The answer to last week's puzzle, which asked what was the probability, given three random points on a circle, that the resulting triangle would contain the centre of the circle, was 1/4.

An analogous question, asking what the probability would be of a quadrilateral whose vertices were four random points on a circle containing the circle's centre, would give an answer of 1/2.

Given six random points on a circle, the probability of the resulting hexagon containing the circle's centre is 13/16.

What is the probability that, given five random points on a circle, that the resulting pentagon would contain the centre of the circle?