Explanation

(c)
Given, $f(x) = \frac{x}{2}$ $\lbrack 0 \leq x \leq 2\rbrack$
$\therefore P(X > 1.5) = \int_{1.5}^{2}{\frac{x}{2}dx = \left\lbrack \frac{x^{2}}{4} \right\rbrack_{1.5}^{2}}$
$= 0.4375$
and $P(X > 1) = \int_{1}^{2}{\frac{x}{2}dx = \left\lbrack \frac{x^{2}}{4} \right\rbrack_{1}^{2}} = 0.75$
$\therefore P\left( \frac{X > 1.5}{X > 1} \right) = \frac{P(X > 1.5)}{P(X > 1)}$
$= \frac{0.4375}{0.75} = \frac{7}{12}$