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?
Let us denote the events :
A1 : a randomly selected item is produced by first plant
A2 : a randomly selected item is produced by second plant
A3 : a randomly selected item is produced by third plant
and D : a randomly selected item is defective
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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