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 tune, 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?

Explanation

`P(A) = 0.5`

`P(B) = 0.3`

`P(C) = 0.2`

`P(D/A) = 0.01`

`P(D/B) = 0.05`

`P(D/C) = 0.07`

By baes theorem

`P(A/D) = (0.5 xx 0.01)/(0.5 xx 0.01 + 0.3 xx 0.05 + 0.2 xx 0.07) `

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