A production line has three machines A$,$ B$,$ and C$,$ with reliabilities of $\mathrm{.}99,\mathrm{.}90,$ and $\mathrm{.}80,$ respectively. The machines are arranged so that if one breaks down, the others must shut down. Engineers are weighing two alternative designs for increasing the line's reliability. Plan $1$ involves adding an identical backup line, and plan $2$ involves providing a backup for each machine. In either case, three machines $($A$,B,$ and C$)$ would be used with reliabilities equal to the original three.

a$.$ Compute overall system reliability under Plan $1.($Round your intermediate calculations and final answer to $4$ decimal places.$)$

Answer is complete and correct.

b$.$ Compute overall system reliability under Plan $2.($Round your intermediate calculations and final answer to $4$ decimal places.$)$

Answer is complete but not entirely correct.

$0\mathrm{.}9409$