$10$ A system is composed of three elements. Component $1$ is in series with the parallel redundant combination of components $2$ and $3,$ which are identical.

${}_1=1\frac{f}{y}r,{}_2={}_3=3\frac{f}{y}r$

${}_1=98\frac{r}{y}r,{}_2={}_3=50\frac{r}{y}r$

$($a$)$ Calculate the reliability of this system for a mission of $1000$ hr $.$

$($b$)$ What is the mean time to failure for this system?