Question

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 was produced by A?

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Solution

Let

The probability that the item produced by operation

The probability that the item produced by operation

The probability that the item produced by operation

The probability that the item is defective is

Find the probability that the item is produced by operation

Given that,

The probability of a defective item produced by operation

The probability of a defective item produced by operation

The probability of a defective item produced by operation

Put these values in equation (1),

Thus, the required probability is

1