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# A school library contains 200 hardcover and 300 paperback books. 30%

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Math Expert
Joined: 02 Sep 2009
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A school library contains 200 hardcover and 300 paperback books. 30% [#permalink]

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13 May 2017, 14:34
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25% (medium)

Question Stats:

80% (01:55) correct 20% (02:19) wrong based on 77 sessions

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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%
[Reveal] Spoiler: OA

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Re: A school library contains 200 hardcover and 300 paperback books. 30% [#permalink]

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13 May 2017, 20:13
Bunuel wrote:
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%

$$30\%$$ of the hardcover books or $$30\% \times 200 = 60$$ hardcover books are fiction.

Hence, from 500 books at the library, there are $$300 + 60 = 360$$ books that are either paperback or fiction.

The probability is $$\frac{360}{500}=\frac{36}{50}=\frac{72}{100}=72\%$$

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Re: A school library contains 200 hardcover and 300 paperback books. 30% [#permalink]

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13 May 2017, 21:11
Bunuel wrote:
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%

Hard cover Fiction = 30% of 200 = 60
Paperback Fiction = 70% of 300 = 210
Remaining Paper back = 300-210 = 90

Total Favourable Books = 60+210+90 = 360

Probability = 360/500 = 18/25 = 72%

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Re: A school library contains 200 hardcover and 300 paperback books. 30% [#permalink]

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14 May 2017, 17:27
First, the probability of PP is 300/500 and since this probability is already takes care of fiction books that are pps, we only need to get the percentage of fiction books from the HC books to reach to our probabilities. Therefore,

$$\frac{300}{500} +\frac{3}{10}*\frac{200}{500}= (\frac{3}{5} + \frac{6}{50})*100=72$$

The correct option is: A
Re: A school library contains 200 hardcover and 300 paperback books. 30%   [#permalink] 14 May 2017, 17:27
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