Summer of Math Exposition

This was really elegant, I liked how the first part had a pretty involved way of deriving the probability and then the second part is just “yeah there are three options and only one of them results in an intersection”. My favourite part was Part 3 since just summing up the probability for 10 choose 2 is a really deceptively simple way of getting from the probability of 2 chords intersecting to the expected number of chords intersecting when you have ten.

I think the part explaining the probability of the intersection of two events at 3:03 was a little unclear but that’s about it

The problem seemed incredibly difficult at the outset but the answer was very simple to explain with very elementary probability in only 9 minutes. Excellent video length to reward ratio

The motivation was not stated. Although some problems are self-motivating either because of the surprising complexity or how fundamental they are, this is not one of them.

The ideas of conditional probability and using integrals for continuous distributions was explained quite well (although not completely rigorous). I would like to see more attention payed to the fact that the same result was reached by two completely different methods.

I found the briefness of explanation oflinearity of expectation quite weird, as a topic of arguably equal complexity (choose function) was covered in much more detail.

Overall, this is a decent video to introduce the ideas in continuous probability, given that viewers have some background in discreet probability. Keep in mind that the criticism includes all the things that went wrong, but not all thing that went right. This video of course still has educational value, and will help consolidate concepts in probability.

This is a relatively good exploration of the problem, though some of the choices of assumed knowledge for the viewer seem a bit strange (assuming calculus but no knowledge of probability, assuming no knowledge of probability density functions but using the linearity of the expectation, etc.). The derivation of the binomial coefficient also seemed a bit backwards/confusing since we had already arrived at the result we needed. The animations are well done.

I loved it. Excellent explanation, the visualization was clear, not too fast, but also not to slow I think, and it tackled multiple things that I’d find difficult to explain so simply in their own video! I initially had no idea how to tackle this problem, but the way you explained it was really clear and obvious how to generalize it to n lines. congrats dude, earned a sub and I hope you will make more videos soon <3

A well crafted video with good visuals and clear explanation. Primary critique is that there is no motivation for why a viewer should care. Also a few nits:

1. introducing the binomial coefficient felt kind of random after you already had the answer for number of pairs of chords. Either the viewer was already familiar and it wasn’t helpful, or they weren’t familiar and it would feel out of nowhere and confuse the viewer.
2. The idea of breaking down a problem into pieces and then using linearity of expectation is a powerful approach for solving many problems. Mentioning that this isn’t a one off trick but actually a common approach would have been nice, and this could have potentially served as a form of motivation for the video (ie, here’s a simple example of using this technique to solve a problem). This would also make the approach in part 3 feel less out of the blue for a student that hadn’t seen it before.

As a teaching resource, I would maybe assign this problem as an exercise to have the students practice using linearity of expectation, and then use this video as the answer key/as a worked example of how to do this.

The visuals were really helpful in this video, allowing the viewer to make sense of the probability calculations and gain an intuition for extending the discrete to the continuous (sums -> integrals) as well. If I had to give one piece of constructive feedback, it would be to maybe approach the video like a walkthrough of the problem-solving process (the content already emphasizes it well), and what intuitions and ideas you would look into, instead of 3 fixed sections. Overall, I really enjoyed this video and also your one on tiling chessboards! Great content and explanations.

Good visuals and clear speech. You need to get me hooked - why should I watch the video (real life use, fun story, etc). Too many answers without explanations. Not comparison with other types of similar puzzle or confirmation that number found is correct

This video builds up a way of solving a statistics / counting problem in an intuitive way with this visual example which can be used to strengthen the foundations of understanding for students in an introductory statistics course. It also manages to do this in less than 10 minutes (great work!), which makes it suitable for showing in class or integrating it in some kind of homework without having to take much time away from the actual class contents. The only thing missing is a reason for why a student might care for the answer, which could lower engagement in an activity involving this video.

Interesting problem and nice solution!

I do question whether covering so much ground in such a short time is ideal for one with little or no probability experience. I personally find the topic very difficult, and I can imagine a beginner being overwhelmed by all the quick definitions, while someone who’s more comfortable with the topic might question why they have to see the fundamentals resummarized.

One last thing: The rolling dice animation was awesome

An interesting problem with an elegant solution!

The video could have been a little faster though.