please write the Solution in legible textFREEDOM

FELIX, a very hungry cat, is placed in compartment $1$ and a mouse called MICKEY is placed in

compartment $2.$ The compartments are connected as shown above. MICKEY can move between

the compartments, while FELIX is not big enough to fit through the passages. Suppose that

MICKEY makes one move every one minute. When MICKEY makes a move, suppose it

randomly chooses a passage and moves to the adjacent section. So$,$ if there are $N$ gates, the

probability that MICKEY chooses any gate is $\frac{1}{N}.$ If MICKEY enters compartment $1,$ FELIX the

cat eats him.

a$.$ Model the situation as a Markov Chain. Describe the states and write the Markov transition

matrix.

b$.$ Find the probability that MICKEY's first transition time from compartment $2$ to compartment

$3$ is $4$ minutes.

c$.$ Find the expected first transition time of MICKEY from bin $2$ to bin $3.$

d$.$ What are the chances that MICKEY will be released?

e$.$ Suppose there is a mass of cheese in compartment $3.$ When MICKEY enters compartment $3,$

he eats the cheese. What is the probability that FELIX puts both MICKEY and the cheese in

his stomach?