A long line of ants find a hole in the pantry door. At time zero the first ant enters the pantry and then, one after the other, the ants pass through the hole at a rate of exactly one every minute. The ants progress through the hole is not random, however, suppose that the hole will remain open for a random time which follows an exponential distribution with an average time of 10 minutes. How many ants are expected to pass through the hole before it closes?
I don't really know how to begin this problem.