Four points, A, B, C, and D, are chosen randomly and independently on the circumference of a circle. What is the probability that segments AB and CD intersect?
Here's my best shot.....
"Anchor" A anywhere on the circle
Now.....going clockwise from A we have the following possibilities
A - B - C - D
A - B - D - C
A - C - D - B
A - C - B - D
A - D - B - C
A - D - C - B
Note that they will intersect only when A and B are separated by another point
So...the probability is 2/6 = 1/3