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The average rate of arrivals

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1. Consider a point on the Trans-Australian Highway, where two old wombats live. Arrivals of cars at this point follow a Poisson distribution; the average rate of arrivals is 1 car per 12  seconds.
a. One of these old wombats requires 12 seconds to cross the highway, and he starts out  immediately after a car goes by. What is the probability he will survive?
b. Another old wombat, slower but tougher, requires 24 seconds to cross the road, but it  takes two cars to kill him. (A single car won't even slow him down.) If he starts out at a  random time, determine the probability that he survives.
c. If both wombats leave at the same time, what is the probability that exactly one of them survives?

Reference no: EM13504220

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