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An ellipse of eccentricity $\frac{2 \sqrt{2}}{3}$ is inscribed in a circle and a point within the circle is chosen at random. The probability that this point lies outside the ellipse is

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1/9

4/9

1/3

2/3

answer is D.

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Detailed Solution

$e = \frac{2 \sqrt{2}}{3}$

We k.t $\frac{b^{2}}{a^{2}} = 1 - e^{2} = 1 - \frac{8}{9} = \frac{1}{9}$

$∴ \frac{b}{a} = \frac{1}{3}$

Req prob. $= \frac{π a^{2} - π a b}{π a^{2}} = 1 - \frac{b}{a} = \frac{2}{3}$

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