The guidance system of a ship is controlled by a computer that has three major modules. In order for the computer to function properly, all three modules must function. Two of the modules have reliabilities of $0\mathrm{.}97,$ and the other has a reliability of $0\mathrm{.}99.$

a$.$ What is the reliability of the computer? $($Round your answer to $4$ decimal places.$)$

b$.$ A backup computer identical to the one being used will be installed to improve overall reliability. Assuming the new computer automatically functions if the main one fails, determine the resulting reliability. $($Round your intermediate calculations and final answer to $4$ decimal places.$)$

c$.$ If the backup computer must be activated by a switch in the event that the first computer fails, and the switch has a reliability of $0\mathrm{.}98,$ what is the overall reliability of the system? $($Both the switch and the backup computer must function in order for the backup to take over.$)($Round your intermediate calculations and final answer to $4$ decimal places.$)$