The problem arose after a discussion why larger digital camera photo sensors is much more expensive than little bit smaller ones, and the reason was given that it's due to difficulty of finding a larger area spot on a big CCD or CMOS panel.
Consider a large clear white sheet (of a given area $S$, and we may consider it of any convenient non-degenerate shape, such as square or circle) with some black dirt dots on it. The average density of the dirt dots is uniform and known to be $p$ dots per unit area. Somebody wants to find a clear round spot of radius $r$ on it.
Question 1: how difficult is it to find such a spot (and the term "difficult" maybe is defined as "the probability of a random disc being clear?"). How many such non-overlapping spots there are on the sheet on average?
Question 2: how much more difficult is it to find a spot of radius $k\cdot r$ with $k \gt 1$ than a spot of a radius $r$?
When $S\gg s=\pi r^2$, this looks easy, but when $S$ is comparable to $s$, the result is not so obvious.