Question: Potholes on a highway can be a serious problem, and are in constant need of repair. With a particular type of terrain and make of

Potholes on a highway can be a serious problem, and are in constant need of repair. With a particular type of terrain and make of concrete, past experience suggests that there are, on the average, 2 potholes per mile after a certain amount of usage. It is assumed that the Poisson process applies to the random variable “number of potholes.”

(a) What is the probability that no more than one pothole will appear in a section of 1 mile?

(b) What is the probability that no more than 4 potholes will occur in a given section of 5 miles?

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