We propose a lemma that clarifies the proof of Theorem 4.1 on densities of sums in Rudelson and Vershynin. More precisely, by denoting by $f_{S+Y}$ the density of an absolutely continuous real-valued random variable $S$ augmented by an independent real-valued Gaussian random variable $Y$ with mean zero and an arbitrarily small variance, we prove that if $f_{S+Y}$ is bounded almost everywhere by a strictly positive constant $C$, then almost everywhere, the density $f_S$ is also bounded by the same constant $C$. Then, using these results, we show how small ball probability estimates such as $\begin{equation*} ℙ{(|\sum_{k=1}^na_k\xi_k}|\leq\varepsilon)\leq C\varepsilon\quad\text{for all}\ \ \varepsilon>0, \end{equation*}$ with $a_k$'s real numbers still hold when $a_k$'s are arbitrary random variables.