Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 22 May 2017, 10:07

### 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 June
Open Detailed Calendar

# A drawer has six loose blue socks and six loose white socks.

Author Message
TAGS:

### Hide Tags

Intern
Joined: 18 Sep 2012
Posts: 7
Followers: 0

Kudos [?]: 6 [2] , given: 18

A drawer has six loose blue socks and six loose white socks. [#permalink]

### Show Tags

23 Sep 2012, 08:06
2
KUDOS
2
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

58% (02:59) correct 42% (02:13) wrong based on 206 sessions

### HideShow timer Statistics

A drawer has six loose blue socks and six loose white socks. If four socks are removed from the drawer at random and without replacement. What is the probability that one pair of each color was selected?

A. 2/33
B. 5/66
C. 5/33
D. 5/11
E. 1/2
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Sep 2012, 09:00, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 38796
Followers: 7712

Kudos [?]: 105739 [1] , given: 11578

Re: A drawer has six loose blue socks and six loose white socks. [#permalink]

### Show Tags

23 Sep 2012, 08:59
1
KUDOS
Expert's post
solo1234 wrote:
A drawer has six loose blue socks and six loose white socks. If four socks are removed from the drawer at random and without replacement. What is the probability that one pair of each color was selected?

A. 2/33
B. 5/66
C. 5/33
D. 5/11
E. 1/2

So, we want the probability of removing 2 blues socks out of 6 and 2 white socks out of 6, while removing 4 socks out of 12.

$$P=\frac{favorable}{total}=\frac{C^2_{6}*C^2_{6}}{C^4_{12}}=\frac{5}{11}$$.

_________________
Intern
Joined: 18 Sep 2012
Posts: 7
Followers: 0

Kudos [?]: 6 [0], given: 18

Re: A drawer has six loose blue socks and six loose white socks. [#permalink]

### Show Tags

23 Sep 2012, 19:05
Bunuel wrote:
solo1234 wrote:
A drawer has six loose blue socks and six loose white socks. If four socks are removed from the drawer at random and without replacement. What is the probability that one pair of each color was selected?

A. 2/33
B. 5/66
C. 5/33
D. 5/11
E. 1/2

So, we want the probability of removing 2 blues socks out of 6 and 2 white socks out of 6, while removing 4 socks out of 12.

$$P=\frac{favorable}{total}=\frac{C^2_{6}*C^2_{6}}{C^4_{12}}=\frac{5}{11}$$.

My book gives wrong anwers for this question.
Intern
Joined: 12 Jun 2012
Posts: 41
Followers: 1

Kudos [?]: 32 [0], given: 28

Re: A drawer has six loose blue socks and six loose white socks. [#permalink]

### Show Tags

24 Sep 2012, 00:51
Can someone explain the maths in more detail - ie what C2/6 means?
_________________

Math Expert
Joined: 02 Sep 2009
Posts: 38796
Followers: 7712

Kudos [?]: 105739 [0], given: 11578

Re: A drawer has six loose blue socks and six loose white socks. [#permalink]

### Show Tags

24 Sep 2012, 02:51
jordanshl wrote:
Can someone explain the maths in more detail - ie what C2/6 means?

Check here:
math-combinatorics-87345.html (Combinations)
math-probability-87244.html (Probability)

Hope it helps.
_________________
Senior Manager
Joined: 03 Sep 2012
Posts: 336
Location: United States
Concentration: Healthcare, Strategy
GMAT 1: 730 Q48 V42
GPA: 3.88
WE: Medicine and Health (Health Care)
Followers: 16

Kudos [?]: 190 [0], given: 31

Re: A drawer has six loose blue socks and six loose white socks. [#permalink]

### Show Tags

25 Sep 2012, 00:27
No of Loose blue socks = 6 (3 pairs)
No. of Loose white Socks = 6 (3 pairs)
total no. of blue and white socks = 12
Total no. of socks to be selected = 4

So we have C (12,4) = no of ways the socks can be selected = 495

No of ways One pair of blue socks is selected ( 2 blue socks) , C (6,2) , No of ways one pair of white socks can be selected C (6,2) ..Because we have to find a scenario where EXACTLY one pair of Blue socks and ONE pair of WHITE socks is selected we will multiply the two .. ie 15 x 15 ..

