A simple system consists of three components, A. B, C, as shown below, with the probability that each component will work. Component A costs $20,000 each, B costs $10,000 each, and C costs $6,000 each.
1- What is the probability that the system will work?
2- Management wishes to have at least a 0.95 probability that the system will work, and proposes to achieve this goal by adding redundant component C’s to the system, which are identical to the existing component C. Each new C would switch on if the preceding C’s failed. How many C’s will be required and the additional cost?
3- Draw the diagram of the new system.