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John has on his shelf four books of poetry

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Magoosh GMAT Instructor
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John has on his shelf four books of poetry [#permalink] New post 09 Jan 2013, 14:15
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88% (02:18) correct 12% (01:05) wrong based on 71 sessions
John has on his shelf four books of poetry, four novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one reference work?
(A) 1/2
(B) 2/5
(C) 3/10
(D) 7/20
(E) 8/45


For a full discussion of probability and counting questions, as well as a complete solution to this question, see:
http://magoosh.com/gmat/2013/gmat-proba ... echniques/

Mike :-)
[Reveal] Spoiler: OA

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Re: John has on his shelf four books of poetry [#permalink] New post 09 Jan 2013, 14:42
You can choose 1 Novel book and 1 Reference work in two ways:
If you choose Novel first and then Reference -> Probability P1 = \frac{4}{10} * \frac{2}{9} = \frac{8}{90}
If you choose Reference first and then Novel -> Probability P2 = \frac{2}{10} * \frac{4}{9} = \frac{8}{90}

Probability(1 novel and 1 reference work) = P1 + P2 = \frac{8}{90}+\frac{8}{90}=\frac{8}{45}.

Hence choice (E)
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Re: John has on his shelf four books of poetry [#permalink] New post 10 Jan 2013, 07:52
(4C2 * 2C2) / (10C2)

8/45. E
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John has on his shelf four books of poetry [#permalink] New post 19 Sep 2014, 10:27
hello,
Why can't we do it this way: 4/10 *2/9= 4/45?
And if we are multiplying by 2 to change the order, then why didn't we do the same for this question:
a-division-of-a-company-consists-of-seven-men-and-five-women-145433.html

Here we used the same approach: 5/12 * 4/11 = 5/33. I'm very confused why the first question has been multiplied by two and not this one as well. After all, there are two ways of picking the women too.
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Re: John has on his shelf four books of poetry [#permalink] New post 12 Oct 2014, 10:18
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usre123 wrote:
hello,
Why can't we do it this way: 4/10 *2/9= 4/45?
And if we are multiplying by 2 to change the order, then why didn't we do the same for this question:
a-division-of-a-company-consists-of-seven-men-and-five-women-145433.html

Here we used the same approach: 5/12 * 4/11 = 5/33. I'm very confused why the first question has been multiplied by two and not this one as well. After all, there are two ways of picking the women too.


This is because this question asks us to pick two separate books. If the question asked us the probability to pick 2 novels then you wouldn't multiply with 2. Similarly, the question you are referring to asks you the probability of picking 2 women. Therefore you don't multiply by 2. Had it asked you the probability of picking one man and one woman then you would multiply by 2 because you could pick the man first or pick the man second. When you pick only women, it doesn't matter what's first or second because they both are women. Hope that helps!
Re: John has on his shelf four books of poetry   [#permalink] 12 Oct 2014, 10:18
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