Sometimes multiple redundant backup components are used for complex "mission critical" systems such as military and civilian aircraft and the ICU wards in hospitals. The result is a very high system reliability for the product in question since failure would be catastrophic.

Determine the system reliability of a component that is $95\%$ reliable with $($not one, but$)$ two backup components in parallel, each with a reliability of $95\%.$ Hint: Resolve the "backup to the backup" first, then use this result as a backup for the original component.

$($Use six decimal places for your calculations$)$

$1\mathrm{.}150000$ or $11\mathrm{.}15\%$ reliable

$0\mathrm{.}950000$ or $95\%$ reliable

$0\mathrm{.}999875$ or $99\mathrm{.}9875\%$ reliable

$0\mathrm{.}997500$ or $99\mathrm{.}75\%$ reliable