A service has four major components required for completion and delivery to the consumer. The component reliabilities are, $0\mathrm{.}90,0\mathrm{.}94,0\mathrm{.}95,$ and $0\mathrm{.}98.$ All four components must be performed for the service to take place.

a$.$ What is the reliability of the current service offering?

b$.$ The boss wants to improve reliability by providing a backup. Because he$/$she is cheap, they have informed you that they will only backup one of the four components with an identical part. $($The backup will have the same reliability as the component it is replacing$).$ Which component should get the backup to achieve the highest reliability?

c$.$ If one backup with a reliability of $0\mathrm{.}93$ can be added to any of the main components, which one should achieve the highest overall reliability?

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