Tests are carried out on three machines A, B and C to assess the likelihood that each machine will produce a faulty component. The results are summarised in the table.

Machine A Machine B Machine C Faulty Not faulty 325 3 12 2 8 15 A component is chosen at random from those tested.

(a) Find the probability that the component chosen (i) is from Machine A, (ii) is a faulty component from Machine C, (iii) is not faulty or is from Machine A,

(b) It is known that the component chosen is faulty. Find the probability that it is from Machine B.