# Round and round we go .....

**Calculus**Level 4

Choose \(3\) points at random on a unit sphere. The probability that none of the points is within an arc length of \(\dfrac{\pi}{2}\) of any other point is \(\dfrac{a}{b\pi},\) where \(a\) and \(b\) are coprime. Find \(a + b.\)

**Clarification:** The arc length distance between any two points on a sphere is measured along the great circle defined by those two points.