Final answer:
The probability of hitting the shaded ring on the dartboard is approximately 0.96.
Step-by-step explanation:
To find the probability of hitting the shaded ring on the dartboard, we need to know the area of the shaded ring and the total area of the dartboard. The shaded ring is the area between the center circle and the outer edge of the dartboard. Since the center circle has a diameter of 2 inches, its radius is 1 inch. The outer edge of the dartboard has a radius of 5 inches (assuming a standard dartboard).
The area of the shaded ring can be calculated by subtracting the area of the center circle from the area of the entire dartboard. The area of the center circle is π * r^2 = π * 1^2 = π square inches. The area of the entire dartboard is π * R^2 = π * 5^2 = 25π square inches. Therefore, the area of the shaded ring is 25π - π = 24π square inches.
The probability of hitting the shaded ring is the ratio of the area of the shaded ring to the area of the entire dartboard. So the probability is (24π/25π) = 24/25 ≈ 0.96, rounded to the nearest hundredth.