TIFR CSE 2022 | Part A | Question: 13

Question

Consider the transition system shown in the figure below with the initial state $s_1$. A token is initially placed at $s_1$, and it moves to $s_2$ with probability $\frac{2}{3}$, and to $s_3$ with probability $\frac{1}{3}$. From $s_2$ and $s_3$, the token always moves to $s_1$ and $s_2$ respectively. A run of the system consists of an infinite sequence of states constructed by moving the token from one state to another following the transitions forever. Assuming such a run is chosen randomly, what is the fraction of times that the state $s_2$ is expected to appear in the run?

• A. $\frac{1}{7}$
• B. $\frac{2}{7}$
• C. $\frac{3}{7}$
• D. $\frac{5}{7}$
• E. None of the above

Comments

Can anyone explain this question??

Answer 1

According to me,
Fraction of times that the state S2 is expected to appear in the run= 1-(S2 never appears in the run)

S2 never appears in the run is only possible when S1→ S3 only and else S2 will be in every run.

1-(1/3)=2/3

Hence E should be correct.
Please do mention if I’m wrong.

Comments

nah its answer is 3/7