A Secret Weapon for Predicting Outcomes: The Binomial Distribution

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0:00 - Introduction
0:41 - Calculating by hand for small numbers
5:54 - Independent events
6:50 - Building Pascal's triangle
9:03 - Binomial coefficient formula
13:27 - Empirical test
Some 0! videos:
• Zero factorial or 0! | Probability an...
• Zero Factorial - Numberphile
• Why is 0! = 1?
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I was unreasonably happy to see that the blob finally made a shot at the end

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The return of the king

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Yeah

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Biggest W of June so far

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Every his video is return?

[@lety18chula]

This has no reason to be as good as it is, thank you, I finally get it

[@Absolutemenace_]

This is literally our math subject rn. Thanks man.

[@NoTNoL]

Same

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This one's for you

[@Absolutemenace_]

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[@duythuchoang5095]

​@@PrimerBlobslmao thanks, I actually learned the stuff in the video in January and it's so nice when I look at the formulas and understand them

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[@dragonfriend9364]

I personally miss the evolution/economic vids. I'll still watch these, but those are what brought me to the channel.

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Me too, me too. There's an econ one cooking currently.

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​let the man cook

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Same! :(

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@@PrimerBlobs thanks, I'm looking forward to it.

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@@PrimerBlobs good to hear

[@angelus8521]

Primer is the only educational KZbinr I watch cause he makes it fun

[@spmagic9083]

I'd recommend a few: 1. 3Blue1Brown has similar math visualizations over a number of math topics. 2. Kurgesagt has really interesting animations over many topics, including science, climate change, space, and aliens. 3. Veritasium shows sciencey things in cool ways. 4. TedEd has short animations on a variety of topics, like science, mythology, fiction, history, and social studies. 5. MinuteEarth has fun, short animations about the Earth, nature, and related science topics. 6. MinutePhysics has short animations about physics. This is by no means an exhaustive list, but I watch these channels more than others. For shorter videos, try starting with TedEd, MinuteEarth, and MinutePhysics. The other channels have slightly longer, more in-depth videos.

[@infinitum-repertorium]

​@@spmagic9083thanks, i was about to write the same. It's so cool that this form of education connects us all even though we don't know each other.

[@Ennar]

What do you mean he makes it fun? Mathematics is fun. What he does is very clean visuals and is quite good at it. That's why I watch, even though I learned all of this many years ago.

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[@suicidebxmber1234]

Not only does he EXPLAIN with absolute eloquence and clarity, but the care he puts into the animations is remarkable.

[@RickachuCXVI]

I just love the presentation and explanations in these videos so much, it makes the entire lesson so much more engaging

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No matter the subject, I’ll watch these all the way through, even if I won’t learn it for years.

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[@joshavery]

You're learning by watching! No need to wait for a formal class.

[@Patrick-Hartford]

same

[@alexanderwolf7514]

By now I've done 4 semesters of statistics classes but none of my professors was able to explain this concept as easily understandable as this video.

[@patrickwienhoft7987]

For binomials and the choose function there are really nice ways to build intuition, experiments to derive rules like in this video. However, in combinatorics you often care about slightly more complex things, where you have more classes than yes/no and dependencies between objects. For example, for a given graph, how many ways are there to label the nodes such that the graphs are isomorphic? When I learned this and taught it to other students I always had the feeling that this was one of the things for which you need a good understanding of the problem to solve it as there is no go-to formula or procedure to solve those. The only way that seemed to work is to solve different instances over until it clicks tl;dr: I found teaching combinatorics really hard.

[@anthonynorman7545]

​@@ensiehsafary7633also, the time/resources are no where equal to what a professor has.

[@47Mortuus]

Because you're expected to explain it to yourself, using different sources. THAT IS THE VERY ESSENCE OF UNIVERSITY

[@anthonynorman7545]

@@47Mortuus that's not how math classes tend to go. It's not like it was a research paper topic.

[@47Mortuus]

@@anthonynorman7545 stay ignorant :)

[@ChrisPhelior]

Chance of your team's Yasuo actually being good: infinitesimal Great video as always

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That LoL reference came completely out of nowhere.

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Yeah I was way too surprised by that lol

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Yeah, Yasuo teammate is the last blob in the video.

