Re: [math-fun] Probability that all molecules of a gas are in one half of the container

Here is a cute question: I place points uniformly in the unit disk (or equivalently on the unit circle). I stop as soon as these points are not all contained in one sector of width pi, or equivalently, as soon as their convex hull contains the origin. What is the average number of points when this first occurs? Hint: the answer is an integer :-) Cris