This questions is almost exactly similiar to the the following question, with an extra condition :
Suppose you have a circular table of radius R. This table has been left outside, and it begins to rain at a constant rate of one droplet per second. The drops, which can be considered points as they fall, can only land in such a way such that they impact the surface of the table. Once they strike the table, they form a puddle of radius r, centered at their point of impact. What is the expected number of droplets it takes to cover the table in water?
Now, suppose every water droplet that falls on the table dries out after $(R/r)^2$ seconds. What will the graph of the propability $P(N)$ that the table will be covered with N droplets versus N look like? Can someone please help me with this?