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 (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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