(a) A bag contains a large number of beads of which 40% are yellow. A random sample of 20 beads are taken from the bag. Calculate the probability that the sample contains: (i) fewer than 12 yellow beads; (2 marks) (ii) exactly 12 yellow beads. (2 marks) (b) Samples, each of 8 articles, are taken at random from a large consignment in which 20% of articles are defective. (i) Find the number of defective articles that is most likely to occur. (3 marks) (ii) It 100 samples of 8 articles are to be examined, calculate the number of samples in which you would expect to find 3 or more defective articles