Author 
Message 
TAGS:

Hide Tags

Manager
Status: Never ever give up on yourself.Period.
Joined: 23 Aug 2012
Posts: 151
Location: India
Concentration: Finance, Human Resources
GMAT 1: 570 Q47 V21 GMAT 2: 690 Q50 V33
GPA: 3.5
WE: Information Technology (Investment Banking)

A chain is comprised of 10 identical links, each of which in [#permalink]
Show Tags
05 Jan 2013, 05:35
10
This post was BOOKMARKED
Question Stats:
64% (00:50) correct 36% (01:17) wrong based on 261 sessions
HideShow timer Statistics
A chain is comprised of 10 identical links, each of which independently has a 1% chance of breaking under a certain load. If the failure of any individual link means the failure of the entire chain, what is the probability that the chain will fail under the load? (A) \((0.01)^{10}\) (B) \(10(0.01)^{10}\) (C) \(1(0.10)(0.99)^{10}\) (D) \(1(0.99)^{10}\) (E) \(1(0.99)^{(10*9)}\)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Don't give up on yourself ever. Period. Beat it, no one wants to be defeated (My journey from 570 to 690) : http://gmatclub.com/forum/beatitnoonewantstobedefeatedjourney570to149968.html



VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1372
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75

Re: A chain is comprised of 10 identical links, each of which in [#permalink]
Show Tags
05 Jan 2013, 06:01
1
This post received KUDOS
Optimus66 wrote: A chain is comprised of 10 identical links, each of which independently has a 1% chance of breaking under a certain load. If the failure of any individual link means the failure of the entire chain, what is the probability that the chain will fail under the load?
(A) \((0.01)^{10}\) (B) \(10(0.01)^{10}\) (C) \(1(0.10)(0.99)^{10}\) (D) \(1(0.99)^{10}\) (E) \(1(0.99)^{(10*9)}\) There are 10 links, each of which has the probability of 0.99 of not failing. If any of them breaks, the chain will not survive. To find the probability that the chain will fail under the load implies to find the the probability that any link breaks. To do so, find the reverse probability: the probability that the chain will not break or none of the 10 links break. Since there are 10 links, hence probability that none of the link breaks is \(0.99^{10}\). Hence P that the chain will break is \(10.99^{10}\).
_________________
Prepositional Phrases ClarifiedElimination of BEING Absolute Phrases Clarified Rules For Posting www.UnivScholarships.com



Current Student
Joined: 27 Jun 2012
Posts: 401
Concentration: Strategy, Finance

Re: A chain is comprised of 10 identical links, each of which in [#permalink]
Show Tags
05 Jan 2013, 11:12
Background: The whole chain will fail if atleast one of the 10 links fails. Probability [that a single link will NOT break] \(= 0.99\) Probability [that none of the 10 links will break] \(= (0.99)^{10}\) Thus probability [that atleast 1 of the link will break] \(= 1  (0.99)^{10}\) Hence (D).
_________________
Thanks, Prashant Ponde
Tough 700+ Level RCs: Passage1  Passage2  Passage3  Passage4  Passage5  Passage6  Passage7 Reading Comprehension notes: Click here VOTE GMAT Practice Tests: Vote Here PowerScore CR Bible  Official Guide 13 Questions Set Mapped: Click here Looking to finance your tuition: Click here



Math Expert
Joined: 02 Sep 2009
Posts: 43896

Re: A chain is comprised of 10 identical links, each of which in [#permalink]
Show Tags
07 Jan 2013, 00:47



