SOLUTION: The proprietor of Cunningham's Hardware Store has decided to install floodlights on the premises as a measure against vandalism and theft. If the probability is 0.0001 that a certa

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Question 1100945: The proprietor of Cunningham's Hardware Store has decided to install floodlights on the premises as a measure against vandalism and theft. If the probability is 0.0001 that a certain brand of floodlight will burn out within a year, find the minimum number of floodlights that must be installed to ensure that the probability that at least one of them will remain functional for the whole year is at least 0.99999.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The proprietor of Cunningham's Hardware Store has decided to install floodlights on the premises as a measure against vandalism and theft. If the probability is 0.0001 that a certain brand of floodlight will burn out within a year, find the minimum number of floodlights that must be installed to ensure that the probability that at least one of them will remain functional for the whole year is at least 0.99999.
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P(at least one lasts) = 1 - P(all fail)
= 1 - 0.0001^x >= 0.99999
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0.0001^x >= 0.00001
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x >= log(0.0001)/log(0.0001)
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x >= -4/-3 >= 4/3
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Answer:: 2
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Cheers,
Stan H.
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