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A factor inspector examined the defects ...

A factor inspector examined the defects in hardness, finishing and dimensions of an item. After examining 100 items he gave the following report:
All three defects 5, defect in hardness and finishing 10, defect in dimensions and finishing 8, defect in dimensions and hardness 20. Defect in finishing 30, in hardness 23 and in dimensions 50. The inspector was fined, why?

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A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?