Garrett throws a dart at a circular dartboard. The dartboard has a radius of 15 inches, and the bull’s eye in the center of the dartboard has a radius of 2 inches. What is the probability that a dart thrown at random within the dartboard will hit the bull’s eye? Round your answer to the nearest tenth, if necessary.

Answer 1

To find the probability that a dart thrown at random within the dartboard will hit the bull's eye, we need to compare the areas of the bull's eye and the entire dartboard.

The area of the bull's eye can be calculated using the formula for the area of a circle: A = πr^2, where r = 2 inches.
So, the area of the bull's eye is: A = π(2)^2 = 4π square inches.

The area of the entire dartboard can also be calculated using the same formula: A = πr^2, where r = 15 inches.
So, the area of the entire dartboard is: A = π(15)^2 = 225π square inches.

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 dartboard:
Probability = (4π) / (225π) = 4 / 225 ≈ 0.0178

Therefore, the probability that a dart thrown at random within the dartboard will hit the bull's eye is approximately 0.0178 or 1.8%.