We throw a dart at the dart board that is equally likely to hit any point inside the square board.
We will determine whether we are more likely to get 10 points or 5 points. To do so, we can find the geometric probability of both getting 10 points and getting 5 points. Therefore, we need to identify the area of favorable regions.
Area of Favorable Region
Getting 10 Points
Area of the pink circle
Getting 5 Points
Area of the green circle except for the area of the pink circle
From here we need to calculate the area of the desired circles and the area of the entire board, which is a square. Notice that one side length of the entire board is 18 inches, which is the diameter of the largest circle. Also, from the figure we know that the radius of the pink circle is 3, and the radius of the green circle is 6.
Area of Favorable Region
Total Area of the Board
Getting 10 Points
π 3^2= π (9)
18^2= 324
Getting 5 Points
π (3+3)^2- π 3^2= π (72)
18^2= 324
Now we will find the probabilities. Let's start with the probability of getting 10 points.
We will compare the probabilities.
0.698 > 0.087
⇓
P(5points)>P(10points)
Since the probability of getting 5 points is bigger, we are more likely to get 5 points.
