Jim throws a dart at a circular dart board. The dart board has a radius of 18 inches, and the bull's eyes in the center of the dart board has a radius of 4 inches. What is the probability that a dart thrown at random within the dartboard will hit the bull's eye?

To find the probability of hitting the bull's eye, we need to calculate the ratio of the area of the bull's eye to the total area of the dart board.

The area of the bull's eye can be calculated using the formula for the area of a circle: A = πr^2, where r is the radius.

For the bull's eye: A = π(4)^2 = 16π square inches

The total area of the dart board can also be calculated using the same formula: A = πr^2

For the dart board: A = π(18)^2 = 324π square inches

Now, we can find the probability of hitting the bull's eye by dividing the area of the bull's eye by the total area of the dart board:

P(hit bull's eye) = 16π / 324π = 16 / 324 ≈ 0.04938

Therefore, the probability that a dart thrown at random within the dart board will hit the bull's eye is approximately 0.04938, or about 4.938%.