Question 1206245
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The failure rate for a guided missile control system is 8 in 1,000. Suppose that 
a duplicate but completely independent control system is installed in each missile 
so that, if the first fails, the second can take over. The reliability of a missile 
is the probability that it does not fail. What is the reliability of the modified missile?
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The probability that one control system will fail is 8/1000 = 0.008.


Since the control systems are independent, the probability that both control systems will fail is

    P = {{{(8/1000)*(8/1000)}}} = {{{(8/1000)^2}}} = {{{64/1000000}}} = 0.000064.


The probability that at least one control system of two will survive and will work is the complement to it

    P' = 1-P = 1 - 0.000064 = 0.999936.


<U>ANSWER</U>.  The probability that at least one control system of two will survive and will work is 0.999936.

         In other words, the reliability of the doubled control system is 0.999936.
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At this point, the problem is solved completely.