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Let {ϵn ∶ n ≥ 1} represent the results of independent rolls of a dice with probability of the face i turning up being pi > 0 for i = 1, 2, …, 6 and  pi = 1. Let {Xn ∶ n ≥ 0} be the Markov chain on the state space {1, 2, …, 6} where Xn = max {ϵ1, ϵ2, …, ϵn+1}. Then,  P(Xn = 4∣X0 = 3) equals

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CSIR UGC (NET) Mathematical Science: Held On (7 June 2023)
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