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?
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%.
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To find the probability that a dart thrown at random within the dart board will hit the bull's eye, we need to compare the area of the bull's eye to the total area of the dart board.
1. Calculate the area of the bull's eye:
The formula for calculating the area of a circle is A = πr^2, where A is the area and r is the radius.
Therefore, the area of the bull's eye is A = π * (2^2) = π * 4 = 12.57 square inches (rounded to two decimal places).
2. Calculate the area of the entire dart board:
Following the same formula, the area of the dart board is A = π * (15^2) = π * 225 = 706.86 square inches (rounded to two decimal places).
3. Calculate the probability:
The probability is given by the ratio of the area of the bull's eye to the area of the dart board.
So, the probability = (area of bull's eye) / (area of dart board) = 12.57 / 706.86 ≈ 0.018
Therefore, the probability that a dart thrown at random within the dart board will hit the bull's eye is approximately 0.018, rounded to the nearest tenth.