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

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Joined: 08 Nov 2008
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A string of 10 lightbulbs is wired in such a way that if any [#permalink]  17 Nov 2008, 07:53
A string of 10 lightbulbs is wired in such a way that if
any individual lightbulb fails, the entire string fails. If for
each individual lightbulb the probability of failing during
time period T id 0.06, what is the probability that the
string of lightbulbs will fail during time period T?

A.0.06
B.(0.06)^10
C.1-(0.06)^10
D.(0.94)^10
E.1-(0.94)^10
Manager
Joined: 08 Aug 2008
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Re: bulbs-25 [#permalink]  17 Nov 2008, 08:07
A.
proability of each=probablility of entire string.
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Re: bulbs-25 [#permalink]  17 Nov 2008, 17:38
I think the answer is E.

The probability of the string not failing is the probability that every single light bulb will not fail (0.94^10)
So, the probability that it will fail is 1 - 0.94^10
Manager
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Re: bulbs-25 [#permalink]  17 Nov 2008, 22:38
If there are two light bulbs in the series, the series will work only if both bulbs are working and NOT work when one of them, both of them have failed.

For two bulbs :

WW -- series works
WF -- series fails
FW -- series fails
FF -- series fails.

Probability of both bulbs working = .94^2
Probability of series failing (one or more bulb failing)= (1- (.94)^2)

Therefore for, 10 bulbs the probability would be 1-(.94)^10

(E)
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Re: bulbs-25   [#permalink] 17 Nov 2008, 22:38
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# A string of 10 lightbulbs is wired in such a way that if any

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