$\underline{\textbf {Answer: C}}$
$\underline{\mathbf {Explanation:}}$
For $\mathbf {p(p+1)}$ being divisible by $4$, either $\mathbf p$ or $\mathbf {(p+1)}$ should be a multiple of $4$,
One among $\mathbf p$, $\mathbf {(p+1)}$ will be even and other will definitely be odd.
$\mathbf{\underline{Eg:}}$ $(3, 4) \; \text{or}\; (4, 5)$.
So, total number divisible by $12$ till $50 = \dfrac{50}{12} = 12.25 = 12\;\text{multiples}$.
These $12$ can be either $\mathbf p$ or $\mathbf {(p+1)}$, So total = $2\times12 = 24$
So, probability of $\mathbf{p(p+1)}$ divisible by $4 = \dfrac{24}{49} = 0.48$
$\therefore \mathbf C$ is the correct option.