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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%.