The probability of dart landing on yellow region = [tex]\frac{182.469}{324}[/tex] = 56.31%.
Step-by-step explanation:
Step 1; We need to determine the area of the blue region and the yellow region. To calculate the different areas we must use the areas of the shapes surrounding the particular shape.
First, we find the areas of all the shapes in the dartboard.
The area of the square with side length 18 inches = 18 × 18 = 324 square inches.
The area of a circle with radius 9 inches = π × 9 × 9 = 254.469 square inches.
The area of 2 triangles with base 6 inches and height 6 inches = 2 × ([tex]\frac{1}{2}[/tex] × 6 × 6) = 2 × 18 = 36 square inches.
The area of the inner square = 6 × 6 = 36 square inches.
The area of the inner circle with radius 3 inches = π × 3 × 3 = 28.274 square inches.
Step 2; Now we calculate the areas of the blue and yellow regions.
The area of the blue region = Area of the outer square - Area of the outer circle = 324 - 254.469 = 69.531 square inches.
The area of the yellow region = Area of the outer circle - Area of 2 triangles - Area of the inner square = 254.469 - 36 - 36 = 182.469 square inches.
The area of the entire board is the same as the outer square area.
Step 3; To find any event's probability we divide the number of favorable outcomes by the total number of outcomes. Here, the favorable outcome is the area of the yellow region and the total number of outcomes is the total area of the dartboard.
The probability of dart landing on yellow region = [tex]\frac{182.469}{324}[/tex] = 0.5631 = 56.31%.
