Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

91% (02:21) correct
9% (01:35) wrong based on 163 sessions

HideShow timer Statistics

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

Re: John has on his shelf four books of poetry [#permalink]

Show Tags

09 Jan 2013, 15:42

1

This post received KUDOS

3

This post was BOOKMARKED

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 \(P2 = \frac{2}{10} * \frac{4}{9} = \frac{8}{90}\)

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.

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!

Hello, I can't remember where I picked up this question. I have tried to solve it, researching and studying about probability. However I could not figure out the solution.

The question is : 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? 1. 1/2 2. 2/5 3. 3/10 4. 7/20 5. 8/45

The solution I have tried is "4/10*2/9 / 10C2" where the numerator consists of "# of novels/total books * # of reference work / total books-1" and the denominator is "total # of possible combinations to select 2 books at random out of 10 books".

Hello, I can't remember where I picked up this question. I have tried to solve it, researching and studying about probability. However I could not figure out the solution.

The question is : 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? 1. 1/2 2. 2/5 3. 3/10 4. 7/20 5. 8/45

The solution I have tried is "4/10*2/9 / 10C2" where the numerator consists of "# of novels/total books * # of reference work / total books-1" and the denominator is "total # of possible combinations to select 2 books at random out of 10 books".

Merging topics.

Please refer to the discussion above and ask if anything remains unclear.

Re: John has on his shelf four books of poetry [#permalink]

Show Tags

05 Nov 2014, 11:23

I agree with one of the above posters. I think the correct answer should 4/5. Once we pick a book, it's no longer on the shelf. So (4/10) * (2/9) = 4/45

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

I agree with one of the above posters. I think the correct answer should 4/5. Once we pick a book, it's no longer on the shelf. So (4/10) * (2/9) = 4/45

incorrect?

When we are picking two books, one novel and one reference work, we could either pick a novel first and then a reference book or pick a reference book and then a novel. Therefore the answer is 4/10*2/9 + 2/10*4/9 = 8/45.

Answer: E.

Or, use combinations: \(P=\frac{C^1_4*C^1_2}{C^2_{10}}=\frac{8}{45}\).

Hi everyone here's the shortest way to tackle such questions - Probability approach Total = 10 Books

4/10*4/9=8/45 (E) Consider to pick 9 books as total for the second choice, as there is 1 book less after the first pick

hi, your answer is correct but approach is wrong... how did you get 4 as numerator in both cases .. reference books are o two in number so it should be 2/9.. so to pick up two books randomly ans is 4/10*2/9, but these two books can be picked up in 2! ways within themselves.. so 4/10*2/9*2!=8/45..
_________________

John has on his shelf four books of poetry [#permalink]

Show Tags

05 Jul 2015, 04:23

chetan2u wrote:

BrainLab wrote:

Hi everyone here's the shortest way to tackle such questions - Probability approach Total = 10 Books

4/10*4/9=8/45 (E) Consider to pick 9 books as total for the second choice, as there is 1 book less after the first pick

hi, your answer is correct but approach is wrong... how did you get 4 as numerator in both cases .. reference books are o two in number so it should be 2/9.. so to pick up two books randomly ans is 4/10*2/9, but these two books can be picked up in 2! ways within themselves.. so 4/10*2/9*2!=8/45..

The second 4 in the numerator is YOUR 2! ... you can write it 2/9*2 or 4/9 I should have written it down in a more detailed way.. just too involved in such kind of questions in the last time.. that's why skipping some basic steps... ))
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

Hi everyone here's the shortest way to tackle such questions - Probability approach Total = 10 Books

4/10*4/9=8/45 (E) Consider to pick 9 books as total for the second choice, as there is 1 book less after the first pick

hi, your answer is correct but approach is wrong... how did you get 4 as numerator in both cases .. reference books are o two in number so it should be 2/9.. so to pick up two books randomly ans is 4/10*2/9, but these two books can be picked up in 2! ways within themselves.. so 4/10*2/9*2!=8/45..

The second 4 in the numerator is YOUR 2! ... you can write it 2/9*2 or 4/9 I should have written it down in a more detailed way.. just too involved in such kind of questions in the last time.. that's why skipping some basic steps... ))

hi, you did mention about denominator 10 and 9, so expected that you will not miss out mentioning about my 2! , after all it is more likely to be missed by students than 9 in denominator.. i know 2/9 * 2! is 4/9, but it is important to understand the reasoning behind it.. otherwise you could have straight way written 8/45 , after all it is equal to 4/10*4/9... Anyway good shortest way to answer such Qs
_________________

John has on his shelf four books of poetry [#permalink]

Show Tags

19 Aug 2016, 14:17

BrainLab wrote:

chetan2u wrote:

BrainLab wrote:

Hi everyone here's the shortest way to tackle such questions - Probability approach Total = 10 Books

4/10*4/9=8/45 (E) Consider to pick 9 books as total for the second choice, as there is 1 book less after the first pick

hi, your answer is correct but approach is wrong... how did you get 4 as numerator in both cases .. reference books are o two in number so it should be 2/9.. so to pick up two books randomly ans is 4/10*2/9, but these two books can be picked up in 2! ways within themselves.. so 4/10*2/9*2!=8/45..

The second 4 in the numerator is YOUR 2! ... you can write it 2/9*2 or 4/9 I should have written it down in a more detailed way.. just too involved in such kind of questions in the last time.. that's why skipping some basic steps... ))

Sorry, but both of you sound off in your approach to this. The second 2 in the numerator appears because you need to account for the order in which you end up picking. i.e. p(novel) x p(ref) + p(ref) x p(novel) (4/10 x 2/9) + (2/9 x 4/10) or (4/10 x 2/9) x 2! This is not the same as 4/10 x (2/9 x 2!)

gmatclubot

John has on his shelf four books of poetry
[#permalink]
19 Aug 2016, 14:17

Hey, guys, So, I’ve decided to run a contest in hopes of getting the word about the site out to as many applicants as possible this application season...

Whether you’re an entrepreneur, aspiring business leader, or you just think that you may want to learn more about business, the thought of getting your Masters in Business Administration...

Term 1 has begun. If you're confused, wondering what my post on the last 2 official weeks was, that was pre-term. What that means is that the school...