Question: #2) Darts

Construct and perform a Monte Carlo simulation of a darts game. Points are awarded as follows:

Dart board area Points
Bulls-eye 50
Yellow 25
Blue 15
Red 10
White 5

From the origin (the center of the bulls-eye), the radius of each ring is as follows:

Ring Thickness (in.) Distance origin to outer ring edge (in.)
Bulls-eye 1.0 1.0
Yellow 1.5 2.5
Blue 2.5 5.0
Red 3.0 8.0
White 4.0 12.0

The board has a radius of 1 ft (12 in.).

Make an assumption about the distribution of how the darts hit on the board. Construct a simulation of the game in an Excel worksheet. Run 1000 simulations to determine the mean score for throwing five darts. Also determine which ring has the highest expected value (point value times the probability of hitting that ring).