# Probability + Ellipse

**Discrete Mathematics**Level 3

An ellipse is inscribed in a circle and a point within the circle is chosen at random. If the probability that this point lies outside the ellipse is \(\large \dfrac{2}{3}\), then the eccentricity of the ellipse is \(\large \frac{a\sqrt b} {c}\) where \(\gcd(a,c)=1\) and \(b\) is a square free integer . Then \(\large{a\times b\times c}\) is