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# A string of 10 lightbulbs is wired in such a way that if any

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Intern
Joined: 06 Aug 2015
Posts: 2
A string of 10 lightbulbs is wired in such a way that if any [#permalink]

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06 Aug 2015, 12:04
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35% (medium)

Question Stats:

61% (01:01) correct 39% (00:56) wrong based on 132 sessions

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A string of 10 lightbulbs is wired in such a way that if any individual lighbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during a certain time period is 0.05, what is the probability that the string of lightbulbs will NOT fail during said time period?
a. 0.05
b. (0.05)^10
c. 1 - (0.05)^10
d. (0.95)^10
e. 1 - (0.95)^10
[Reveal] Spoiler: OA
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Re: A string of 10 lightbulbs is wired in such a way that if any [#permalink]

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06 Aug 2015, 12:12
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tonytran14896 wrote:
A string of 10 lightbulbs is wired in such a way that if any individual lighbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during a certain time period is 0.05, what is the probability that the string of lightbulbs will NOT fail during said time period?
a. 0.05
b. (0.05)^10
c. 1 - (0.05)^10
d. (0.95)^10
e. 1 - (0.95)^10

Probability of a 'fail' = P(F) = 0.05 --> Probability of 'no fail' = 1-P(F) = 1-0.05 = 0.95

Thus, the probability of 10 bulbs to not fail = 0.95*0.95*0.95*0.95*0.95*0.95*0.95*0.95*0.95*0.95 = 0.95^10, D is the correct answer.
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Re: A string of 10 lightbulbs is wired in such a way that if any [#permalink]

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06 Aug 2015, 23:48
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Expert's post
tonytran14896 wrote:
A string of 10 lightbulbs is wired in such a way that if any individual lighbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during a certain time period is 0.05, what is the probability that the string of lightbulbs will NOT fail during said time period?
a. 0.05
b. (0.05)^10
c. 1 - (0.05)^10
d. (0.95)^10
e. 1 - (0.95)^10

Think about it: When will the string of lightbulbs not fail? Only when all lightbulbs stay alive simultaneously.

P (a lightbulb will stay alive) = 1 - 0.05 = 0.95

So probability that all lightbulbs stay live simultaneously $$= 0.95 * 0.95 * 0.95.....0.95 = (0.95)^{10}$$
(0.95s will be multiplied because it is an "and" situation. You need the first "and" the second "and" the third etc to stay alive)

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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 02 Sep 2014 Posts: 9 Location: United States Concentration: Strategy, Technology GMAT Date: 08-22-2015 GPA: 3.1 WE: Consulting (Consulting) A string of 10 lightbulbs is wired in such a way that if any [#permalink] ### Show Tags 16 Aug 2015, 02:04 VeritasPrepKarishma wrote: tonytran14896 wrote: A string of 10 lightbulbs is wired in such a way that if any individual lighbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during a certain time period is 0.05, what is the probability that the string of lightbulbs will NOT fail during said time period? a. 0.05 b. (0.05)^10 c. 1 - (0.05)^10 d. (0.95)^10 e. 1 - (0.95)^10 Think about it: When will the string of lightbulbs not fail? Only when all lightbulbs stay alive simultaneously. P (a lightbulb will stay alive) = 1 - 0.05 = 0.95 So probability that all lightbulbs stay live simultaneously $$= 0.95 * 0.95 * 0.95.....0.95 = (0.95)^{10}$$ (0.95s will be multiplied because it is an "and" situation. You need the first "and" the second "and" the third etc to stay alive) Answer (D) asking this out of curiosity .what will be the question if the answer would be c . my thinking is a bit weird please forgive me. Math Expert Joined: 02 Sep 2009 Posts: 43891 Re: A string of 10 lightbulbs is wired in such a way that if any [#permalink] ### Show Tags 16 Aug 2015, 11:35 tonytran14896 wrote: A string of 10 lightbulbs is wired in such a way that if any individual lighbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during a certain time period is 0.05, what is the probability that the string of lightbulbs will NOT fail during said time period? a. 0.05 b. (0.05)^10 c. 1 - (0.05)^10 d. (0.95)^10 e. 1 - (0.95)^10 Similar question to practice: a-string-of-10-light-bulbs-is-wired-in-such-a-way-that-if-131205.html _________________ Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7955 Location: Pune, India Re: A string of 10 lightbulbs is wired in such a way that if any [#permalink] ### Show Tags 19 Aug 2015, 21:54 1 This post received KUDOS Expert's post crackgmat15 wrote: VeritasPrepKarishma wrote: tonytran14896 wrote: A string of 10 lightbulbs is wired in such a way that if any individual lighbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during a certain time period is 0.05, what is the probability that the string of lightbulbs will NOT fail during said time period? a. 0.05 b. (0.05)^10 c. 1 - (0.05)^10 d. (0.95)^10 e. 1 - (0.95)^10 Think about it: When will the string of lightbulbs not fail? Only when all lightbulbs stay alive simultaneously. P (a lightbulb will stay alive) = 1 - 0.05 = 0.95 So probability that all lightbulbs stay live simultaneously $$= 0.95 * 0.95 * 0.95.....0.95 = (0.95)^{10}$$ (0.95s will be multiplied because it is an "and" situation. You need the first "and" the second "and" the third etc to stay alive) Answer (D) asking this out of curiosity .what will be the question if the answer would be c . my thinking is a bit weird please forgive me. .05 is the probability of a light bulb failing. (.05)^10 is the probability of EVERY light bulb failing. 1 - (.05)^10 is the probability that not every light bulb fails. In a situation like this, you could use it: A room has 10 light bulbs and a weaver needs to weave a cloth there this evening. He needs at least one light bulb working to weave. What is the probability that he will be able to weave? _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: A string of 10 lightbulbs is wired in such a way that if any [#permalink]

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29 Jan 2018, 07:09
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Re: A string of 10 lightbulbs is wired in such a way that if any   [#permalink] 29 Jan 2018, 07:09
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