Question

A company runs three plants. The first produces 45% of the total with a 1% defective rate, the second 30% with 2% defective, and the last 25% with 3% defective. Production is combined in a central warehouse for distribution. An item is randomly selected from stock.

**a)** What is the probability that it is
defective?

**b)** If it is defective, what is the probability
that it was from plant 2?

Answer #1

Let us denote the events :

A_{1} : a randomly selected item is produced by first
plant

A_{2} : a randomly selected item is produced by second
plant

A_{3} : a randomly selected item is produced by third
plant

and D : a randomly selected item is defective

Given

and

a) The probability that it is defective

b) The probability that of the randomly selected item is defective, the probability that it was from plant 2

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