I need help with section c, d and e

Q.4 A system has upper branch B and lower branch C as shown in Figure Q4. The branch B has only one micro-processor B. The branch C has two micro-processors C, and C2 in serial. These three micro-processors are independent. Each of these three micro-processors is active with probability 0.8 due to scheduling. A branch is active only when all the micro-processors in the branch are active. The system is active when either branch is active. B 62 Figure Q4. System with two branches. (a) Find the probability that branch C is active. PCCIn Cz) = PCCJPCC] (2 marks) = 0.64 (b) What is the probability that the system is active? PCactive] = PCB VC] (2 marks) = PC BJ + PCC)- PCBNC) = 0 8+ 0.64 - 05/2 =0.928 (c) Given C1 is inactive and C2 is active, find the probability that the system is active. PCActive | Cinc 2 ] = P[ AnB | Cic 2] + PC AnBC | cinci] = PCA I BA (CEnC)] PCBICincx] + PCAIBCnccina)] PCB[cincz] (4 marks) = 1 xPCB] + 0*PCB] = 0.8* (d) Given C2 is active, find the probability that the system is active. (4 marks) (e) Given the system is active, find the probability that B is active and the probability C2 is active. P CALCI) = PCACI[C2] + PCAC/ /c]