Machines A and B turn out respectively 10% and 90% of the total production of a certain type of article. The probability that machine A turns out a defective item is 0.01 and the probability that machine B turns out a defective item is 0.05.

(a) draw the tree diagram of the above scenario

(b) What is the probability that an article taken at random from the production line is defective?

(c) What is the probability that an article taken at random from the production line was made by machine A, and not defective?