Distribution function is $$D(x)=\sum_{k=1, k\geq x}^{\infty} 2^{-k}$$.
We need to find $\mathbb{P}_D(\{14\}\cup\{15\})$ and $\mathbb{P}_D([0,5])$.
1) So I think $\mathbb{P}_D(\{14\}\cup\{15\})= \mathbb{P}_D(\{14\})+ \mathbb{P}_D(\{15\})=D(14)+D(15)$ Is it right?
2) What about $\mathbb{P}_D([0,5])$?
$\mathbb{P}_D([0,5])=D(5)-D(0)$?
is $D(0) = 0$?