If [tex]r[/tex] is the radius of the circle, then the side length of the triangle is [tex]2r\sqrt3[/tex].
The area of the circle is [tex]\pi r^2[/tex], while the area of the triangle is [tex]3r^2\sqrt3[/tex].
So, the probability of selecting a random point in the white space is
[tex]1-\dfrac{\pi r^2}{3r^2\sqrt3}=1-\dfrac{\pi}{3\sqrt3}\approx0.395\approx40\%[/tex]
