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Consider a disk $D$ of radius 1 centered at the origin. Let $X$ be a point uniformly distributed on $D$ and let the distance of $X$ from the origin be $R$. Let $A$ be the (random) area of the disk with radius $R$ centered at the origin. Then $\mathbb{E}[A]$ is

- $\frac{\pi}{3}$
- $\frac{\pi}{6}$
- $\frac{\pi}{4}$
- $\frac{\pi}{2}$
- None of the above