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Question: An ornithologist observes that each of 5 tagged birds independently arrives at a stopover site at a uniformly random time within a 2-hour window. What is the probability that at least two birds arrive within the same 30-minute interval, assuming the window is divided into four non-overlapping 30-minute intervals?
Thus, with 5 birds and only 4 intervals, at least two must be in the same interval.
Solution: To find the average distance, we add the two distances and divide by 2:

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