Four independent components and are arranged as follows: • Components and are…
MATHEMATICS · Multi-part · AP · AP Statistics · Probability Random Variables Distributions · Probability Random Variables Distributions
Problem
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.
(i) Find the probability that the entire system works.
(ii) Find the probability that the system fails because Subsystem I fails.
(iii) Given that the system has failed, calculate the probability that exactly one of R or S failed.