Question

if a point is taken at random from within a circle with a radius r, what is the probability that its distance from the center will exceed r/2

Answer 1

The required probability is given by the ratio of the area of the circle between r/2 and r and the total area of the circle:
\[\frac{\pi r ^{2}-\pi (\frac{r}{2})^{2}}{\pi r ^{2}}=\frac{\frac{3}{4} \pi r ^{2}}{\pi r ^{2}}\]

Answer 2

@kropot72 thanks

Answer 3

You're welcome :)