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.
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. At the same point of the highway there is another old wombat, slower but tougher than in the previous exercise. He requires 24 seconds to cross the road, but it takes two cars to kill him. (A single car won’t even slow him down. The arrival rate of cars is still one car per 12 seconds.) If he starts out at a random time, determine the probability that he survives.
C. If both wombats from the previous two questions leave at the same time, what is the probability that exactly one of them survives?
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