A production line has three machines A$,$ B$,$ and C$,$ with reliabilities of $0\mathrm{.}99,0\mathrm{.}96,$ and $0\mathrm{.}93,$ 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 $($i$.$e$.,$ a series backup$),$ and Plan $2$ involves providing a backup for each machine $($i$.$e$.,$ a parallel backup$).$ In either case, three additional machines $($A$,$ B$,$ and C$)$ would be used with reliabilities equal to the original threed. Assume that a single switch is used in Plan $1$ to transfer production to the backup line if the first line fails, and this switch is $98$ percent reliable, while reliabilities of the machines remain the same. Recalculate the reliability of Plan $1.$ Compare this reliability with the reliability of Plan $1$ calculated in solving the original problem. How much did reliability of Plan $1$ decrease as a result of a $98$ percent reliable switch?e$.$ Assume that three switches are used in Plan $2$ to transfer production to the backup machines if the original machines fail, and these switches are all $98$ percent reliable, while reliabilities of the machines remain the same. Recalculate the reliability of Plan $2.$ Compare the reliability of this plan with the reliability of Plan $2$ calculated in solving the original problem. How much did reliability of Plan $2$ decrease?