Last visit was: 30 Dec 2024, 07:52 It is currently 30 Dec 2024, 07:52
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep 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 GRE 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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
PREVIOUS TOPIC
NEXT TOPIC

A leather pouch contains 10 light bulbs, two of which are de

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

avatar
Bunuel
Senior Manager
Senior Manager
Joined: 20 May 2014
Posts: 285
Own Kudos [?]: 727 [8]
Given Kudos: 225
A leather pouch contains 10 light bulbs, two of which are de [#permalink] New post   29 Oct 2017, 01:18
2
6
Bookmarks
00:00

Question Stats:

65% (00:51) correct 34% (01:03) wrong based on 128 sessions

Hide Show timer Statistics

A leather pouch contains 10 light bulbs, two of which are defective.

Quantity A
Quantity B
The probability of drawing two defective light bulbs (without replacement)
The probability of drawing two defective light bulbs (without replacement) and then a non-defective bulb



A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

Kudos for correct solution.
ShowHide Answer
Official Answer
C
avatar
IlCreatore
Director
Director
Joined: 03 Sep 2017
Posts: 518
Own Kudos [?]: 708 [4]
Given Kudos: 0
Send PM
Re: A leather pouch contains 10 light bulbs, two of which are de [#permalink] New post   30 Oct 2017, 07:01
4
The probability of extracting two defective light bulbs without replacement is equal to \(\frac{2}{10}*\frac{1}{9} = \frac{1}{45}\).

The probability of extracting two defective light bulbs without replacement and then a non-defective one is equal to \(\frac{2}{10}*\frac{1}{9}*\frac{8}{8} = \frac{1}{45}\).

The idea is that there are 2 defective light bulbs out of 10 in the first draw, then there is just one out of the 9 light bulbs remained. Once the two defective light bulbs are extracted there are eight out of 8 non defective light bulbs.

The two quantities are equal.

Answer C
avatar
Fatemeh
Manager
Manager
Joined: 22 Feb 2018
Posts: 163
Own Kudos [?]: 215 [0]
Given Kudos: 0
Send PM
Re: A leather pouch contains 10 light bulbs, two of which are de [#permalink] New post   20 Dec 2018, 14:54
Answer: C
10 light bulbs: 8 non-defective + 2 detective
A: The probability of drawing two defective light bulbs (without replacement):
For taking the first one, the probability of being defective is 2/10, for the next one the probability is 1/9, so A equals: 2/10 * 1/ 9 = 2 / 90

B: The probability of drawing two defective light bulbs (without replacement) and then a non-defective bulb:
For taking the first one, the probability of being defective is 2/10, for the next one the probability is 1/9, for the third one, because now we have already taken the two defective lights and there are 8 non-defective lights, the probability of taking a non-defective light is 8/8, so B equals: 2/10 * 1/ 9 * 8/8 = 2 / 90

A and B are equal. The answer is C.
avatar
S
YB114
Manager
Manager
Joined: 11 Oct 2023
Posts: 69
Own Kudos [?]: 44 [0]
Given Kudos: 25
Send PM
Re: A leather pouch contains 10 light bulbs, two of which are de [#permalink] New post   29 Dec 2023, 09:19
Carcass sir, why we are not taking permutation here?
D.B = defective , non-defective

A) D.B , D.B thus (2C1/10C1 * 1C1/9C1) * 2!/2!

B) D.B , D.B , ND.B = 2C1/10C1 * 1C1/9C1 * 8C1/8C1 * 3!/2!
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30554
Own Kudos [?]: 36906 [1]
Given Kudos: 26108
Send PM
Re: A leather pouch contains 10 light bulbs, two of which are de [#permalink] New post   29 Dec 2023, 10:29
1
Expert Reply
Sir this is a probaility question

Probability is the measure of the chance of occurrence of a future event. It tells us how likely we expect the event to happen.


permutation and combination are different things

1. Each of the different orders of arrangements, obtained by taking some, or all, of a number of things, respective of the order in which the things appear in the group, is called a Permutation.

2. Each of the different groups, or collections, that can be formed by taking some, or all, of a number of things, irrespective of the order in which the things appear in the group, is called a Combination.


See here on probability https://gre.myprepclub.com/forum/gre-pr ... tml#p83091

here on permutation and combination https://gre.myprepclub.com/forum/gre-pe ... tml#p83002
avatar
S
YB114
Manager
Manager
Joined: 11 Oct 2023
Posts: 69
Own Kudos [?]: 44 [1]
Given Kudos: 25
Send PM
Re: A leather pouch contains 10 light bulbs, two of which are de [#permalink] New post   31 Dec 2023, 19:57
1
Carcass sir, Understood i oversight "THEN" in quantity B which states a specific order thus no need of permutation.

A) D.B , D.B thus (2/10 * 1/9) * 2!/2! = 1/45

B) D.B , D.B , ND.B = 2/10 * 1/9 * 8/8 =1/45

thus C
Prep Club for GRE Bot
gmatclubot
Re: A leather pouch contains 10 light bulbs, two of which are de [#permalink]
31 Dec 2023, 19:57
Moderators:
adewale223
GRE Instructor
88 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1116 posts
VibhuAnurag
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact