Three machines-A, B, and C-are used to produce a large quantity of identical parts at a factory. Machine A produces 60% of the parts, while Machines B and C produce 30% and 10% of the parts,
respectively. Historical records indicate that 10% of the parts produced by Machine A are defective,
compared with 30% for Machine B and 40% for Machine C. Suppose we randomly select a part
produced by one of these three machines at random.
a) Draw a tree diagram to represent this chance process. Make sure to include the probabilities of each
branch. (hint: start with three branches) (6 points)
b) What's the probability that the part is defective? (3 points)
c) What's the probability that is from Machine C, given the part is defective? (3 points)