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A chain is comprised of 10 identical links, each of which in [#permalink]
05 Jan 2013, 05:35

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Difficulty:

35% (medium)

Question Stats:

67% (01:42) correct
33% (01:03) wrong based on 93 sessions

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?

Re: A chain is comprised of 10 identical links, each of which in [#permalink]
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?

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 \(1-0.99^{10}\). _________________

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

Expert's post

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?

Re: A chain is comprised of 10 identical links, each of which in [#permalink]
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?

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 \(1-0.99^{10}\).

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

Re: A chain is comprised of 10 identical links, each of which in [#permalink]
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.

Re: A chain is comprised of 10 identical links, each of which in [#permalink]
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.

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