SOLUTION: A certain item is manufactured by 3 factories. Suppose we have a stockpile of the items in which *30% of the items were made in factory A *20% of the items were made in factory

SOLUTION: A certain item is manufactured by 3 factories. Suppose we have a stockpile of the items in which 30% of the items were made in factory A 20% of the items were made in factory

Question 1044687: A certain item is manufactured by 3 factories. Suppose we have a stockpile of the items in which
*30% of the items were made in factory A
*20% of the items were made in factory B
*50% of the items were made in factory C
Moreover, suppose that
*2% of the items from factory A are defective
*3% of the items from factory B are defective
*4% of the items from factory C are defective.
1) Find the probability that an item selected at random from the stockpile is defective.
2) If a randomly selected item is found to be defective, what is the probability that this item came from factory B?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
===Defective=====non-defective====Total
A-----6--------------294-----------300
B-----6--------------194-----------200
C----20--------------480-----------500
Tot---32-------------968-----------1000
Probability of a defective item chosen at random is 3.2%
If an item is defective (n=32) probability it was made in factory B is 6/32 or 18.8%
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