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A firm manufactures PVC pipes in three p...

A firm manufactures PVC pipes in three plants viz, X, Y and Z. The daily production volumes from the three firm X, Y and Z are respectively 2000 units, 3000 units and 5000 units. It is known from the past experience that `3%` of the output from plant X, `4%` from plant Y and `2%` from plant Z are defective. A pipe is selected at random from a day's total production
(i) find the probability that the selected pipe is defective one.
(ii) If the selected pipe is a defective, then what is the probability that it was produced by plant Y ?

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