Question 1012226: 10. Parts and materials for the skis made by the Downhill Adventures Company are supplied by two suppliers. Supplier A’s materials made up 30% of what is used, with Supplier B providing the rest. Past records indicate that 15% of Supplier A’s materials are defective and 10% of B’s are defective. Since it is impossible to tell which supplier the materials came from once they are in inventory , the manager wants to know which supplier more likely supplied the defective materials the foreman has brought to his attention
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 30% of the parts came from supplier A.
70% of the parts came from supplier B.
15% of the parts from supplier A are defective on the average.
10% of the parts from supplier B are defective on the average.
it apears that the defective parts would most likely come from supplier B.
here's why.
suppose inventory contained 1000 parts, 30% came from supplier A and 70% from supplier B.
this means that 300 parts came from supplier A and 700 came from supplier B.
since 15% of the parts from supplier A are defective, then .15 * 300 = 45 parts are defective from supplier A.
since 10% of the parts from supplier B are defective, then .10 * 700 = 70 parts are defective from supplier B.
so, out of the 1000 parts, there are 45 defective from supplier A and 70 defective from supplier B.
if you take a random part from the inventory, the probability it will be defective is 45 + 70 = 115 / 1000 = 11.5%.
the probability it will be defective and from supplier A is 45/1000 = .045.
the probability it will be defective and frm supplier B is 70/1000 = .07.
if the part is defective, the probability that it will be from supplier A is 45/115 = 39.13%.
if the part is defective, the probability that it will be from supplier B is 70/115 = 60.87%.
the probability is higher that the defective part will be from supplier B.
while supplier B is more reliable than supplier A, there are a lot more parts in inventory from supplier B which makes the probability that the defective part will be from supplier B higher.
.15 * .3 = .045
.10 * .7 = .07
|
|
|