Filling the information in the Probability formula we get P (A) = (15 x 15) / 495 = 5 : 11 (D)
_________________

"When you want to succeed as bad as you want to breathe, then you’ll be successful.” - Eric Thomas

Intern
Joined: 25 May 2013
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: A drawer has six loose blue socks and six loose white socks. [#permalink]

### Show Tags

26 May 2013, 09:43
Bunuel wrote:
solo1234 wrote:
A drawer has six loose blue socks and six loose white socks. If four socks are removed from the drawer at random and without replacement. What is the probability that one pair of each color was selected?

A. 2/33
B. 5/66
C. 5/33
D. 5/11
E. 1/2

So, we want the probability of removing 2 blues socks out of 6 and 2 white socks out of 6, while removing 4 socks out of 12.

$$P=\frac{favorable}{total}=\frac{C^2_{6}*C^2_{6}}{C^4_{12}}=\frac{5}{11}$$.

Hi, i was going through this question and tried a different approach and thus my answer differs ..please correct
me if iam wrong..

4 cards are selected at random without replacement.
1st card then 2nd card then 3rd and then 4th card.
and we have 6B and 6W

So P(selecting 2 cards of same color one by one and the 2 cards of other same color)=6*5*6*5/12*11*10*9 = 5/66

[arent we drawing 1 card at a time and not 4 cards at a tiime ]

Regards,
Math Expert
Joined: 02 Sep 2009
Posts: 38796
Followers: 7712

Kudos [?]: 105739 [0], given: 11578

Re: A drawer has six loose blue socks and six loose white socks. [#permalink]

### Show Tags

27 May 2013, 00:48
apd2006 wrote:
Bunuel wrote:
solo1234 wrote:
A drawer has six loose blue socks and six loose white socks. If four socks are removed from the drawer at random and without replacement. What is the probability that one pair of each color was selected?

A. 2/33
B. 5/66
C. 5/33
D. 5/11
E. 1/2

So, we want the probability of removing 2 blues socks out of 6 and 2 white socks out of 6, while removing 4 socks out of 12.

$$P=\frac{favorable}{total}=\frac{C^2_{6}*C^2_{6}}{C^4_{12}}=\frac{5}{11}$$.

Hi, i was going through this question and tried a different approach and thus my answer differs ..please correct
me if iam wrong..

4 cards are selected at random without replacement.
1st card then 2nd card then 3rd and then 4th card.
and we have 6B and 6W

So P(selecting 2 cards of same color one by one and the 2 cards of other same color)=6*5*6*5/12*11*10*9 = 5/66

[arent we drawing 1 card at a time and not 4 cards at a tiime ]

Regards,

Mathematically the probability of picking 4 socks simultaneously, or picking them one at a time (without replacement) is the same.
_________________
Intern
Joined: 25 May 2013
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: A drawer has six loose blue socks and six loose white socks. [#permalink]

### Show Tags

27 May 2013, 03:08
In your approach to solution ,you are replacing (taking number of different combinations of 4 at a time, that means you are replacing the socks back,
otherwise why is the count of socks not decreasing? and this is done in both -while calculating the favorable and total outcomes.)
Math Expert
Joined: 02 Sep 2009
Posts: 38796
Followers: 7712

Kudos [?]: 105739 [0], given: 11578

Re: A drawer has six loose blue socks and six loose white socks. [#permalink]

### Show Tags

27 May 2013, 03:59
apd2006 wrote:
In your approach to solution ,you are replacing (taking number of different combinations of 4 at a time, that means you are replacing the socks back,
otherwise why is the count of socks not decreasing? and this is done in both -while calculating the favorable and total outcomes.)

$$C^2_6$$ is picking 2 out of 6 without replacement.

Check here for more: math-combinatorics-87345.html

Hope it helps.
_________________
Intern
Joined: 17 Mar 2013
Posts: 7
GMAT 1: 720 Q49 V39
Followers: 0

Kudos [?]: 0 [0], given: 39

Re: A drawer has six loose blue socks and six loose white socks. [#permalink]

### Show Tags

22 Jul 2013, 01:34
Hi, I was trying through the probability approach:

the probability of selecting 2 blue and 2 white socks in the order (12/12 * 5/11 * 6/10 * 5/9) = 5/33

No. of possible orders = 4!/(2! * 2!) = 6 and all have same probability

p = 6 * 5 /33 = 10/11.

