4. A system includes three components (A, B and C), one of which will fail over a time period. The probabilities of the mutually exclusive compon failures are P(A)-0.3 P(B)-0.5 P(C)-0.2 The probability of a system failure (F) depends on which compo nent fails: If A fails, the system fails 4 % of the time. If B fails, the system fails 12 % of the time. If C fails, the system fails 16 % of the time. (a) Find the total probability, P(F), that the system will fail in the time period. P(F) (b)If the system has failed, what are the probabilities that the failure was due to A, B and C respectively? Use Bayes' formula. P(AIF) P(B F) P(CIF)_