Visitors arrive at a park as a rate-one Poisson process. Each stays an independent Exp(rate 1) time,independent of arrivals. Currently 10 visitors are present. If p is the probability of exactly two more arrivals before the next departure,find 1/p.
Memorylessness gives departure rate equal to the current number of visitors. At population 10,the next event is arrival with probability 1/11;at 11,another arrival has probability 1/12;at 12,a departure has probability 12/13. Exactly two arrivals before departure therefore has probability (1/11)(1/12)(12/13)=1/143. Answer **143**.
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