Question: 6. A simple system consists of three components, A, B, C, as shown below, with the probability that each component will work. Component A costs

6. A simple system consists of three components, A, B, C, as shown below, with the probability that each component will work. Component A costs $19,000 each, B costs $12,000 each, and C costs $8,000 each. P(A) = 99 P(B) = 97 P(C)=7 .88 a. What is the probability that the system will work? (10) b. Management wishes to have at least a .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? (15) (Bonus) How much will it cost to achieve a 95 probability by adding C's? (5) Page 3 of 5

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