>>14015699Brady played the character who doesn't grok probability distributions.
If you try to imagine all lines which could lie on a plane, you'll soon realize that choosing some of them requires assumptions that affect the probability of which ones you'll identify.
I wish Grant could go into the math of the distributions the three methods of picking result in. Grant in one of his videos (or maybe it was Khan Academy) said the pinnacle of school math should not be calculus, but statistics. Real life is hard to translate into probabilities but it could be done a lot more than it is currently. Maybe if mainstream media actually provided numbers to give context for their stories, and if the audience had a better math background, then they would have a better idea of what issues were important. inb4 despite
The cardinality of the set of chords with length bigger than the triangle side length, and the cardinality of the set of chords with length shorter are the same. But the probability isn't necessarily 50%.
The cardinality of the set of prime numbers is the same cardinality as the set of positive integers. But the probability of choosing a random positive integer and it being prime is a function of your sample space. If you choose between 0 and n (with uniform distribution) then the probability is about 1/log(n). If your sample space is infinite, with n going to infinity, then the probability of choosing a prime randomly is 0%.
The best way I could think to find lines on the plane randomly is to choose some sufficiently large sample space [0,X] and [0,Y], much larger than whatever circle you want to analyze within, and choose points (x,y) and angle theta [0°,180°). I'm not smart enough to know if this provides a uniform distribution of lines. You could compare the results to see if they conform to some invariant, and so it seems to me Grant is right that invariants are the way to go.