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@@TheAlexN1305 Nah, don't be mean to the blob

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i clicked on this video from the recommended sidebar while watching a league video so this actually was extremely fitting hahaha

[@Lionbug]

The encouragements to pause and think through things are _vital_ to get people to actually _understand_ and not just watch the video and forget immediately. Very well done all around!

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Can black blob with sunglasses become a recurring character? I think his character arc involving missing all the shots was very interesting

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The only educational channel I'll watch when I already understand the subject

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Same. Learned this beginning of last year but it is so much more engaging

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[@_________________404]

41%

[@navetal]

4:28 I love the enthusiasm of the blob on the left who keeps on trying to score.

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I hadn't noticed this, thanks!

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This isn't over-explained at all. This is the kind of explanation I've been looking for for so long!

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its a good *year* when Primer uploads

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hey

[@pnku]

"your team's yasuo actually being good" is a reference i didn't expect at all, love your videos, was super excited to see this video in my sub box

[@frootjupes]

I wish I'd had this when covering counting problems! Your explanations and visuals are so much easier to comprehend than the lectures I read.

[@justinlindfors8512]

He should be the next channel to be featured in schools!

[@Bambutcher2]

I'm so glad you did this video cos just the other day I was cracking my head on a similar problem and couldn't make out how binomial coefficient work on my own, thanks a lot for making it crystal clear. Great job, as always!

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I can not believe it. I love your videos so much. I actually discovered your channel this morning. When I entered it and saw your last video was from ten months ago I thought you wouldn't be doing more videos. So the fact that on the same day I found you, you put a video makes me so happy. Keep it up, the blobs are the best

[@Zmit]

Oh how I have missed the blobs engaging in simulations. So nice to see a new video. As always a pure delight to be able to learn and be entertained at the same time. All education should be this way.

[@ImThylacine]

This is a wonderfully succinct and comprehensive explanation of this topic that actually covers the reasons *why* the formula was constructed the way that is, not just how to use it. My math-teacher mom and I approve. I love the rest of your bio, econ, and math stuff, too. Here’s hoping the algorithm feeds this to more people!

[@kelkin2576]

15:12 I cheered so loud congrats buddy you did it

[@feyblack2197]

So glad you brought this equation back to talk about. One of my favorite videos you've done is the coin flip one and I like using the binomial distribution formula when I can, but always forget what the values would stand for and I'd have to go to the linked video to remind myself. This will be much easier to find and sit through.

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I love these blobs! And the topics in your videos are covered in such an easy-to-follow fashion. Thank you so much for making them!

[@_chishika_]

one day in the future, this is gonna be played in a classroom for a maths class, and your gonna make a lot of people laugh and understand this a much better and get their foot into the doors of stats and further stats. amazing vid

[@strawberry942]

This is great timing! I have my maths A level mock in a few weeks, and I'm not the biggest fan of stats, so this is really useful for brushing up on it.

[@jeremyelser8957]

Such impressive visualizations. The little extra efforts like making the numbers move or blink to guide the eye are very helpful.

[@Meymoi]

Oh wow I was just looking at your channel and wondering when you would post next, I'm glad to be able to watch a new video of yours, they're always great!

[@SL-ef8jv]

Just learned this in class, and you helped me understand this so much better. Thank you so much!

[@Misstborn]

As someone who just took stat, this was a really nice reminder of the logic behind everything and made me actually think about math for the first time in a few weeks. Fantastic video!

[@_________________404]

41%

[@richardcampbell4506]

Easily the best description of Binomial distributions and, most importantly, the fundamentals that support it. Fantastic! I’ll be sharing it with my son. thank you 👍

[@PrometheusMMIV]

I love these videos. You have a great way of explaining things in a very intuitive way. I especially liked the demonstrations for calculating the binomial coefficient. Showing that the Nth blob added to the list can be inserted in N different positions really helps solidify why ordering is calculated using factorials*. And then using that to remove the duplicates from each group made a lot more sense than just trying to memorize the formula. * The way I usually think about ordering is if I have N items, then the first one in the list could be any of the N items, then the second could be any of the remaining N-1 items, then N-2, and so on until the last one.

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You can’t imagine how happy I was to see you coming back! Your videos are so good! Keep going! ❤

[@matchanik]

No puedo explicar cuanto hubiera querido tener este tipo de explicación en la época de estudiante. Excelente!

