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Four points J, K, L, and M are chosen at random on the circumference of a circle. What is the probability that chord JK and chord LM intersect?

 Feb 11, 2020
 #1
avatar+111389 
+2

"Anchor" J  at any point on the  circumference

 

Proceeding in a clock-wise direction we could have the following possibilities for  the four points

 

JKLM

JKML

JLKM

JLMK

JMLK

JMKL

 

Note that the  two entries in red  are  the ones  where  chords JK  and LM  intersect

 

So.....the probability of intersecting chords  is   2 / 6    =     1 / 3

 

 

 

 

 

cool cool cool

 Feb 11, 2020
 #2
avatar+217 
+1

Thank you so much!!

mathmathj28  Feb 11, 2020

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