(Solution) - In a server farm such as that used by Amazon -(2025 Original AI-Free Solution)

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In a server farm such as that used by Amazon or the Gap, a single failure does not cause the whole system to crash. Instead, it will reduce the number of requests that can be satisfied at any one time.
a. If a company has 10,000 computers, and it experiences catastrophic failure only if 1/3 of the computers fail, what is the MTTF for the system?
b. If it costs an extra $1000, per computer, to double the MTTF, would this be a good business decision? Show your work.