A factory has 3 machines, A, B and C, that produce electrical components, A produces 45 per cent of the output, B 30 per cent and C the rest. Some of the components are faulty. A produces 5 per cent, B produces 8 per cent and C produces 6 per cent faulty components. (a) Draw a tree diagram to illustrate this information. Find the probability that a randomly selected component is (b) produced by A and is faulty (c) faulty. Given that a component is faulty (d) find the probability that it was produced by A.