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Linear AlgebraEasyMarkov Chains & Long-Run Behavior

Markov Chains & Long-Run Behavior · Easy problem

A two-state chain moves from A to B with probability 1/41/4 each step (otherwise it stays at A) and from B to A with probability 1/61/6 (otherwise it stays at B). In the long run, what fraction of the time is the chain in state B? Express your answer as a common fraction.