[@giuseppebuonomo7241]

Beautifully explaine dand visualized. I love how in detail everything is explained. Thanks!

[@marcboss]

I have been waiting for more videos, thanks for posting!

[@VexWythe]

my immediate thought when watching this, given the free-throw example from basketball, is calculating the odds of any given baseball pitcher throwing a perfect game (a game where not a single opposing batter gets on base over all nine innings) based on their WHIP statistic (walks and hits per inning pitched)! very cool video, as always :)

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I love your videos, every time you release one it’s like everything else freezes and I half to watch your video. Keep up the good work

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I'm abot

[@bogdanbusui5249]

On Friday I just had my Uni Probability exam and part of what we learned is exactly this. Awesome video and explanations, as always actually!!

[@user-db4lk7yg3o]

I recently finished alg 2 and we learned this but skipped over most of the explanation and went right to the combinations and permutations, it's nice to learn more about what makes these formulas work.

[@christinemeili2398]

I’ll keep this in my pocket for when I have my statistics class this autumn

[@bassoonatic777]

This is quite good. If I still taught Prob and Stats, I'd share this in my class.

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How did you reply to this 1 day ago???

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Hold up how did this comment become 1 day old but the video isn't an hour old

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wtf how did you comment one day ago the video was made 38 seconds ago

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​@@loopeater8338 Video was unlisted before releasing, and they had the link to view it.

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@Don't Read My Profile Picture wasn't planning on it

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The blobs are adorable! Definitely going to ask for a plush or two this Christmas And seeing that this channel doesn’t overload one with videos, I subscribed pretty dang fast.

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It was amazing to watch the whole content. super high quality, kudos to the amazing team and hard work behind it

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*"You miss all the shots you don't take"* - Michael Scott, The Office

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The blob at the end is just footage of me trying to play basketball

[@midnight4685]

Thanks! This was something I studied earlier in the year, was really interesting to see it explained again, and quite well too.

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these videos really cement in the fact that i prefer statistics/combinatorics to things like calculus. i struggle to pay attention to and care about what goes on in my calculus classes, but i willingly watch, stay engaged with, and seek out more content focusing on this sort of stuff. thanks for reminding me that not all math is nightmarish 😉

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Love your videos.Keep up the good work.

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I will try. >_

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[@MaskedDeath_]

I've had combinatorics in high school, and we did "learn" the formula there - as in, "this is the formula, you need to remember it because it works". Thanks to this video, I've finally understood where the formula comes from. Thanks!

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Thank you for that great video, your videos always make me understand those topics deeper.

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If Primer uploads a video, you know it's a good day

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primer

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This isn't overexplained, this is the explanation I wish I'd gotten in school. Thx 👌

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This video is such an amazing tool to understand the subject. The visuals are just perfect to support the theoratical part❤ Yet again amazing job!!

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I wish this video came out like 5 years ago when I had to learn this

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Whenever Primer uploads. It’s a good day.

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Beautiful! Oh this is perfect! I tutor genetics and have some students that struggle with statistics, and I am going to tuck this into my tool box! Thanks for making the math pretty, well chewed, and easy to digest. I've already used some of your other videos with positive feedback, I just hope the next wait for a new one isn't as long as the last.

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Keep up the good work!

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Thanks, Sara!

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OMG it’s Primer

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A única coisa ruim desse canal é que ele deveria postar vídeos todos os dias. MUITO BOM!

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I really enjoy the style that you present in and would love to see more videos. I love getting your notifications.

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A statistics video from Primer right as I am about to start my Stats this semester and I love it!

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I litteraly just learnt this exact thing for the first time in my maths lesson yesterday!! What are the chances!?

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100%

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@@PrimerBlobs Did you use the formula to get to that conclusion 😅

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My teams yasuo being good is always 0%

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I'm a bot

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This is so amazing! The graphics are super well done too. Thank you Primer!

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It really makes sense now why you subtract in the parentheses before the factorial. Thanks for the video!

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I always watch primer, regardless of the subject, because if I do not know it its a great opportunity to learn it, and if I already know it its still a great opportunity to learn about communication and didactics. I always end the video feeling smarter and that keeps me engaged. Thank you very much for the effort in making these as easy-to-understand as possible!