Why is this going wrong?
Math Expert
Joined: 02 Sep 2009
Posts: 38796
Followers: 7712

Kudos [?]: 105739 [1] , given: 11578

Re: A drawer has six loose blue socks and six loose white socks. [#permalink]

### Show Tags

22 Jul 2013, 03:37
1
KUDOS
Expert's post
kv18 wrote:
Hi, I was trying through the probability approach:

the probability of selecting 2 blue and 2 white socks in the order (12/12 * 5/11 * 6/10 * 5/9) = 5/33

No. of possible orders = 4!/(2! * 2!) = 6 and all have same probability

p = 6 * 5 /33 = 10/11.

Why is this going wrong?

It should be (6/12 * 5/11 * 6/10 * 5/9) * 4!/(2! * 2!) = 5/11.

Hope it helps.
_________________
Intern
Joined: 17 Mar 2013
Posts: 7
GMAT 1: 720 Q49 V39
Followers: 0

Kudos [?]: 0 [0], given: 39

Re: A drawer has six loose blue socks and six loose white socks. [#permalink]

### Show Tags

22 Jul 2013, 05:00
Bunuel wrote:
kv18 wrote:
Hi, I was trying through the probability approach:

the probability of selecting 2 blue and 2 white socks in the order (12/12 * 5/11 * 6/10 * 5/9) = 5/33

No. of possible orders = 4!/(2! * 2!) = 6 and all have same probability

p = 6 * 5 /33 = 10/11.

Why is this going wrong?

It should be (6/12 * 5/11 * 6/10 * 5/9) * 4!/(2! * 2!) = 5/11.

Hope it helps.

Ohh...thank you so much Bunuel...looks like I need to get my basics right..
Current Student
Joined: 03 Oct 2014
Posts: 145
Location: India
Concentration: Operations, Technology
GMAT 1: 720 Q48 V40
WE: Engineering (Aerospace and Defense)
Followers: 2

Kudos [?]: 32 [0], given: 89

Re: A drawer has six loose blue socks and six loose white socks. [#permalink]

### Show Tags

13 Feb 2015, 06:16
Intern
Joined: 28 Nov 2012
Posts: 39
Schools: NUS '20
Followers: 0

Kudos [?]: 9 [0], given: 25

A drawer has six loose blue socks and six loose white socks. [#permalink]

### Show Tags

12 Dec 2015, 07:11
Hello Bunuel

If the socks are identical, then the number of ways of selecting a sock in any turn would be 2 (either a W or B). If they form a pair they will be identical?

IMO - all possible selections are - {bbbb, wwww, bbbw, wwwb, wwbb} out of which wwbb is what we require ~ hence answer should be 1/5?

For e.g. if white and blue here would be boys and girls and then we are asked to find a team which has exactly 2 boys and 2 girls - In this case, the solution you mentioned should be valid.

Thank you

Bunuel wrote:
solo1234 wrote:
A drawer has six loose blue socks and six loose white socks. If four socks are removed from the drawer at random and without replacement. What is the probability that one pair of each color was selected?

A. 2/33
B. 5/66
C. 5/33
D. 5/11
E. 1/2

So, we want the probability of removing 2 blues socks out of 6 and 2 white socks out of 6, while removing 4 socks out of 12.

$$P=\frac{favorable}{total}=\frac{C^2_{6}*C^2_{6}}{C^4_{12}}=\frac{5}{11}$$.

Verbal Forum Moderator
Joined: 02 Aug 2009
Posts: 4511
Followers: 394

Kudos [?]: 4180 [0], given: 109

Re: A drawer has six loose blue socks and six loose white socks. [#permalink]

### Show Tags

12 Dec 2015, 07:35
rsaahil90 wrote:
Hello Bunuel

If the socks are identical, then the number of ways of selecting a sock in any turn would be 2 (either a W or B). If they form a pair they will be identical?

IMO - all possible selections are - {bbbb, wwww, bbbw, wwwb, wwbb} out of which wwbb is what we require ~ hence answer should be 1/5?

For e.g. if white and blue here would be boys and girls and then we are asked to find a team which has exactly 2 boys and 2 girls - In this case, the solution you mentioned should be valid.

Thank you

Bunuel wrote:
solo1234 wrote:
A drawer has six loose blue socks and six loose white socks. If four socks are removed from the drawer at random and without replacement. What is the probability that one pair of each color was selected?

