Monte Carlo integration

Imagine that we want to measure the area of a pond with arbitrary shape. Suppose that this pond is in the middle of a field with known area $A$. If we throw $N$ stones randomly, such that they land within the boundaries of the field, and we count the number of stones that fall in the pond $N_{in}$, the area of the pond will be approximately proportional to the fraction of stones that make a splash, multiplied by $A$:

$$A_pond=\frac{N_{in}}{N}A.$$

This simple procedure is an example of the ``Monte Carlo'' method.