Monte Carlo algorithm

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Monte Carlo method applied to approximating the value of π. After placing 30000 random points, what is the probability that the estimate for π is within 0.07% of the actual value?

A Monte Carlo algorithm is an algorithm for computers. It is used to simulate the behaviour of other systems. It is not an exact method, but a heuristical one. Usually it uses randomness and statistics to get a result.

It is a computation process that uses random numbers to produce an outcome(s). Instead of having fixed inputs, probability distributions are assigned to some or all of the inputs. This will generate a probability distribution for the output after the simulation is run.

For example, a Monte Carlo algorithm can be used to estimate the value of π. The amount of area within a quarter-circle of radius 1 depends on the value of π. The probability that a randomly-chosen point will lie in that quarter-circle depends on the area of the circle. If points are placed randomly in a square with sides of length 1, the percentage of points that fall within a quarter-circle of radius 1 will depend on the value of π. A Monte Carlo algorithm would randomly place points in the square and use the percentage of points falling inside of the circle to estimate the value of π.