Monte Carlo Method: A process used to approximate probabilities by simulating an event.

A Monte Carlo Method is used to approximate the area
of an irregular region. 100 darts are thrown onto
a rectangular map with the irregular region inside.
Answer the following questions about this situation.

Choose each answer from the menu

Graded Response

a) How should the darts be thrown onto the map in
order to create the best possible simulation using
the Monte Carlo Method?

b) Suppose the rectangular map has an area of 1 square
meter. Approximate the area of the irregular region
if 70 out of 100 darts land inside the irregular region.

b)
m^{2}

c) Suppose 25 out of 100 darts land inside the irregular
region, and the irregular region has an area equal
to 10 square meters. Approximate the area of the rectangular
map where the darts are thrown.

c)
m^{2}

d) How can the experiment be performed
to increase the chance at more accurately estimating
the area of the irregular region?