A fair die is tossed until six is obtained on it. Let X be the...

$P\left(\dfrac{x \ge 5}{x > 2}\right) = \dfrac{P ( x \ge 5 \cap x > 2 )}{P ( x > 2 )}$

$= \dfrac{{\left(\dfrac{5}{6}\right)}^{4}\dfrac{1}{6} + {\left(\dfrac{5}{6}\right)}^{5}\dfrac{1}{6} + . . . . . . . \infty}{{\left(\dfrac{5}{6}\right)}^{2} \cdot \dfrac{1}{6} + {\left(\dfrac{5}{6}\right)}^{3}\dfrac{1}{6} + \ldots \ldots \ldots . \infty}$

$= \dfrac{\dfrac{{\left(\dfrac{5}{6}\right)}^{4} \cdot \dfrac{1}{6}}{1 - \dfrac{5}{6}}}{\dfrac{{\left(\dfrac{5}{6}\right)}^{2}\dfrac{1}{6}}{1 - \dfrac{5}{6}}} = {\left(\dfrac{5}{6}\right)}^{2} = \dfrac{25}{36}$