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I need help with this question, with a good explanation, thanks!

The probability a HP network server is down is .025. If you have two independent servers, what is the probability that at least one of them is operational?

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Welcome to MSE! Do you have any thoughts on the problem and can share what you have to done to help responders? Regards –  Amzoti Jun 16 '13 at 2:02
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1 Answer

Hint: Consider that $P( \geq 1 \text{ is operational}) = 1 - P(\text{none are operational})$.

And for none to be operational, we need both to not be working. And they are independent, so that $$P(\text{server A and B are/are not working}) = P(\text{A is/is not working}) \cdot P(\text{B is/is not working})$$

Can you work it out from here?

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Is the answer .95 because the probability of none being operational is .05, because .25 times 2 is .05? –  user82649 Jun 16 '13 at 1:35
    
@user82649 I assume that $P(\text{A doesn't work})$ is equal to $.025$ as that is what you listed above. Then rather than multiplying by two, you should multiply $P(\text{A doesn't work})$ by $P(\text{B doesn't work})$ –  Zvpunry Jun 16 '13 at 1:37
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