SOLUTION: 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

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Question 1206245: 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?
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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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 = %288%2F1000%29%2A%288%2F1000%29 = %288%2F1000%29%5E2 = 64%2F1000000 = 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.


ANSWER.  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.

At this point, the problem is solved completely.