Four independent components P,Q,R and S are arranged as follows:
• Components P and Q are connected in parallel, forming Subsystem I (the subsystem works if at least one of P or Q works).
• Components R and S are connected in parallel, forming Subsystem II (the subsystem works if at least one of R or S works).
The entire system works only when both subsystems work.
Suppose P(P)=0.80,P(Q)=0.90,P(R)=0.85 and P(S)=0.90.
a. (i) Find the probability that the entire system works.
b. (ii) Find the probability that the system fails because Subsystem I fails.
c. (iii) Given that the system has failed, calculate the probability that exactly one of R or S failed.