GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Nov 2018, 03:31

### GMAT Club Daily Prep

#### 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

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

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### How to QUICKLY Solve GMAT Questions - GMAT Club Chat

November 20, 2018

November 20, 2018

09:00 AM PST

10:00 AM PST

The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
• ### The winning strategy for 700+ on the GMAT

November 20, 2018

November 20, 2018

06:00 PM EST

07:00 PM EST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

# On a shelf there are 6 hardback books and 2 paperback book.

Author Message
TAGS:

### Hide Tags

Intern
Joined: 30 Jun 2012
Posts: 7
On a shelf there are 6 hardback books and 2 paperback book.  [#permalink]

### Show Tags

Updated on: 30 Jun 2012, 06:52
1
2
00:00

Difficulty:

25% (medium)

Question Stats:

73% (01:45) correct 27% (01:55) wrong based on 209 sessions

### HideShow timer Statistics

On a shelf there are 6 hardback books and 2 paperback book. If we pick up 4 books at random, what is the probability that we pick up at least one paperback book?

A. 11/14
B. 5/7
C. 2/7
D. 3/14
E. 1/7

Originally posted by ferrarih on 30 Jun 2012, 06:18.
Last edited by ferrarih on 30 Jun 2012, 06:52, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 50661
Re: On a shelf there are 6 hardback books and 2 paperback.....  [#permalink]

### Show Tags

30 Jun 2012, 06:35
2
2
On a shelf there are 6 hardback books and 2 paperback book. If we pick up 4 books at random, what is the probability that we pick up at least one paperback book?
A. 11/14
B. 5/7
C. 2/7
D. 3/14
E. 1/7

Let's find the probability of the opposite event and subtract this value from 1.

The opposite event would be if out of 4 books we pick all ll will be hardback: $$P(H=4)=\frac{C^4_6}{C^4_8}=\frac{15}{70}=\frac{3}{14}$$.

Hence, $$P(P\geq{1})=1-\frac{3}{14}=\frac{11}{14}$$.

_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12883
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: On a shelf there are 6 hardback books and 2 paperback book.  [#permalink]

### Show Tags

22 Apr 2017, 15:18
1
1
Hi All,

The 'math' behind this question can be approached in a couple of different ways - and you can actually avoid using the Combination Formula altogether.

The prompt tells us that there are 6 hardcover books and 2 paperback books. We're asked for the probability of selecting AT LEAST one paperback book when we randomly select 4 books from the overall group of 8 books. Since the question focuses on getting AT LEAST one paperback book, we can determine what we DON'T want (meaning 0 paperback books) and subtract that result from 1 (to determine what we DO want).

Working one book at a time, the probability of NOT getting a paperback book is....
1st book = 6/8 chance of NOT getting a paperback
2nd book = 5/7 chance of NOT getting a paperback
3rd book = 4/6 chance of NOT getting a paperback
4th book = 3/5 chance of NOT getting a paperback

Thus, the probability of NOT getting a paperback book for the first 4 books is (6/8)(5/7)(4/6)(3/5). You should notice that the 6s and 5s 'cancel out', leaving us with...

(4)(3)/(8)(7) = 12/56 = 3/14

Thus, the probability of getting AT LEAST one paperback would be 1 - 3/14 = 11/14

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Senior Manager
Joined: 22 Feb 2018
Posts: 395
On a shelf there are 6 hardback books and 2 paperback book.  [#permalink]

### Show Tags

22 Oct 2018, 09:03
ferrarih wrote:
On a shelf there are 6 hardback books and 2 paperback book. If we pick up 4 books at random, what is the probability that we pick up at least one paperback book?

A. 11/14
B. 5/7
C. 2/7
D. 3/14
E. 1/7

OA:A

The probability of picking up at least one paperback book $$= 1 -$$ The probability of picking up no paperback book $$= 1- \frac{C(6,4)}{C(8,4)}= 1-\frac{3}{14}=\frac{11}{14}$$
_________________

Good, good Let the kudos flow through you

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4170
Location: United States (CA)
Re: On a shelf there are 6 hardback books and 2 paperback book.  [#permalink]

### Show Tags

23 Oct 2018, 18:24
ferrarih wrote:
On a shelf there are 6 hardback books and 2 paperback book. If we pick up 4 books at random, what is the probability that we pick up at least one paperback book?

A. 11/14
B. 5/7
C. 2/7
D. 3/14
E. 1/7

The phrase “at least one paperback” means “one or more paperbacks.” Thus, the only way we would NOT pick up at least one paperback would be if all 4 books were hardbacks. Thus, we can use the formula:

P(at least one paperback) = 1 - P(all hardbacks)

The number of ways to select all hardbacks is 6C4:

6! / (4! x 2!) = (6 x 5) / (2 x 1) = 15

The number of ways to select 4 books from 8 is 8C4:

8! / (4! x 4!) = (8 x 7 x 6 x 5) / (4 x 3 x 2 x 1) = 7 x 2 x 5 = 70

The probability of all hardbacks is 15/70 = 3/14 and thus P(at least on paperback) = 1 - 3/14 = 11/14.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: On a shelf there are 6 hardback books and 2 paperback book. &nbs [#permalink] 23 Oct 2018, 18:24
Display posts from previous: Sort by