Given n points drawn randomly on the circumference of a circle, what is the probability they will all be within any common semicircle?

The first point can be placed anywhere in the circle,the second point as well, the farthest these two can be are on end points of a diameter.We then are in a position to define what is in the same semi-circle and what is not.

It is very clear that the next point onwards there is a 1/2 chance of it falling in the req semi-circle.
So are we looking at (1/2)^n-2 ????????

Posted by sendil on 2003-05-20 01:06:32