Use the image to answer the question. A corn hole is pictured. 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 circle on the board, we need to compare the area of the circle to the area of the entire board.
The area of the circle is given by the formula A = πr², where r is the radius of the circle. Since the diameter of the circle is 6 inches, the radius is half that, so r = 6/2 = 3 inches.
Therefore, the area of the circle is A = π(3)² = 9π square inches.
The area of the entire board is given by the formula A = length x width = 48 x 24 = 1152 square inches.
To find the geometric probability, we divide the area of the circle by the area of the board:
Geometric Probability = Area of Circle / Area of Board = 9π / 1152.
Depending on the required level of precision, we can either leave the answer as 9π / 1152, or we can use an approximation for π (such as 3.14) to calculate the numerical value of the probability.