Question 629744
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There are three components that operate in a series so all must function properly if it is to be complete. 
The probability of failure during one period of operation are .03, .05, .06. 
Component failures are statistically independent.
a) Fine the probability that the system functions properly.
b) Find the probability that the system fails during one period of operation
This is what I have done so far but I'm not sure its the right answer please help me and show 
how you got to the answer so I understand
a) .97*.95*.94=.866
b)(.03+.05+.06)-(.03*.05*.06)=.14
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        I will explain it in a short and clear way.



<pre>
(a)  The system functions properly, if and only if all three components function properly.

     Therefore, since the components are statistically independent,

         P(the system functions properly) = (1-0.03)*(1-0.05)*(1-0.06) = 0.97*0.95*0.94 = 0.86621.



(b)  P(the system fails) = 1 - P(the system works properly) = 1 - 0.86621 = 0.13379.


     The probability to fail is the COMPLEMENT to the probability to function properly.


     It is the MAJOR CONCEPTION to learn from part (b) of this problem.
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Solved.