An electrical system consists of four components. The system works if components A and B work and either of the components C or D works. The reliability (probability of working) of each component is given by P(A) = 0.9, P(B) = 0.9, P(C) = 0.8, and P(D) = 0.8. Find the probability that (a) the entire system fails to work and (b) component C does not work, given that the entire system fails to work. Assume that the four components work independently. Thus far I have solved part a by solving for the probability that the entire system works, denoted P(E) where E is the event that the entire system works, then subtracting that from 1; this gave me the result P(E') = 0.2224 (where E' is the complement of E). I am just having trouble solving part b. I have found that P(C'|E') = [P(C')xP(E'|C')]/P(E') = P(C' n E')/P(E') where n is read "intersect". I really do not see where to go from here though. I have values for P(C') and P(E') but no values for P(E'|C') or P(C' n E'). Any help would be very much appreciated. Thank you in advance.