Random Chords

Probability Level 1

Pick two points at random on a circle and draw the chord connecting them.

Pick two more points and connect them with a second chord.

What is the probability that these chords intersect?

1 4 \frac{1}{4} 1 3 \frac{1}{3} 1 e \frac{1}{e} 1 2 \frac{1}{2} 2 3 \frac{2}{3}

Jeremy Galvagni by Jeremy Galvagni , 48, USA

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1 solution

Jeremy Galvagni
Apr 13, 2018

Pick the 4 points and before connecting them label them in order A,B,C,D. The chords will only intersect if A is connected to C.

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