G4.4 A bag contains $d$ balls of which $x$ are black, $x+1$ are red and $x+2$ are white. If the probability of drawing a black ball randomly from the bag is less than $\frac{1}{6}$, find the value of $d$.
$\begin{array}{l}\frac{x}{3 x+3}<\frac{1}{6} \\ \Rightarrow \frac{x}{x+1}<\frac{1}{2} \\ \Rightarrow 2 x<x+1 \\ \Rightarrow x<1 \\ \Rightarrow x=0 \\ \Rightarrow d=3 x+3=3\end{array}$