A recent study reports that the average number of severe potholes per mile of Interstate 576 is 4.0 (λ = 6 potholes per mile). The occurrences appear random and unrelated. Assume all the Poisson conditions regarding independence, etc., are met. You have just learned that one of your company’s trucks is sitting fender-deep in a pothole along the Interstate.
a. How likely is it that the driver would have to walk at least a mile along the Interstate before he finds another pothole?
b. How likely is it that the driver would find a pothole no more than a quarter of a mile ahead?