There are some experiments in which the outcomes cannot be identified discretely. For example, an ellipse of eccentricity $2\sqrt{2}/3$ is inscribed in a circle and a point within the circle is chosen at random. Now, we want to find the probability that this point lies outside the ellipse. Then, the point must lie in the shaded region shown in Figure. Let the radius of the circle be a and length of minor axis of the ellipse be 2b. Given that

$1-\frac{{\mathrm{b}}^2}{{\mathrm{a}}^2}=\frac{8}{9}\text{ or }\frac{{\mathrm{b}}^2}{{\mathrm{a}}^2}=\frac{1}{9}$

Then, the area of circle serves as sample space and area of the shaded region represents the area for favorable cases. Then, required probability is

$\begin{array}{c}\mathrm{p}=\frac{\text{ Area of shaded region }}{\text{ Area of circle }}\\ =\frac{{\mathrm{\pi a}}^2-\mathrm{\pi ab}}{{\mathrm{\pi a}}^2}=1-\frac{\mathrm{b}}{\mathrm{a}}=1-\frac{1}{3}=\frac{2}{3}\end{array}$

Now answer the following questions.