It is currently 15 Nov 2018, 10:33
My Tests

Close

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
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.

A drawer contains 8 pairs of socks. For each sock, there is

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
2 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 1175
Followers: 44

Kudos [?]: 1048 [2] , given: 6

CAT Tests
A drawer contains 8 pairs of socks. For each sock, there is [#permalink] New post 26 May 2017, 11:13
2
This post received
KUDOS
Expert's post
00:00

Question Stats:

50% (02:50) correct 50% (00:47) wrong based on 8 sessions
A drawer contains 8 pairs of socks. For each sock, there is exactly one matching sock. If Ed randomly selects 6 socks without replacement, what is the probability that he will have at least one pair of matching socks?

A) 1/4
B) 19/51
C) 111/143
D) 3/4
E) 145/189
[Reveal] Spoiler: OA

_________________

Brent Hanneson – Creator of greenlighttestprep.com
Image
Sign up for our free GRE Question of the Day emails

3 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 1175
Followers: 44

Kudos [?]: 1048 [3] , given: 6

CAT Tests
Re: A drawer contains 8 pairs of socks. For each sock, there is [#permalink] New post 29 May 2017, 16:41
3
This post received
KUDOS
Expert's post
GreenlightTestPrep wrote:
A drawer contains 8 pairs of socks. For each sock, there is exactly one matching sock. If Ed randomly selects 6 socks without replacement, what is the probability that he will have at least one pair of matching socks?

A) 1/4
B) 19/51
C) 111/143
D) 3/4
E) 145/189


Here's an approach that uses probability rules.

When it comes to probability questions involving "at least," it's best to try using the complement.
That is, P(Event A happening) = 1 - P(Event A not happening)

So, here we get: P(at least 1 matching pair) = 1 - P(zero matching pairs)

P(zero matching pairs)
P(zero matching pairs) = P(pick ANY sock 1st AND 2nd sock doesn't match 1st sock AND 3rd sock doesn't match other selections AND 4th sock doesn't match other selections AND 5th sock doesn't match other selections AND 6th sock doesn't match other selections)
= P(pick ANY sock 1st) x P(2nd sock doesn't match 1st sock) x P(3rd sock doesn't match other selections) x P(4th sock doesn't match other selections) x P(5th sock doesn't match other selections) x P(6th sock doesn't match other selections)
= 1 x 14/15 x 12/14 x 10/13 x 8/12 x 6/11
= 32/143

So, P(at least 1 pair) = 1 - P(zero pairs)
= 1 - 32/143
= 111/143

Answer:
[Reveal] Spoiler:
C


ASIDE: Once we draw the first sock, there are 15 sock s remaining, and only 1 matches the 1st selection.
This means there are 14 sock s that DON'T match the first.
So, P(no match on 2nd draw) = 14/15

Then, once we draw the second sock (without a match), there are 14 socks remaining, and 2 of them match either the 1st or 2nd selection.
This means there are 12 socks that DON'T match.
So, P(no match on 3rd draw) = 12/14

etc

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
Image
Sign up for our free GRE Question of the Day emails

Manager
Manager
Joined: 25 Nov 2017
Posts: 51
Followers: 0

Kudos [?]: 41 [0], given: 5

Re: A drawer contains 8 pairs of socks. For each sock, there is [#permalink] New post 21 Dec 2017, 05:45
Can we do as follows
We have 8 pairs so the probability of chosing one pair out of 8 8C1 = 8
Then since we have 16 socks and we are taking 6 socks out of 16. 16C6
The proba will be 8 / 16C6
Can we do with combinatorics?
Because I cant find the result
Re: A drawer contains 8 pairs of socks. For each sock, there is   [#permalink] 21 Dec 2017, 05:45
Display posts from previous: Sort by

A drawer contains 8 pairs of socks. For each sock, there is

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.