New probability video!

It's true, there's probably a better canonical example of a binary feature I could choose.

3blue1brown

The first thing I thought about when watching is that there are technically more than 2 genders. Sorry for tainting math with politics but I would hate for you to take any slack about the final product.

really really mind blowing idea! How did you come up with this?

As you say, there is 4/5 chance of not getting Ali in the 1st pick, 3/4 chance of not getting Ali in the 2nd pick, and 2/3 in the 3rd pick. So the probability of no Ali is (4/5*3/4*2/3)=0.4. In contrast, the probability of having Ali is 1- (4/5*3/4*2/3)=0.6.

Okay, this is a math question. You ask what is the probability of choosing a group of 3 out of 5 and Ali being in the group of three? You choose the first guy and you have a 1/5 chance of getting Ali and a 4/5 chance of not getting Ali. If you did not get Ali on the first pick you choose again and you have a 1/4 chance of getting Ali in the in the second pick multiplied by the 4/5 chance that you did not get Ali in the first pick. Finally, if you did not get Ali in the first 2 picks there are 3 people left. You have a 1/3 chance of picking Ali multiplied by the 3/4 chance of being in the 'no Ali in the second pick' world in the first place. Of course, I know that this is wrong but I don't understand why it is wrong and where I am going off the rails? I can visualize this approach the way we visualize the brick wall in our heads so it seems like it should be right? In the first choice you have the rectangle divided into 1/5 and 4/5. The second choice is taking a 1/4th piece out of the remaining 4/5 section of the rectangle and so on. Why does that not work?

Okay, thanks for letting me know!

3blue1brown

at 1:46 the equation is 6*5*4/(3*2*1) you switched the 4 with a 3. Just thought I'd let you know.

Hey Grant! Thanks for the video. I was wondering what your timeline of release for the future videos in these series is? I'm asking because I'm taking a theory of statistics course (one required for a math minor), and being able to learn it from you like I did with Linear Algebra would make that class a cake walk!

I'm not sure if I will in this series, but perhaps towards the end. It's certainly something worth covering somewhere at some point.

3blue1brown

Excellent video! Just wondering if u r planning to dive into measure theory in this series of probability? That would be fantastic.

Is this shifting and adding (which by the way looks like a convolution) is equivalent to Pascal's identity?

Eduardo Diniz

Probability!!!!!!!!!!!! I always struggle with the first few questions = =

Great feedback, thanks for sharing, this is exactly the kind of thing I benefit from hearing from Patrons. I'll share it around with some people unfamiliar with the topic, and see what they have to say if/when the pattern seems confusing, focussing especially on the generating-pascals part.

3blue1brown

I (and another viewer) found that this video didn't chime with us as much as most of your other videos -- we didn't come away feeling like we had the magically improved insight into combinatorics that we have come to expect! One thing is I was a bit thrown by the way you'd arranged the bit patterns -- I wasn't sure to what extent I was supposed to see it as a natural arrangement. After watching the first time I went back and paused it and see that they were ranked as binary numbers, but I think that non-CS viewers will likely think "what's that apparently rather messy pattern?" which will be distracting when they are repeatedly instructed to focus on the pattern itself, without being told what the rule for ordering them is. I also found the procedure for generating pascals triangle by adding shifted arrays of counts to be quite a challenging concept when viewers are probably not yet comfortable with deriving basic combinatorics results. For what it's worth, in addition to the number-of-permutations-corrected-for-ordering approach, when I help people derive n-choose-2, one thing I do is tell them to arrange the choices in a square matrix and see that what they want is the lower triangle. So (n^2 - n)/2 is subtract-the-diagonal-and-take-half-of-the-remaining-cells-in-the-square.

Dan Davison

Most certainly, conditional probability will be one of the first few chapters.

3blue1brown

Really nice video, as always! How are you going to continue with probability? Are you also going to talk about conditional probability, because that's what I am interested in.

Thanks!

