A bank's Data Center has 100 servers. Each server has a 'Mean Time Between Failures' (MTBF) of 10,000 hours. If the servers operate 24/7, calculate the statistically expected number of server failures the IT department will have to handle in a year (8,760 hours).

In a CBS network, a branch is connected to the central switch via a primary fiber link and a secondary backup satellite link. The probability of the primary link failing in a year is 5% (0.05). The probability of the backup link failing is 10% (0.10). The central switch itself has a failure probability of 0.1% (0.001). Assuming these are independent events, calculate the total probability (in percentage) that the branch will lose ALL connectivity to the central system during the year.

A production line uses three machines in sequence to manufacture a product. The first machine has a failure rate of 5%, the second has 3%, and the third has 2%. If the company can only improve the reliability of one machine, which machine's optimization will achieve the greatest reduction in the overall production line failure rate?