Intern
Joined: 11 Jul 2012
Posts: 12

Re: A chain is comprised of 10 identical links, each of which in [#permalink]
Show Tags
08 Jan 2013, 11:02
Marcab wrote: Optimus66 wrote: A chain is comprised of 10 identical links, each of which independently has a 1% chance of breaking under a certain load. If the failure of any individual link means the failure of the entire chain, what is the probability that the chain will fail under the load?
(A) \((0.01)^{10}\) (B) \(10(0.01)^{10}\) (C) \(1(0.10)(0.99)^{10}\) (D) \(1(0.99)^{10}\) (E) \(1(0.99)^{(10*9)}\) There are 10 links, each of which has the probability of 0.99 of failing. If any of them breaks, the chain will not survive. To find the probability that the chain will fail under the load implies to find the the probability that any link breaks. To do so, find the reverse probability: the probability that the chain will not break or none of the 10 links break. Since there are 10 links, hence probability that none of the link breaks is \(0.99^{10}\). Hence P that the chain will break is \(10.99^{10}\). not failing you mean! am sure you got caught up!
_________________
all you need is a will.



VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1372
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75

Re: A chain is comprised of 10 identical links, each of which in [#permalink]
Show Tags
08 Jan 2013, 18:18



Senior Manager
Joined: 13 May 2013
Posts: 456

Re: A chain is comprised of 10 identical links, each of which in [#permalink]
Show Tags
16 May 2013, 13:56
My three weaknesses on the GMAT are combinatorics, word problems, and probability!!!
I am having difficulty figuring out how to solve this problem. The book says to take the probability of each link NOT failing, multiplying them by one another and subtracting the result from one. I understand superficially that this is a time/work saving measure, but why does it work and how would I know how to do that come test time?!
While we're on the topic, does anyone have a good guide on basic, intermediate and advanced probability/combinatoric skills? I have been using the Manhattan guides and in general they are quite good, but they don't have a lot of problems on probability nor do they have many lessons lessons on them.
Thanks!



Math Expert
Joined: 02 Sep 2009
Posts: 43896

Re: A chain is comprised of 10 identical links, each of which in [#permalink]
Show Tags
16 May 2013, 22:38
WholeLottaLove wrote: My three weaknesses on the GMAT are combinatorics, word problems, and probability!!!
I am having difficulty figuring out how to solve this problem. The book says to take the probability of each link NOT failing, multiplying them by one another and subtracting the result from one. I understand superficially that this is a time/work saving measure, but why does it work and how would I know how to do that come test time?!
While we're on the topic, does anyone have a good guide on basic, intermediate and advanced probability/combinatoric skills? I have been using the Manhattan guides and in general they are quite good, but they don't have a lot of problems on probability nor do they have many lessons lessons on them.
Thanks! This topic might help with your doubts: astringof10lightbulbsiswiredinsuchawaythatif131205.htmlIn addition check probability chapter of Math Book for theory: mathprobability87244.htmlAlso check some probability questions to practice: DS: search.php?search_id=tag&tag_id=33PS: search.php?search_id=tag&tag_id=54Hard questions on combinations and probability with detailed solutions: hardestareaquestionsprobabilityandcombinations101361.html (there are some about permutation too) Hope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



NonHuman User
Joined: 09 Sep 2013
Posts: 13762

Re: A chain is comprised of 10 identical links, each of which in [#permalink]
Show Tags
15 Jun 2015, 15:44
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 Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Manager
Joined: 10 Jun 2015
Posts: 126

Re: A chain is comprised of 10 identical links, each of which in [#permalink]
Show Tags
17 Aug 2015, 22:47
daviesj wrote: A chain is comprised of 10 identical links, each of which independently has a 1% chance of breaking under a certain load. If the failure of any individual link means the failure of the entire chain, what is the probability that the chain will fail under the load?
(A) \((0.01)^{10}\) (B) \(10(0.01)^{10}\) (C) \(1(0.10)(0.99)^{10}\) (D) \(1(0.99)^{10}\) (E) \(1(0.99)^{(10*9)}\) It is easier to find if you apply 1 P(the chain never breaks)=P( the chain will fail) the probability that one link does not break is 1.01=.99 the entire chain does not break if the first link does not break and the second link does not break and the third link does not break and so on till the tenth link therefore, 0.99*0.99*0.99*... ten times so, the answer is 1(0.99)^10 Hence, the correct option is D



