At least one of three darts in the bullseye disc

A circular dartboard of radius $3$ ft has inner circles of radius $1$ ft and $2$ ft. Three darts each land at an independent, uniformly random point on the board. What is the probability that at least one dart lands within $1$ ft of the centre?

$\tfrac{217}{729}$. A single dart lands in the inner disc with probability equal to the area ratio $\tfrac{\pi}{9\pi}=\tfrac19$. All three miss it with probability $\left(\tfrac89\right)^3=\tfrac{512}{729}$, so the answer is $1-\tfrac{512}{729}=\tfrac{217}{729}$.