Problem 6:
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 1 items, 6% of supplier 2 items, 4% of supplier 3 items, and 10% of supplier 4 items are defective.
1- What is the probability that a randomly selected device is coming from supplier 3 and is defective?
2- If an item is selected randomly from the batch, what is the probability that the selected item is defective?
3- If an item is selected at random and it is defective, what is the probability that it is coming from supplier 3?