Parts and Materials for the skis made by the Downhill Adventures Company are sup
ID: 2926961 • Letter: P
Question
Parts and Materials for the skis made by the Downhill Adventures Company are supplied by two suppliers. Supplier A's materials make 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 most likely supplied the defective materials the foreman has brought to his attention. Provide the manager this information.
Supplier AExplanation / Answer
answer
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