Problem #4 (15pts) A firm has ordered a batch of identical electronic device fro

Question

Problem #4 (15pts) A firm has ordered a batch of identical electronic device from 4 different suppliers with the following distribution: 30% supplier 1, 20% supplier 2,35% supplier 3, and 15% supplier 4. The historical data shows that 8% of supplier l items, 6% of supplier 2 items, 4% of supplier 3 items, and 10% of supplier 4 items are defective. What is the probability that a randomly selected device is coming from supplier 3 and is defective? If an item is selected randomly from the batch, what is the probability that the selected item is defective? If an item is selected at random and it is defective, what is the probability that it is coming from supplier 3? 1- 2- 3-

Explanation / Answer

1) P(supplier 3 and defective) = P(Defective | Supplier 3)*P(Supplier 3) = 0.04 * 0.35 = 0.014

2) P(defective) = P(Defective | Supplier 1)*P(Supplier 1) + P(Defective | Supplier 2)*P(Supplier 2) +P(Defective | Supplier 3)*P(Supplier 3) + P(Defective | Supplier 4)*P(Supplier 4)
= 0.08*0.3 + 0.06*0.2 + 0.04*0.35 + 0.1*0.15 = 0.065

3) P(Supplier 3 | Defective) = P(Supplier 3 and defective)/P(Defective) = 0.014/0.065 = 0.2154

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