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

Question

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) \(1-(0.99)^{(10*9)}\)

(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)}

Marcab · Answer

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} .

PrashantPonde · Answer

Background: The whole chain will fail if atleast one of the 10 links fails.

Probability    = 0.99

Probability  none  of the 10 links will break]  = (0.99)^{10}

Thus probability    = 1 - (0.99)^{10}

Hence (D).

Bunuel · Answer

Similar question to practice: a-string-of-10-light-bulbs-is-wired-in-such-a-way-that-if-131205.html

californiaNY · Answer

not failing you mean! am sure you got caught up!

Marcab · Answer

sorry....edited the typo!!
thanks

WholeLottaLove · Answer

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!

Bunuel · Answer

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.

mathivanan · Answer

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

Abhishek009 · Answer

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}

anairamitch1804 · Answer

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

ScottTargetTestPrep · Answer

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

KrishnakumarKA1 · Answer

P(link fails) = 1 - P(link not fail) = 1 - (1-0.01)(1-0.01)(1-0.01)(1-0.01)(1-0.01)(1-0.01)(1-0.01)(1-0.01)(1-0.01)(1-0.01) = 1 - 0.99^10

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