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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    $\begingroup$ There's an assumption you have to make there... $\endgroup$ – David Mitra Nov 17 '11 at 18:05
  • $\begingroup$ Assumptions of independence are often not made explicit. They usually ought to be. $\endgroup$ – Michael Hardy Nov 17 '11 at 18:22
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    $\begingroup$ 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. $\endgroup$ – André Nicolas Nov 17 '11 at 18:30

Your answer is right if the three events are independent.


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.

  • $\begingroup$ If the assumption of independence does not hold, then there's really not enough information. $\endgroup$ – Michael Hardy Nov 17 '11 at 18:23
  • $\begingroup$ @MichaelHardy unless the posted problem is not the complete version ;) $\endgroup$ – N. S. Nov 17 '11 at 18:30

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