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Four points P, Q, R,  and S are chosen at random on the circumference of a circle. Find the probability that chord PQ and chord RS intersect.

 Feb 4, 2020
 #1
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Out of 4 ways, there is only one way to set up the chords so that PQ and RS intersect so the probability is 1/4.

 Feb 4, 2020
 #2
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"Anchor"  P   at any place on the  circle

 

Now....going clock-wise.....we  could have the following  sequences of points

 

QRS

QSR

RQS

RSQ

SQR

SRQ

 

Notice that only 2 of  these  are the intersecting chords PQ  and RS

 

So....the probability is   2/6    =   1/3

 

 

cool cool cool

 Feb 4, 2020

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