A professor has three pet questions one of which occurs on every test he gives. The students know these habits well. He never uses the same questions twice in a row. If he used questions one last time, he tosses a coin and uses question two if a head comes up. If he used question two, he tosses two coins and switches to question three if both come up heads. If he used question three, he tosses three coins and switches to questions one if all three come up heads. Compute in the long run which question does he use most often and with how much frequency is it used?

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