N red balls are distributed uniformly over a square of length L. One white ball is also placed within the square randomly. What is the average minimum distance between the white ball and a red ball?
How will the result change if the white ball is placed in the center of the square?
Instead of a square, if we consider a circle of radius R, how does the result change in both of the above mentioned cases (the white ball is placed somewhere inside the circle or in the centre) given the red balls are placed uniformly over the area of the circle?