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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
+109822
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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
+1

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.

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