GATE EC 2022 Set 1 — Question 48
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Engineering Mathematics → Probability → Definitions of Probability
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Question
A state transition diagram with states and and transition probabilities is shown in the figure ( is the self-loop at ; e.g., denotes the probability of transition from state to ). For this state diagram, select the statement(s) which is/are universally true.
Correct answer
(A) p₂ + p₃ = p₅ + p₆; (C) p₁ + p₄ + p₇ = 1
Solution
In a state transition diagram (Markov Chain), the sum of outgoing transition probabilities from any given state must equal 1.
1.From state : (to B), (to C), and (to A) are the outgoing transitions. Therefore, . This makes statement (C) universally true.
2.From state : (to B) and (to A) are the outgoing transitions. Therefore, .
3.From state : (to C) and (to A) are the outgoing transitions. Therefore, .
Since and , it follows that . This makes statement (A) universally true.Continue learning with Success Tracker
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