A taxicab driver moves between the airport A and two hotels B and C according to the following rules. If he is at the airport, he will be at one of the two hotels next with equal probability. If at a hotel then he returns to the airport with probability or goes to the other hotel with probability . Suppose the driver begins at the airport at time 0. Find the probability for each of his possible locations at time 2 and the probability he is at hotel B at time 3.

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