Suppose I have on the map a square of dimensions 100 x 100 meters of which I know its center (by means of its latitude and longitude, (L,l)). Let's imagine that I am given a point of coordinates (X,Y) and its horizontal accuracy. How can I calculate the probability that this point is really inside this rectangle based on the horizontal accuracy?
I had thought of modeling the problem by a multinomial distribution of mean the midpoint of the rectangle and variance related to the dimensions of the square, but I don't know how to formalize the problem well.