Question

1.There are three machines In a factory. Machine A produces 60% of the items, 5% of all items produced by machine A is defective; machine B produces 10% of which 1% are defective, and machine C produces 30% of which 2% are defective. An item is selected at random from a day’s production of 1000 items. What is probability that the item is defective? An item is selected at random from a day’s production of 1000 items and is found to be defective. What is probability that this defective item is produced by machine A?  

Answer 1

Of the 1000 items

1) Machine A has produced 600 of which 30(5%) are defective

2) Machine B has produced 100 of which 1(1%) is defective

3) Machine C has produced 300 of which 6(2%) are defective

Probability that items is defective = Defective Items/Total Items = (30+1+6)/1000 = 37/1000 = .037

If an item selected in defective, probability that it is produced by A = Defective items produced by A/total defective items = 30/37 = 0.81