Paper 2, Section II, F

Probability | Part IA, 2007

Let A,BA, B and CC be three random points on a sphere with centre OO. The positions of A,BA, B and CC are independent, and each is uniformly distributed over the surface of the sphere. Calculate the probability density function of the angle AOB\angle A O B formed by the lines OAO A and OBO B.

Calculate the probability that all three of the angles AOB,AOC\angle A O B, \angle A O C and BOC\angle B O C are acute. [Hint: Condition on the value of the angle AOB\angle A O B.]

Typos? Please submit corrections to this page on GitHub.