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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 firms `X`,` Y` and `Z` are respectively `2000` units, `3000` units `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 a defective one.
(ii) if the selected pipe is a défective, then what is the probability that it was plant `Y`?

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