The object of the game is to toss a beanbag in the circular hole of a 48-by-24-inch
board. If the diameter of the circle is 6 inches, what is the geometric probability an
object will hit the circle on the board? Assume that the object will hit the board.
Show your work or explain how you got your answer.
To find the geometric probability of hitting the circular hole on the board, we can divide the area of the circle by the area of the entire board.
The area of a circle is given by the formula:
Area = π * r^2
where r is the radius of the circle. In this case, the diameter of the circle is given as 6 inches, so the radius is half of that, which is 3 inches.
Now, the area of the circle is:
Area = π * (3)^2 = 9π square inches
The area of the entire board is given by the formula:
Area = length * width
In this case, the length is 48 inches and the width is 24 inches. So, the area of the board is:
Area = 48 * 24 = 1152 square inches
Now, to find the geometric probability, we divide the area of the circle by the area of the board:
Geometric probability = (Area of the circle) / (Area of the board)
Geometric probability = (9π) / 1152
Using a calculator and rounding to a reasonable decimal place, the geometric probability of hitting the circle on the board is approximately 0.0078.