SOLUTION: a manufacturer found that among 500 randomly selected smoke detectors only 450 worked properly. Based on this information, how many smoke detectors would you have to install to be

Question 1152260: a manufacturer found that among 500 randomly selected smoke detectors only 450 worked properly. Based on this information, how many smoke detectors would you have to install to be sure that the probability that at least one of them will work will be at least 99.9%
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The point estimate of the reliability is 0.9
want to know if we raise 0.9 to some power, what is the probability at least 1 works.
This is 1- probability none of them works, and that must be 0.001
The probability one doesn't work is 0.1
The probability that none of x doesn't work is 0.1^x
when x=3, there are 3 smoke detectors that have a probability of 90% working and 10% not working.
The probability of all 3 not working is .001, so the probability of at least one working is 0.999.
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