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Suppose an item is manufacture by three machines X, Y and Z. All the three machines have equal capacity and are operated at the same rate. It is known that the percentages of defective items produced by X, Y and Z are 1, 7, and 12 percent respectively. All the items produced by X, Y and Z are put into one bin. From this bin, one item is drawn at random and is found to be defective. What is probability that this item was produced on Y?
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