What’s the Probability That Two Randomly Drawn Chords in a Circle Intersect?

Key Takeaways

Here's a simple yet surprisingly tricky question. What's the probability that two randomly drawn chords in a circle intersect? A random chord is formed by selecting two random points on the circle circumference and connecting them with a straight line. Now imagine drawing two such chords. What are the possibilities? First, they might intersect. Secondly, they might be parallel. And lastly, they might not intersect and also not be parallel. Although two chords could theoretically overlap or share an end point, the probability of this happening is infinite decimally small. That's because you select chords among infinitely many possibilities. And including or excluding these edge cases doesn't significantly affect the probability. One of the easiest and most intuitive solutions to this problem begins before drawing the chords. Two arbitrary chords can always be represented by any four points chosen on the circle. There are three distinct ways to pair the four points into the first chord. Once the first chord is chosen, the second chord is determined. Out of the three selections, only in one case the chords intersect. Thus, the final answer is 1/3. Like and subscribe if you like the video. [Music]