We throw a dart at the dart board and are equally likely to hit any point inside the square board.
We are asked to decide if we are more likely to score points (10, 5, or 2) or get 0 points. To do so we can find the geometric probabilities of both scoring points and getting 0 points. Therefore, we need to identify the area of favorable regions. Just be careful that to score points (10, 5, or 2) we need to throw a dart anyplace inside the largest circle.
Area of Favorable Region
Scoring Points
Area of the largest circle
Getting 0 Points
Area of outside of the largest circle
From here, we need to find the area of the desired regions and the area of the entire board which is a square. From the figure we know that the radius of the bigest circle is 9. Also, notice that one side length of the entire board is 18 inches, which is the diameter of the largest circle.
Area of Favorable Region
Total Area of the Board
Scoring Points
Ï€ (3+3+3)^2=Ï€ (81)
18^2= 324
Getting 0 Points
18^2- π 9^2= 324- π (81)
18^2= 324
With this information we will evaluate the probabilities. Let's start with the probability of scoring points.
Let's compare the probabilities.
0.785 &> 0.215
&⇓
P(10,5, or 2points)&>P(0points)
Since the probability of scoring points is bigger, we are more likely to get 10, 5, or 2 points.
