The total area of the dart board can be found using the formula for the area of a circle:
A = πr^2
where r is the radius of the entire dart board. Thus,
A = π(15)^2
A = 225π
The area of the bull's eye can also be found using the same formula, but with the radius of the bull's eye instead:
A = π(2)^2
A = 4π
The probability of hitting the bull's eye is then the ratio of the area of the bull's eye to the area of the entire dart board:
P = (area of bull's eye) / (area of dart board)
P = (4π) / (225π)
P = 0.0178
Therefore, the probability of hitting the bull's eye is approximately 0.018 or 1.8%.
Garett throws a dart at a circular dart board. The dart board has a radius of 15 inches, and the bull's eye of the center of the dartboard has a radius of 2 inches. What is the probability that a dart thrown at random within the dart board will hit the bull's eye? Round your answer to the nearest tenth, if necessary?
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