If p is chosen at random in $\left[0,5\right]$, what is the probability of the equation ${\mathrm{x}}^2+\mathrm{px}+\frac{\mathrm{p}+2}{4}=0$ to have real roots is $\frac{\mathrm{\lambda }}{10}$ then $\mathrm{\lambda }$ =________

Let A be the event that the length of the interval in which the given equation has real roots and S be the sample space, i.e. the length of the interval  .
$\mathrm{D}\ge 0\to {\mathrm{p}}^2-4.1.\frac{(\mathrm{p}+2)}{4}\ge 0\Rightarrow {\mathrm{p}}^2-\mathrm{p}-2\ge 0\Rightarrow (\mathrm{p}-2)(\mathrm{p}+1)\ge 0\Rightarrow \mathrm{p}\le -1,\mathrm{p}\ge 2$
$\text{ Thus, }\mathrm{A}=[2,5]\text{, since }\mathrm{p}\in [0.5]\text{. Hence the required probability }=\frac{\mathrm{n}\left(\mathrm{A}\right)}{\mathrm{n}\left(\mathrm{S}\right)}=\frac{3}{5}$