Consider an expensive part with 96.6% reliability. If the part fails, it will cost the company $12,000.

a. What is the expected failure cost per part?

b. On each part, a rather unreliable backup can be installed that has a reliability of only 30%. What is the maximum amount the company should be willing to pay per piece to install the backrest? Support your answer.

C. Suppose that a second 30% reliable backup part could be installed, so that if both the original and the first backup part fail, then the second backup part will be used. If that second backing piece costs $100, should it be installed? Support your answer.