3blue1brown

It's both surprising and not surprising how insightful this was. Nothing to add to what the others have been saying, but there is a typo I spotted: ~2:35 should read "1 woman".

wye

Excellent point! It could even be a pedagogically productive comment, making a point about how many toy probability problems oversimplify the nuances and intricacies of the real world.

3blue1brown

Ah, thank, good catch. I think I accidentally let that happen a lot with sloppy editing.

3blue1brown

Beautifully explained! For future videos, though, it might be worth being an extra bit careful when talking about gender. The idealized version of reality, where there are exactly two (equally common) genders, gives rise to great examples and problems in probability theory -- but if we aren't careful with the language, it's easy to wound up hurting and alienating intersex and nobinary folks by making them feel forgotten and invisible. I guess this is hard to avoid, but at least saying something somewhere that just quickly highlights the assumptions being made and that in one way or another acknowledges the existence of these groups can go a long way :)

Really glad to hear, hopefully you keep enjoying it :)

3blue1brown

This is nitpicking, but I noticed some animation elements don't have 0% opacity before entry -- "3 choices" at 10:55, and after exit -- "First" at 9:01.

Thanks!

3blue1brown

Great job on the visuals on this video! It's clear you're improving very quickly on this front. The 'slickness' of the animation and the concepts behind the visualisations themselves were really wonderful.

Thanks!

3blue1brown

Ah, good catch. Indeed it was randomly generated, so I suppose we had a (2!3!/5!) chance of that happening :)

3blue1brown

Seriously. Please don't stop making these videos. I actually enjoy math now!

Anthony Lee

Vi-Hart and Matt Parker got a 2017 award for Maths communications. Time to look out for nominating here for 2018: <a href="http://www.ams.org/profession/prizes-awards/ams-awards/jpbm-comm-award" rel="nofollow noopener" target="_blank">http://www.ams.org/profession/prizes-awards/ams-awards/jpbm-comm-award</a>

Christopher Burke

On the denominator are the k consecutive numbers beginning with 1. On the numerator are k consecutive numbers starting at n - k + 1. The key point is that in any consecutive sequence of k numbers, at least one of these numbers must be divisible by each of 1, 2, ..., k. Consider some integer m. If m itself is not divisible by, say, 4, then one of m + 1, m + 2, or m + 3 *must* be divisible by 4.

Just an observation. If you have something like (7*6*5*4)/(4*3*2*1), to me it's not entirely obvious that everything will actually cancel out and you will end up with a whole number. I mean I know it has to be, because it's just the number of ways you can choose 4 things out of 7, but is there a way to understand that without referring to this 7 choose 4 thing?

Anton Novikov

I had exactly the same initial idea and the same feeling.

Daniel Armesto

I had never seen the Pascal´s triangle so clearly explained. That idea of adding one option and sliding the columns has that feeling of real genius: it makes you think "how come I never thought of this before?" And, as always, the graphics are so smooth that eveything seems to flow so naturally! You do not just understand it; you see it happen.

Daniel Armesto

Dude, what international award can we candidate you for the advancement in the UNDERSTANDING of mathematics? Seriously asking.

Does order matter? Check out James Tanton's take on combinations and permutations: <a href="https://youtu.be/CKKn1g2B-T8" rel="nofollow noopener" target="_blank">https://youtu.be/CKKn1g2B-T8</a>

Beautiful as always, Grant. Nicely done. Particularly liked the part of comparing side-by-side the Cam/Ben/Ali order with the 10011 order and explaining the way to think about how its the “First”, “Second”, and “Third” where the order you say them doesn’t matter.

Steve Muench

I almost didn't watch this one because I thought, I've been doing that stuff for decades. Oh - how wrong I was, as always - whilst I didn't learn anything new - my understanding just took a massive forward lurch. Thanks again.

Christopher Burke

Super rad! I'm really excited for the next video! Just thought I'd point out a tiny thing. At 8:43 when you are talking about how order matters with the binary strings, the first animation of 11100 swaps the two zeros making it redundant. I guess that that was just a random generated animation thing. But I don't want that to confuse anyone.