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Four points A, B, C, and D are chosen at random on the circumference of a circle. Find the probability that chords \(\overline{AB}\) and \(\overline{CD}\) intersect.

 Nov 3, 2019
 #1
avatar+105919 
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If you put any 4 distinct points on a circle then label them A1, A2, B1, B2

Then join the 2 A points together and also join the 2 B points together.

Then exactly half the time they weill cross over each other.

 

Using this logic I think the probability that they wil cross is 50%.

 

I have not seen this question before. Maybe I am over simplifying it but it seems logical to me.

 Nov 3, 2019
 #2
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The probability that when labeling the points the chords intersect is not 1/2, it is 1/3

Guest Nov 3, 2019
 #3
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Thanks Guest,

 

I just drew it up all 6 possibilities. You are right, only 2 of them crossed.  laugh

So I concur, the prob is 1/3

Melody  Nov 3, 2019
edited by Guest  Nov 3, 2019
edited by Guest  Nov 3, 2019
edited by Melody  Nov 3, 2019

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