A. 2/33
B. 5/66
C. 5/33
D. 5/11
E. 1/2

So, we want the probability of removing 2 blues socks out of 6 and 2 white socks out of 6, while removing 4 socks out of 12.

$$P=\frac{favorable}{total}=\frac{C^2_{6}*C^2_{6}}{C^4_{12}}=\frac{5}{11}$$.

Hi rsaahil90,
you may be correct in the 5 types of combination ..
however you have 6 pairs from which you have to choose these combinations and each combination does not have same weightage...
lets see this question only..
combinations ..
1) bbbb- 6C4.. choosing 4 black socks out of avail 6= 15..
2)wwww- same as 1)-15
3)bbbw-6C3*6C1=120
4)wwwb-same as 3)=120
5)wwbb-6C2*6C2=15*15=225

now total ways =15+15+120+120+225=495..
the wwbb way=225
so prob=225/495=5/11..
hope the concept was clear..
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Intern
Joined: 28 Nov 2012
Posts: 39
Schools: NUS '20
Followers: 0

Kudos [?]: 9 [0], given: 25

Re: A drawer has six loose blue socks and six loose white socks. [#permalink]

### Show Tags

12 Dec 2015, 07:44
Hello Chetan

This is my whole concern - if all six of the socks are identical then there is just one way to choose 2 or 3 or 6 socks from that color. For e.g. if you have 5 red colored balls, in how many ways you can choose three i.e. 1 way as all the red balls are identical. If in this example balls would have been boys, then 5C3 ways are possible but not in case of red balls or socks in the concerned question

Thanks

Bunuel wrote:
solo1234 wrote:
A drawer has six loose blue socks and six loose white socks. If four socks are removed from the drawer at random and without replacement. What is the probability that one pair of each color was selected?

A. 2/33
B. 5/66
C. 5/33
D. 5/11
E. 1/2

So, we want the probability of removing 2 blues socks out of 6 and 2 white socks out of 6, while removing 4 socks out of 12.

$$P=\frac{favorable}{total}=\frac{C^2_{6}*C^2_{6}}{C^4_{12}}=\frac{5}{11}$$.

Hi rsaahil90,
you may be correct in the 5 types of combination ..
however you have 6 pairs from which you have to choose these combinations and each combination does not have same weightage...
lets see this question only..
combinations ..
1) bbbb- 6C4.. choosing 4 black socks out of avail 6= 15..
2)wwww- same as 1)-15
3)bbbw-6C3*6C1=120
4)wwwb-same as 3)=120
5)wwbb-6C2*6C2=15*15=225

now total ways =15+15+120+120+225=495..
the wwbb way=225
so prob=225/495=5/11..
hope the concept was clear..[/quote]
Intern
Joined: 12 Nov 2016
Posts: 14
Followers: 0

Kudos [?]: 0 [0], given: 3

A drawer has six loose blue socks and six loose white socks. [#permalink]

### Show Tags

12 Nov 2016, 12:56
Bunuel wrote:
kv18 wrote:

It should be (6/12 * 5/11 * 6/10 * 5/9) * 4!/(2! * 2!) = 5/11.

Hope it helps.

I think this question coming I believe from Kaplan's book is not clearly written, the answer 5/11 is only correct, if it really matters that I pull out a pair. As it was noted earlier, the case is that 4 socks are drawn (no matter simultaneously or not) and there are only 5 possible scenarios (W- White, B - Black, order does not matter): WWWW, BBBB, WWWB, BBBW, BBWW. Why in the world, the probability is not simply 1/5?
The other point is that 5/11 = 45% in other words, it is almost 50/50 chance of getting socks right, which looks strange from common sense view..Suppose you have 4 hands and one can catch only one sock you put your hands into a drawer with 12 socks laying in any order, do you really have almost 50/50 chance to pull out 2 pairs?
A drawer has six loose blue socks and six loose white socks.   [#permalink] 12 Nov 2016, 12:56
Similar topics Replies Last post
Similar
Topics:
3 There are 30 socks in a drawer. 60% of the socks are red and the... 1 16 Aug 2016, 08:03
5 A drawer contains red socks, black socks, and white socks. What is the 13 09 Nov 2016, 10:20
11 George's drawer has 10 loose black socks, 15 loose blue socks, and 8 8 16 May 2017, 20:39
5 There are 2 blue socks, 4 white socks, 6 black socks, and 8 red socks 2 15 May 2016, 12:55
There are 30 socks in a drawer. Sixty percent of the socks are red, an 3 26 Feb 2011, 18:58
Display posts from previous: Sort by