What is the probability that the roots of the equation $x^2+x+n=0$ are real, where $n \in \mathbb{N}$ and $n \lt 4$ ?

A quadratic equation has only two roots. Here, $x^2+x+n=0$ and $n \in N$ where $n \lt 4$ $\therefore n=1,2,3 \Rightarrow$ Three equations are possible. Thus, Total number of Roots, $n=6$ $\rightarrow$ For equation $x^2+x+n=0 ; \mathrm{D}=1-4 n$ $\mathrm{D} \lt 0$ when $n=1,2$ and 3 $\therefore$ Equation will give complex roots not real. Thus, favourable number of roots, $r=0$ Hence, probability $=\frac{r}{n}=\frac{0}{6}=0$