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Part $1$

Rick$$Wing$,$ salesperson for Wave Soldering$$Systems$,$ Inc.$($WSSI$),$ has provided you with a proposal for improving the temperature control on your present machine. The machine uses a$$hot$-$air knife to cleanly remove excess solder from printed circuit$$boards; this is a great$$concept$,$ but the$$hot$-$air temperature control lacks reliability. According to$$Wing$,$ engineers at WSSI have improved the reliability of the critical temperature controls. The new system still has the four sensitive integrated circuits controlling the$$temperature$,$ but the new machine has a backup for each. The four integrated circuits have reliabilities of

$0\mathrm{.}880\mathrm{.}88,$

$0\mathrm{.}900\mathrm{.}90,$

$0\mathrm{.}920\mathrm{.}92,$

and

$0\mathrm{.}940\mathrm{.}94.$

The four backup circuits all have a reliability of

$0\mathrm{.}880\mathrm{.}88.$

Part $2$

$$a$)$ The overall reliability of the new temperature controller$=$

enter your response here$\%$

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