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

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



cool cool cool

CPhill  Apr 26, 2018

Wow! Thanks CPhill!

TheMathCoder  Apr 26, 2018

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