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A factory has three machines X, Y and Z...

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

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