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A factory has three machines X, Y, an...

A factory has three machines X, Y, and Z producing 1000, 2000 and 3000 bolts per day respectively. the machine X produces 1% defective bolts, Y produces 1.5% and Z produces 2% defective bolts. At the end of a day, a bolt is drawn at random and is found to be defective. What is the probability that this defective bolt has been produced by machine X?

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