A manufacturer produces boxes of candy, each containing ten pieces. Two machines are used for this purpose. After a large batch has been produced, it is discovered that one of these machines, which produces 60% of the total output, has a fault that has led to the introduction of an impurity into 10% of the pieces of candy it makes. From a single box of candy, one piece is selected at random and tested. If that piece contains no impurity, what is the probability that the box from which it came was produced by the faulty machine?

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