Question

An application of the Monte Carlo method to find the area Ac inside a circle uses a random sample of points Ns in a square area As surrounding the circle and counts the number of points that are found inside the circle Nc. Which expression describes the estimate for the area inside the circle

Answer 1

As*Nc/Ns

Explanation:

The square has Ns discrete points. The points are quite large and are close around each other

As = Area of square

Nc = number of points inside square

Ns = total number of points inside square

Ac = area of circle

Such that

Nc/Ns = Ac/As

We cross multiply

AcNs = NcAs

Dividing through by Ns will give:

Ac = NcAs/Na

Which Is also

= As *Nc/Na

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