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Suppose on each turn of a game, the status is either Blue, Yellow, or Red. (The rules for the turn, such as what deck to
Suppose on each turn of a game, the status is either Blue, Yellow, or Red. (The rules for the turn, such as what deck to use or what actions are available, depend on the status, and Blue is the safest while Red is the most dangerous.) If the status is Blue on this turn, then it is Blue again on the next turn with probability 0.75 and Yellow on the next turn with probability 0.25. It never changes from Blue to Red in one turn. If the status is Yellow on this turn, then it is Yellow again on the next turn with probability 0.64 and Red on the next turn with probability 0.36. If the status is Red on this turn, then it is Red again on the next turn with probability 0.16 and Blue on the next turn with probability 0.84. (Under these rules, the status X", on turn t is a 3-state Markov chain, and the steps are turns of the game.) What proportion of turns will be Blue, in the long run? In decimal form, to four places: 0.63 To the nearest percentage: 0.375
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