NonHuman User
Joined: 09 Sep 2013
Posts: 13762

Re: A chain is comprised of 10 identical links, each of which in [#permalink]
Show Tags
12 Nov 2016, 08:16
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 Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3326
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: A chain is comprised of 10 identical links, each of which in [#permalink]
Show Tags
12 Nov 2016, 11:20
daviesj wrote: A chain is comprised of 10 identical links, each of which independently has a 1% chance of breaking under a certain load.If the failure of any individual link means the failure of the entire chain, what is the probability that the chain will fail under the load?
(A) \((0.01)^{10}\) (B) \(10(0.01)^{10}\) (C) \(1(0.10)(0.99)^{10}\) (D) \(1(0.99)^{10}\) (E) \(1(0.99)^{(10*9)}\) Probability of failure = Probability of non failure of atleast 1 link Probability of failure of the chain = 1  Probability of no failure Probability of failure of the chain = \(1(0.99)^{10}\) Hence, answer will definitely be (D) \(1(0.99)^{10}\)
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )



Director
Joined: 26 Oct 2016
Posts: 682
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: A chain is comprised of 10 identical links, each of which in [#permalink]
Show Tags
14 Mar 2017, 16:09
Qualitatively, many failure scenarios could occur: • None of the links will fail, • Exactly 1 of the links will fail, • Exactly 2 of the links will fail, • etc. Given the complexity of the failure scenarios, it is easier for us to look at the opposite scenario: probability that at least 1 link will fail = 1 – probability that all links will not fail For each of the links, the probability that it will not fail is 1 – 0.01 = 0.99. The probability that all ten will not fail is thus (0.99)^10, since the probability that all ten will not fail is simply the product of the probabilities of the individual links not failing. Therefore, the Probability that at least 1 link will fail = 1 – (0.99)^10. The correct answer is D
_________________
Thanks & Regards, Anaira Mitch



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2192
Location: United States (CA)

Re: A chain is comprised of 10 identical links, each of which in [#permalink]
Show Tags
20 Mar 2017, 05:50
daviesj wrote: A chain is comprised of 10 identical links, each of which independently has a 1% chance of breaking under a certain load. If the failure of any individual link means the failure of the entire chain, what is the probability that the chain will fail under the load?
(A) \((0.01)^{10}\) (B) \(10(0.01)^{10}\) (C) \(1(0.10)(0.99)^{10}\) (D) \(1(0.99)^{10}\) (E) \(1(0.99)^{(10*9)}\) We can use the following equation: 1 = P(at least 1 of 10 links failing) + P(nolinks failing) Since we need to determine the probability that the chain will fail, we are looking for P(at least 1 of 10 links failing). However, we can solve for P(nolinks failing) and then subtract that probability from 1. Since each link has a 1% chance of failing, each link has a 99% chance of NOT failing. Thus, P(nolinks failing) = (0.99)^10, so: P(at least 1 of 10 links failing) = 1  (0.99)^10. Answer: D
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Senior Manager
Joined: 05 Jan 2017
Posts: 434
Location: India

Re: A chain is comprised of 10 identical links, each of which in [#permalink]
Show Tags
21 Mar 2017, 03:20
daviesj wrote: A chain is comprised of 10 identical links, each of which independently has a 1% chance of breaking under a certain load. If the failure of any individual link means the failure of the entire chain, what is the probability that the chain will fail under the load?
(A) \((0.01)^{10}\) (B) \(10(0.01)^{10}\) (C) \(1(0.10)(0.99)^{10}\) (D) \(1(0.99)^{10}\) (E) \(1(0.99)^{(10*9)}\) P(link fails) = 1  P(link not fail) = 1  (10.01)(10.01)(10.01)(10.01)(10.01)(10.01)(10.01)(10.01)(10.01)(10.01) = 1  0.99^10




Re: A chain is comprised of 10 identical links, each of which in
[#permalink]
21 Mar 2017, 03:20






