Question

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.

Answer 1

Geometric probability of an object hitting a circular hole is 0.0245.

Explanation:

We have given,

A board of size 48 by 24 inch. There is a circular hole in the board having diameter 6 inches.

So,

Area of a board = 48 × 24 = 1152 square inches

And area of circular hole = π×r² {where r = diameter/2 = 6 / 2 = 3 inches}

Area of circular hole = π×3² = 9π = 28.27 square inches

Now, we need to find the geometric probability of an object will hit the circle.

Geometric probability = Area of circular hole / Area of board

Geometric probability =

Geometric probability = 0.0245

hence geometric probability of an object hitting a circular hole is 0.0245.