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

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tonytran14896
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A string of 10 lightbulbs is wired in such a way that if any [#permalink] New post   06 Aug 2015, 13:04
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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
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D
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Re: A string of 10 lightbulbs is wired in such a way that if any [#permalink] New post   06 Aug 2015, 13:12
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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] New post   07 Aug 2015, 00:48
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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


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)
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Re: A string of 10 lightbulbs is wired in such a way that if any [#permalink] New post   16 Aug 2015, 03:04
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. :roll:
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Re: A string of 10 lightbulbs is wired in such a way that if any [#permalink] New post   16 Aug 2015, 12:35
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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


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 string of 10 lightbulbs is wired in such a way that if any [#permalink] New post   19 Aug 2015, 22:54
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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. :roll:




.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?
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Re: A string of 10 lightbulbs is wired in such a way that if any [#permalink] New post   29 Jan 2018, 08:09
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Re: A string of 10 lightbulbs is wired in such a way that if any [#permalink]
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