nonfiction books is given by :-
\(P=\frac{180}{400}\times\frac{179}{399}\)
