A system consists of five components with component 1 functi

A system consists of five components, with component 1 functioning on its own and components 2, 3, 4, 5 connected in parallel. The five components are independent of one another. Let S_i denote the event component i is operational with P(S1)=0.99 and P(S2)=P(S3)=P(S4)=P(S5)=q.

A. Calculate P(System is operational) in terms of q.

B. Given that component S1 is operational, calculate the probability that the system is operational.

C. Given that component S3 is operational, calculate the probability that the system is operational.

D. Assume q=0.5. Given that the system is operational, calculate the probability that component S3 is operational.

Solution

D. Assume q=0.5. Given that the system is operational, calculate the probability that component S3 is operational.