Probability function for distance d from the center of a point picked at random in a unit disk

Consider two bands of points: those whose distances from the center are on the interval $[0.1,0.2]$, and those whose distances are on the interval $[0.8,0.9]$. Note that the second band has greater area than the first band, and it is thus more likely to pick a point in the second band, if the distribution is uniform.

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