[00:01] Imagine you choose 10 random chords on a circle. The puzzle is, what's the expected number of intersection points inside that circle? And what about if instead it was 100 [music] randomly chosen chords?
[00:15] of you say, I remember something fishy about choosing random chords on a circle. That is right, there's a famous paradox here called Bertrand's paradox. of Numberphile videos. So, let me be a little bit more precise here. When I say
[00:29] choose a random chord, I mean start by choosing one point uniformly on the circle. Loosely speaking, that means every point is equally likely. If you're precise, it really means the probability that a point lands in a given arc is
[00:42] proportional to that arc's length. Then choose a second point the same way and mean when I say choose a random chord. So again, imagining you choose 10 such number of intersection points inside that circle?
[00:58] that circle? And what if it was 100 such chords? is a reason that this puzzle and the ones from the last 2 months were put ones from the last 2 months were put together.