Consider a state space having $3$ states: $s_1,s_2$ and $s_3.$ The value of each state is $V(s_1)=0,V(s_2)=4,V(s_3)=2.$ There can be transitions from $s_1$ to $s_2,s_2$

to $s_1$ and $s_3,$ and $s_3$ to $s_2.$ Starting at $s_1,$ what is the probability that we end up back at $s_1$ after $2$ steps of simulated annealing? Assume that we follow a

temperature schedule of $10,5,1.$ Next state is chosen uniformly at random whenever there are multiple possibilities.

Round answer to $3$ digits after decimal point $($eg$,$ if the answer is $0\mathrm{.}1346,$ return $0\mathrm{.}135).$