The probability, in a geometric or measurement context, is the ratio of the measure of one part of a geometric object G with n dimensions and one part A with n dimensions of G (the target).
Formula
Consider a geometric object G with one dimension that has a finite length and A, a part with one dimension of the object G. The probability of randomly choosing A is:
P(A) = \(\dfrac {\textrm{mA}} {\textrm{mG}}\)
Consider a geometric object G with two dimensions that has a finite area and A, a part with two dimensions of the object G. The probability of randomly choosing A is:
P(A) = \(\dfrac {\textrm{Area of A}}{\textrm{Area of G}}\)
Example
Geometric probability is very useful in meteorology, where it can be used to determine the probability of precipitation in a given sector of an area, among other things.