A game controller has two components. Under the current redesign, Component $1$ has a reliability of $98\%,$ while Component $2$ has a reliability of $97\%.$ This redesign requires that if there are any backups, there must be the same number of backups for both components.

If the required reliability level is $99\mathrm{.}8\%,$ at least how many backup components should be designed into the system?

Question $16$ options:

a$)$

$1$

b$)$

$2$

c$)$

$3$

d$)$

$4$