In the certain assembly plant, four machines, A, B, C and D, make 20%, 18%, 32% and 30%, respectively, of products. It is known from past experience that 2%, 5%, 4% and 1% of products made by each and machine, respectively are defective. Please show work.
A) Make a tree diagram of the scenario.
B) If the product is selected at random, what is the probability that it is defective?
C) Given randomly chosen product was found to be defective, what is the likelihood it is from Machine B?
D) Given a randomly chosen product was found to be defective, which machine is it most likely produced from? Describe the probability/reasoning.