# Probability that two of three devices will not work

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