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Linear AlgebraEasyMarkov Chains & Long-Run Behavior

Markov Chains & Long-Run Behavior · Easy problem

From a transient state TT, each step a chain moves to absorbing state A with probability 1/21/2, to absorbing state B with probability 1/41/4, and stays at TT with probability 1/41/4. Starting at TT, what is the probability that the chain is eventually absorbed at A? Express your answer as a common fraction.