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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?

 Apr 26, 2018
 #1
avatar+101952 
+3

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

 Apr 26, 2018
 #2
avatar+290 
+2

Wow! Thanks CPhill!

 Apr 26, 2018

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