A system has four components, A, B, C, D. The probability that every component will work is P(A) =.95, P (B) = .85, P (C) =.90, and P (D) = .60; all components must operate in order for the system to work.  Since the probabilities associated with components B and D are low, backup components, B-B and D-D, with the similar probabilities are given:

i.    Draw the box and line diagram for this system.

ii.    What is the probability that every component will not work?
                                         
iii.    What is the probability that the system will work without the backup components? .
                                          
iv.    List the ways in which the system can work with the backup components.
                                           
v.    How much improvement in reliability do the backup components give?