Question content area

Part $1$

Upper R $2$equals$0\mathrm{.}87$

Upper R $1=0\mathrm{.}92$

Upper R $4$equals$0\mathrm{.}78$

Upper R $3$equals$0\mathrm{.}67$

Xiaohei designed the system above with her engineering team.

$($a$)$ The overall system reliability is

$$

$41\mathrm{.}83\%($enter your response as a percentage rounded to two decimal $$places$).$

$($b$)$ If they have to pay $$$$4$ comma $200$ to fix a failed$$ system, what is the expected failure cost of the$$ system? $$$

$$

enter your response here $($round your response to the nearest $$dollar$).$

$($c$)$ If Xiaohei installs R$5$ as a backup for R$4.$ R$5$ has a reliability of$95\%.$ The probability of failure of the system with R$5$ is

$$

enter your response here$\%($enter your response as a percentage rounded to two decimal$$ places$).$

$($d$)$ How much should they pay for R$5$ at the$$ maximum? $$$

$$

enter your response here $($round your response to the nearest $$dollar$).$