SOLUTION: A machine has 7 identical components which function independently. The probability that a component will fail is 0.2. The machine will stop working if more than three components fa

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Question 1136999: A machine has 7 identical components which function independently. The probability that a component will fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the machine will be working.
Answer by ikleyn(52863) About Me  (Show Source):
You can put this solution on YOUR website!
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The probability that the machine will be working is the probability that NO MORE THAN 3 component fail


    P = P(0) + P(1) + P(2) + P(3) = 


       = %281-0.2%29%5E7 + C%5B7%5D%5E1%2A%281-0.2%29%5E6%2A0.2 + C%5B7%5D%5E2%2A%281-0.2%29%5E5%2A0.2%5E2 + C%5B7%5D%5E3%2A%281-0.2%29%5E4%2A0.2%5E3 = 


       =  = 0.9667 = 96.67%   (approximately).    ANSWER