Here is a simple model of a queue. The queue runs in discrete time (t = 0, 1, 2, . . .), and at each unit of time the first person in the queue is served with probability p and, independently, a new person arrives with probability q. At time t = 0, there is one person in the queue. Find the probabilities that there are 0, 1, 2, 3 people in line at time t = 2.
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