Bayes rule:

John owns a retail store for selling phones. The phones are manufactured at three different factories, A, B,

C, where factory A, B, and C produces 20%, 30%, and 50% of the phone being sold at John's store. The

probabilities of the defective phones from stores A, B, and C are 2%, 1%, and 0.6%, respectively. The total

number of phones being sold at John's store is 10,000. One day, a customer walks up to John's store, and ask

for a refund for a defective phone.

1. What is the probability of a phone being defective?

2. What is the probability that this defective phone is manufactured at factory A?

3. What is the probability that this defective phone is manufactured at factory B?

4. What is the probability that this defective phone is manufactured at factory C?