In a certain factory, three machines, B1 , B2, and B3 make 30%, 45% and 25% respectively of products manufacted. It is known that 8% of items from machine 1 are defective, 4% of the items from machine 2 are defective, and 6% of items from machine 3 are defective. If we select a finished product at random
a) What is the probability that it is defective?
b) What is the probability that it was produced by machine 1 given that it was defective?