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There are three devices A, B and C. Each of this device has probability of failure a, b and c respectively where $a, b, c \in (0, 1)$. What is probability that A and B will be broken and C will work ok?

I was thinking about: $P = a \cdot b \cdot (1 - c)$, but I'm not sure.

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    One is presumably supposed to assume independence, else the problem cannot be solved. In many cases, independence is unreasonable, since$a$power surge often fries more than one component. There should also have been an explicit time interval over which the probabilities $a$, $b$, and $c$ are taken. No device lives forever.2011-11-17

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Your answer is right if the three events are independent.

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Given the above-mentioned, crucial assumption, your solution looks good.

However, if that assumption does not hold, you would have to re-work your answer.

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    @MichaelHardy unless the posted problem is not the complete version ;)2011-11-17