[@samjam1992feb]

Very Few Times I have seen someone explaining such concepts with such clarity.Thanks, A lot

[@Eggmanlover]

holy moley I never learned about this in school, but I've occasionally been interested in calculating probabilities for certain things, and my eyes glazed over when I looked up binomial distribution, but seeing it here, it's gotten a LOT easier to understand... nice video!

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I do a lot of statistics for work, and I still watched this video because a) always great to review the fundamentals and b) your videos are just that good.

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Always glad to see another Primer vid!

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what a amazing video, the best class I've ever watched about binomial distribution along with this clear and well-done animation transformed this simple 15min video into a masterpiece, congrats 👏🏼👏🏼👏🏼

[@vkn3682]

Exactly the explanation I was looking for! Great video!

[@sajinth2006]

Thank you for this, I always struggled with binomial distribution but this video makes it very easy to understand

[@streambotnt2095]

I am supposed to learn this for school and my teacher unfortunately isn't the best when it comes to explaining, so it is very nice to have you make a video on this topic.

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I love these videos you make, they are instructive with a fun way to learn.

[@laughsingay]

Yay! Finally another post! I love your videos, they're educational but in a way that entirely makes sense and is also fun to watch because of the animations. :)

[@pimderijke4560]

You make this so understandable and clear! Keep up the good work man

[@matthijsperabo7282]

Just had a test about this last week, awesome video, would have loved to see it back then.

[@atlas4733]

Literally did my final math exam (12th grade) today and I did revision for analytical combinatorics covering this exact subject! I'm surprised how well I understood this video. There were a few aha moments where a couple things at a time slotted into place :)

[@flipgalaxy711]

Perfect timing for my A-level Stats paper in two days time!!!

[@antwidavid389]

I absolutely loved this! You should do one on geometric distribution and normal distribution!!

[@dsfmdiya7500]

OMG I WISH I’D FOUND THIS VIDEO EARLIER! Just had a test about this a few days ago and didn’t understand anything but I totally get it now!

[@petermoras6893]

One of the things i think should always be brought up when mentioning Pascal's triangle, is that you can describe it by multiplying odds as if it was a polynomial. For example: Lets say you had that you could either make a shot or miss it. This could be described as (X + Y), where X is a missed shot, Y is a made shot. If you make 2 shots, it would look like (X + Y)^2 = 1X^2 + 2XY + 1Y^2. This holds with n shots, or (X + Y)^n. You may also notice that the expanded polynomial is also pascal's triangle, which is how we can easily calculate the triangle in the first place. This also works with more than 2 distinct outcomes, like (A + B + C +D)^n.

[@brightsideofmaths]

Thanks for that! I am huge fan of your videos and the binomial distribution :)

[@hollowshiningami3080]

Brooo... It's Primer! He's back! Jokes aside I love your videos man, hope to see more of you soon 👊

[@Ma-pz5kl]

so great. and the blobs made it fun to learn. well done sir !

[@memesalldayjack3267]

this is awesome, a while back i was trying to figure those factorial bits by myself, i gave up hoping i'd someday find a good tutorial, if you don't know how to ask for instructions, it's hard to get them, and i didn't know what the formula i wanted was called, i wanted it to help me optimize yugioh deck building ratios, also it looked kinda fun, really cool to see this channel talking about something that can help with that

[@B0NES48]

It’s always a great day for a Primer video!!!

[@chazhovnanian6897]

a primer vid on my math curriculum just in time for exams, literally what could be better

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Fantastic video! The quality has really gone up recently!

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Yay I’ve been waiting for a video from you!!!

[@lycanlycan1802]

It’s a good year when primer upload ❤

[@Skeffles]

Great video. Really well explained!

[@Thiago100Zwetsch]

I was really missing these videos!!

[@vighneshraman1784]

So glad to see your video after sooooo long

[@rokushou]

I have taken enough stats classes to thoroughly understand and use the binomial distribution, but this is the best explanation of the binomial coefficient formula I have heard.

[@gabrielgs7925]

Love the way you ensured people like me will sit through the whole end cut - like, of course I wanna support the poor blob at the end until it succseeds! 😆☺️ Love it!

[@DolphinLearner]

the info may not be sticking in my brain but it is still fun to watch! thx man :)