SOLUTION: Your home's security system has a component which is 90% reliable with a back-up component that is 70% reliable. Assume that the reliabilities of the two components are independent

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Question 274425: Your home's security system has a component which is 90% reliable with a back-up component that is 70% reliable. Assume that the reliabilities of the two components are independent. If someone burglarizes your home, what is the probability that
(a) both components fail?
(b) at least one component functions properly?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Your home's security system has a component which is 90% reliable with a back-up component that is 70% reliable. Assume that the reliabilities of the two components are independent. If someone burglarizes your home, what is the probability that
(a) both components fail?: 0.9*0.7 = 0.63
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(b) at least one component functions properly?
P(at least one) = 1 - P(both fail) = 1-0.63 = 0.37
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Cheers,
Stan H.