Two Buses in a Row
Three bus lines stop at a corner. Buses of line A arrive as a Poisson process with rate 1 per hour, line B with rate 2 per hour, and line C with rate 3 per hour, all independent. You arrive at a random moment. What is the probability that the next two buses to arrive are both line A? Give a reduced fraction.
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Source: Classic exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.