NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 14:18 It is currently 25 Apr 2024, 14:18
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

A box contains 20 bulbs,12 are defective.Four bulbs are selected at

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
B
kanigmat011
Manager
Manager
Joined: 27 Jul 2014
Posts: 202
Own Kudos [?]: 361 [15]
Given Kudos: 15
Schools: ISB '15
GMAT 1: 660 Q49 V30
GPA: 3.76
Send PM
GMAT ToolKit User Reviews Badge
A box contains 20 bulbs,12 are defective.Four bulbs are selected at [#permalink] New post   Updated on: 25 Jun 2015, 06:14
5
Kudos
10
Bookmarks
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

69% (02:26) correct 31% (02:20) wrong based on 202 sessions
Hide Show timer Statistics
A box contains 20 bulbs, 12 are defective. Four bulbs are selected at random. What is the probability that at least one of the four selected is defective?

A. 33/323
B. 1/9690
C. 14/969
D. 955/969
E. 5/12
ShowHide Answer
Official Answer
D

Originally posted by kanigmat011 on 25 Jun 2015, 06:10.
Last edited by Bunuel on 25 Jun 2015, 06:14, edited 4 times in total.
Renamed the topic and edited the question.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619012 [3]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: A box contains 20 bulbs,12 are defective.Four bulbs are selected at [#permalink] New post   25 Jun 2015, 06:19
1
Kudos
2
Bookmarks
Expert Reply
kanigmat011 wrote:
A box contains 20 bulbs, 12 are defective. Four bulbs are selected at random. What is the probability that at least one of the four selected is defective?

A. 33/323
B. 1/9690
C. 14/969
D. 955/969
E. 5/12


12 are defective, 8 not defective.

P(at least one defective out of 4) = 1 - P(none is defective out of 4) = 1 - 8/20*7/19*6/18*5/17 = 955/969.

Answer: D.
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5960
Own Kudos [?]: 13387 [1]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: A box contains 20 bulbs,12 are defective.Four bulbs are selected at [#permalink] New post   25 Jun 2015, 06:34
1
Kudos
Expert Reply
kanigmat011 wrote:
A box contains 20 bulbs, 12 are defective. Four bulbs are selected at random. What is the probability that at least one of the four selected is defective?

A. 33/323
B. 1/9690
C. 14/969
D. 955/969
E. 5/12


Bunuel's solution is perfect however another insight to answer the questions is

Since 60% are defective (12/20) therefore the probability of one of the 4 selected bulb defective should be pretty high and should be close to 1

only Option D gives a close enough value as in every other option the probability is even less than 1/2

Answer: Option D
User avatar
adityadon
Manager
Manager
Joined: 18 Mar 2014
Posts: 205
Own Kudos [?]: 138 [0]
Given Kudos: 175
Location: India
Concentration: Operations, Strategy
Schools: INSEAD Jan '17 NTU '17 NUS '17 (D) Rutgers '18 SMU '16 (A) Weatherhead '18 (S) Broad '17 (M)
GMAT 1: 670 Q48 V35
GPA: 3.19
WE:Information Technology (Computer Software)
Send PM
GMAT ToolKit User
Re: A box contains 20 bulbs,12 are defective.Four bulbs are selected at [#permalink] New post   25 Jun 2015, 11:02
is this a gmat question ?? looked like some indian exam question !!
Too mch calculations in it..
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619012 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: A box contains 20 bulbs,12 are defective.Four bulbs are selected at [#permalink] New post   26 Jun 2015, 01:50
Expert Reply
adityadon wrote:
is this a gmat question ?? looked like some indian exam question !!
Too mch calculations in it..


I don't think that it's a question from a reliable GMAT source.
User avatar
B
ravindra88
Intern
Intern
Joined: 03 Jul 2015
Posts: 10
Own Kudos [?]: 34 [1]
Given Kudos: 2
Location: India
Send PM
Re: A box contains 20 bulbs,12 are defective.Four bulbs are selected at [#permalink] New post   01 Aug 2015, 06:27
1
Kudos
kanigmat011 wrote:
A box contains 20 bulbs, 12 are defective. Four bulbs are selected at random. What is the probability that at least one of the four selected is defective?

A. 33/323
B. 1/9690
C. 14/969
D. 955/969
E. 5/12


Defective = 12, Not defective = 8

Total possible no. of combinations of 4 = \(20C4\)

Total possible no. of non defective combinations of 4 = \(8C4\) (since only 8 are non defective)

P(none is defective) \(= 8C4/ 20C4 = 14/969\)

P(at least one defective) = 1 - P(none is defective) = \(955/969\)

Answer D
User avatar
B
TimeTraveller
Senior Manager
Senior Manager
Joined: 28 Jun 2015
Posts: 250
Own Kudos [?]: 293 [0]
Given Kudos: 47
Concentration: Finance
GPA: 3.5
Send PM
Re: A box contains 20 bulbs,12 are defective.Four bulbs are selected at [#permalink] New post   01 Aug 2015, 06:42
Probability that at least one of the four bulbs is defective = 1 - (none of the 4 are defective).

Probability that none of the 4 balls are defective = 8C4/20C4 = 70/4845 = 14/969

Probability that at least one is defective = 1 - 14/969 = 955/969. Ans (D).
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5344
Own Kudos [?]: 3964 [0]
Given Kudos: 160
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge
Re: A box contains 20 bulbs,12 are defective.Four bulbs are selected at [#permalink] New post   25 Dec 2022, 08:12
Given: A box contains 20 bulbs, 12 are defective. Four bulbs are selected at random.
Asked: What is the probability that at least one of the four selected is defective?

The probability that none of the four selected in defective = 8*7*6*5/20*19*18*17 = 7*2/19*3*17 = 14/969
The probability that at least one of the four selected is defective = 1 - 14/969 = 955/969

IMO D
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32679
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: A box contains 20 bulbs,12 are defective.Four bulbs are selected at [#permalink] New post   15 Mar 2024, 07:08
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: A box contains 20 bulbs,12 are defective.Four bulbs are selected at [#permalink]
15 Mar 2024, 07:08
Moderators:
Bunuel
Math Expert
92915 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions