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?

TheMathCoder
Apr 26, 2018

#1**+2 **

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

CPhill
Apr 26, 2018