There are two restaurants in a small town: $�$ and $�.$ A survey shows that $10\%$ of $�$ customers in this week will switch to B restaurant next week, and $30\%$ of B customers will go to M next week.

$($a$)(5)$ If the market share for $�$ restaurant is currently $50\%$ this week, what is the $�$ restaurant's market share next week?

$($b$)(5)$ What is the steady$-$state market share for these two restaurants?

$($c$)(5)$ What is the mean first passage time from B to M$?$