There are n circles (each of different size) drawn on a board at randomly chosen locations. Assume that the area of the i-th circle is 1/i (we assume that the space is unit, i.e., the probability that a randomly placed arrow falls inside the i-th circle is 1/i).
An arrow x is thrown on the board and some circles contain it and the remaining circles do not contain it. What is the probability that another arrow y thrown on the board is contained by exactly the same circles that contain x and is not contained by exactly the same circles that do not contain x. The events x and y are independent.
If the problem is too complex, some assumptions can be made.
Any advice and help will be highly appreciated. Thanks