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A chain is comprised of 10 identical links, each of which in

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A chain is comprised of 10 identical links, each of which in [#permalink] New post 05 Jan 2013, 05:35
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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)}
[Reveal] Spoiler: OA

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Re: A chain is comprised of 10 identical links, each of which in [#permalink] New post 05 Jan 2013, 06:01
Expert's post
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 1-0.99^{10}.
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Re: A chain is comprised of 10 identical links, each of which in [#permalink] New post 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).
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Re: A chain is comprised of 10 identical links, each of which in [#permalink] New post 07 Jan 2013, 00:47
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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)}


Similar question to practice: a-string-of-10-light-bulbs-is-wired-in-such-a-way-that-if-131205.html
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Re: A chain is comprised of 10 identical links, each of which in [#permalink] New post 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 1-0.99^{10}.


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Re: A chain is comprised of 10 identical links, each of which in [#permalink] New post 08 Jan 2013, 18:18
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Re: A chain is comprised of 10 identical links, each of which in [#permalink] New post 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!
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Re: A chain is comprised of 10 identical links, each of which in [#permalink] New post 16 May 2013, 22:38
Expert's post
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: a-string-of-10-light-bulbs-is-wired-in-such-a-way-that-if-131205.html

In addition check probability chapter of Math Book for theory: math-probability-87244.html

Also check some probability questions to practice:
DS: search.php?search_id=tag&tag_id=33
PS: search.php?search_id=tag&tag_id=54

Hard questions on combinations and probability with detailed solutions: hardest-area-questions-probability-and-combinations-101361.html (there are some about permutation too)

Hope it helps.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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Re: A chain is comprised of 10 identical links, each of which in   [#permalink] 16 May 2013, 22:38
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