A system for milling $2$x$6$s has four sensitive components connected in series with reliabilities of $0\mathrm{.}93,0\mathrm{.}94,0\mathrm{.}92$ and $0\mathrm{.}97.$ According to the quality department of the lumber mill, the current system lacks reliability. At the manufacturing plant, the engineers have proposed to improve the reliability of the system. The new system still has four components, but the system has a backup for each component. The four backup components all have a reliability of $0\mathrm{.}94.$ What is the reliability of the series $($old$)$ system? What is the reliability of the new $($proposed$)$ system? If you pay a premium, the manufacturer can improve all four of the backup units to $0\mathrm{.}97($the third

option$).$ What is the reliability of the third option?