BTGModeratorVI wrote: ↑Wed Jan 06, 2021 8:11 am
A school library contains 200 hardcover and 300 paperback books. 30% of the hardcover books and 70% of the paperbacks are fiction. If a book is selected at random from the 500 books at the library, what is the probability that the book is either paperback or fiction?
A. 72%
B. 76%
C. 80%
D. 82%
E. 84%
Answer:
A
Solution:
We are given that 30% of the 200 hardcover books are fiction, and thus 200 x 0.3 = 60 hardcover books are fiction. We are also given that 70% of the 300 paperback books are fiction, and thus 0.7 x 300 = 210 paperback books are fiction. We see that there are a total of 60 + 210 = 270 fiction books.
Recall that P(A or B) = P(A) + P(B) - P(A and B). If we let B be paperback and F be fiction, we have:
P(B or F) = P(B) + P(F) - P(B and F)
P(B or F) = 300/500 + 270/500 - 210/500
P(B or F) = 360/500 = 72/100 = 72%
Alternate Solution:
The group of books referred to as “either paperback or fiction” consists of all of the paperback books plus the hardcover books that are fiction. Since there are 300 paperback books and 200 x 0.3 = 60 hardcover fiction books, there are 300 + 60 = 360 books that are either paperback or fiction, out of a total of 500. Thus, the probability is 360/500 = 72/100 = 72%.
Answer: A
