Two Pieces, One Density

The time $X$, in hours, that a support ticket waits before it gets its first human reply is modelled by the probability density

$f(x) = \begin{cases} c\,x^{2}, & 0 \le x \le 2 \\[4pt] c\,(12 - 4x), & 2 < x \le 3 \\[4pt] 0, & \text{otherwise} \end{cases}$

for some constant $c > 0$. The two pieces meet without a jump at $x = 2$, and the density falls to zero at $x = 3$.

A ticket is picked at random.

What is the probability that it waits more than $1.5$ hours for its first reply? Round your answer to 4 decimal places.