Probability of getting positive integral roots of the equation $x^{2}-n=0$ for the integer $n, 1 \leq n \leq 40$ is

$x^{2}-n=0 \Rightarrow x=\sqrt{n}$ For each integral value of $x \in[1,40]$, There is a positive root. Hence for 40 integral values of $\mathrm{x}$ from 1 to 40 , there are 40 positive roots, out of which only six roots $1,2,3,4,5$ and 6 are positive integral roots. Hence, probability of getting positive integral roots $=\frac{6}{40}=\frac{3}{20}$