Machine A $-0\mathrm{.}70$

Machine B $-0\mathrm{.}95$

Machine C $-0\mathrm{.}95$

There is one back$-$up machine for Machine A$.$ What is the reliability of the system without the back$-$up and what is the reliability of the system including the back$-$up$?($Choose closest answer$)$

Without back$-$up: $0\mathrm{.}900,$ With the back$-$up: $0\mathrm{.}953$

Without back$-$up: $0\mathrm{.}684,$ With the back$-$up: $0\mathrm{.}821$

Without back$-$up: $0\mathrm{.}833,$ With the back$-$up: $0\mathrm{.}920$

Without back$-$up: $0\mathrm{.}766,$ With the back$-$up: $0\mathrm{.}887$

Without back$-$up: $0\mathrm{.}821,$ With the back$-$up: $0\mathrm{.}886$

Without back$-$up: $0\mathrm{.}632,$ With the back$-$up: $0\mathrm{.}821$