(a) A bolt is manufactured by 3 machines A, B, and C. A turns twice as many items as B, and machine B and C produce an equal number of items. Two percent of bolts produced by A and B are defective, and 4% of bolts produced by C are defective. All bolts are put into one stockpile, and one is chosen from this pile. What is the probability that it is defective?
(b) A manufacturer of a flu vaccine is concerned about the quality of its flu serum. Batches of serum are processed by three different departments having rejection rates of 0.10, 0.08, and 0.12 respectively. The inspections by the departments are sequential and independent. (i) What is the probability that a batch of serum survives the second department inspection but is rejected by the third department? (ii) What is the probability that a batch of serum is rejected by all the departments?