GATE 2022 EC – Question 48
A state transition diagram with states $A$, $B$, and $C$, and transition probabilities $p_1,p_2,\dots,p_7$ is shown in the figure (e.g., $p_1$ denotes the probability of transition from state $A$ to $B$). For this state diagram, select the statement(s) which is/are universally true.
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Correct answer: (A) $p_2+p_3=p_5+p_6$; (C) $p_1+p_4+p_7=1$
Explanation
The probabilities leaving each state must sum to 1. From $A$: $p_1$ (to $B$), $p_4$ (to $C$) and the self-loop $p_7$, so $p_1+p_4+p_7=1$ (C). From $B$: the self-loop $p_2$ and $p_3$ (to $A$), so $p_2+p_3=1$. From $C$: the self-loop $p_5$ and $p_6$ (to $A$), so $p_5+p_6=1$. Then $p_2+p_3=p_5+p_6$ (A) is true, while B and D do not follow from these equations.