Consider the two lines  $L_1,L_2$  and  a circle C
$L_1:2x+3y+p-3=0,L_2:2x+3y+p+3=0$ 
 $C:x^2+y^2+6x+10y+30=0,(p\in I)$
It is given that at least one of the lines  $L_1,L_2$  is a chord of C then the probability that both are chords of C is

For  $L_1$  to be a chord of the circle, possible integral value of p are $\{17,18,\mathrm{.....31}\}$ . Similarly, for $L_2$ to be a chord, possible integral value of p are  $\{11,12,\mathrm{......},25\}$.
So, in total possible p=21 and common  values are 9.
Hence, probability $=\frac{9}{21}=\frac{3}{7}$