A Secret Weapon for Predicting Outcomes: The Binomial Distribution

2024 ж. 4 Мам.
999 044 Рет қаралды

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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

    @trees9363@trees936310 ай бұрын
    • :)

      @PrimerBlobs@PrimerBlobs10 ай бұрын
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      @Kathen@Kathen10 ай бұрын
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      @volodyadykun6490@volodyadykun649010 ай бұрын
    • This has no reason to be as good as it is, thank you, I finally get it

      @lety18chula@lety18chula10 ай бұрын
  • This is literally our math subject rn. Thanks man.

    @Absolutemenace_@Absolutemenace_10 ай бұрын
    • Same

      @NoTNoL@NoTNoL10 ай бұрын
    • This one's for you

      @PrimerBlobs@PrimerBlobs10 ай бұрын
    • @@PrimerBlobs 🙏

      @Absolutemenace_@Absolutemenace_10 ай бұрын
    • ​@@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

      @duythuchoang5095@duythuchoang509510 ай бұрын
    • ‎‎‎‎‎‎‎‎‎‎‎‎‎E

      @EEEEEEEE@EEEEEEEE10 ай бұрын
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    @dragonfriend9364@dragonfriend936410 ай бұрын
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      @PrimerBlobs@PrimerBlobs10 ай бұрын
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      @piggydabest@piggydabest10 ай бұрын
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      @jaideepshekhar4621@jaideepshekhar462110 ай бұрын
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      @dragonfriend9364@dragonfriend936410 ай бұрын
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      @CrittingOut@CrittingOut10 ай бұрын
  • Primer is the only educational KZheadr I watch cause he makes it fun

    @angelus8521@angelus852110 ай бұрын
    • 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.

      @spmagic9083@spmagic908310 ай бұрын
    • ​@@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.

      @infinitum-repertorium@infinitum-repertorium10 ай бұрын
    • 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@suicidebxmber123410 ай бұрын
  • I just love the presentation and explanations in these videos so much, it makes the entire lesson so much more engaging

    @RickachuCXVI@RickachuCXVI10 ай бұрын
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      @EEEEEEEE@EEEEEEEE10 ай бұрын
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      @joshavery@joshavery10 ай бұрын
    • same

      @Patrick-Hartford@Patrick-Hartford10 ай бұрын
  • 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.

    @alexanderwolf7514@alexanderwolf751410 ай бұрын
    • 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.

      @patrickwienhoft7987@patrickwienhoft798710 ай бұрын
    • ​@@ensiehsafary7633also, the time/resources are no where equal to what a professor has.

      @anthonynorman7545@anthonynorman754510 ай бұрын
    • Because you're expected to explain it to yourself, using different sources. THAT IS THE VERY ESSENCE OF UNIVERSITY

      @47Mortuus@47Mortuus10 ай бұрын
    • @@47Mortuus that's not how math classes tend to go. It's not like it was a research paper topic.

      @anthonynorman7545@anthonynorman754510 ай бұрын
    • @@anthonynorman7545 stay ignorant :)

      @47Mortuus@47Mortuus10 ай бұрын
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    @ChrisPhelior@ChrisPhelior10 ай бұрын
    • That LoL reference came completely out of nowhere.

      @doomse150@doomse15010 ай бұрын
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      @xavierburval4128@xavierburval412810 ай бұрын
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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

      @jiyuandong8964@jiyuandong896410 ай бұрын
  • 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!

    @Lionbug@Lionbug10 ай бұрын
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      @trimonmusic@trimonmusic10 ай бұрын
  • This isn't over-explained at all. This is the kind of explanation I've been looking for for so long!

    @APaleDot@APaleDot10 ай бұрын
  • its a good *year* when Primer uploads

    @UserStillLoading@UserStillLoading10 ай бұрын
    • hey

      @PrimerBlobs@PrimerBlobs10 ай бұрын
  • "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

    @pnku@pnku10 ай бұрын
  • 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.

    @frootjupes@frootjupes10 ай бұрын
    • He should be the next channel to be featured in schools!

      @justinlindfors8512@justinlindfors851210 ай бұрын
  • 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!

    @Bambutcher2@Bambutcher210 ай бұрын
  • 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

    @nataliabasile752@nataliabasile75210 ай бұрын
  • 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.

    @Zmit@Zmit10 ай бұрын
  • 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!

    @ImThylacine@ImThylacine10 ай бұрын
  • 15:12 I cheered so loud congrats buddy you did it

    @kelkin2576@kelkin257610 ай бұрын
  • 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.

    @feyblack2197@feyblack219710 ай бұрын
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    @viliuskripas4425@viliuskripas442510 ай бұрын
  • 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

    @_chishika_@_chishika_10 ай бұрын
  • 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.

    @strawberry942@strawberry94210 ай бұрын
  • Such impressive visualizations. The little extra efforts like making the numbers move or blink to guide the eye are very helpful.

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    @Meymoi@Meymoi10 ай бұрын
  • Just learned this in class, and you helped me understand this so much better. Thank you so much!

    @SL-ef8jv@SL-ef8jv10 ай бұрын
  • 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!

    @Misstborn@Misstborn10 ай бұрын
    • 41%

      @_________________404@_________________4046 ай бұрын
  • 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 👍

    @richardcampbell4506@richardcampbell450610 ай бұрын
  • 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.

    @PrometheusMMIV@PrometheusMMIV10 ай бұрын
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    @batmanthedarkestknight@batmanthedarkestknight10 ай бұрын
  • No puedo explicar cuanto hubiera querido tener este tipo de explicación en la época de estudiante. Excelente!

    @matchanik@matchanik10 ай бұрын
  • Beautifully explaine dand visualized. I love how in detail everything is explained. Thanks!

    @giuseppebuonomo7241@giuseppebuonomo72414 ай бұрын
  • I have been waiting for more videos, thanks for posting!

    @marcboss@marcboss10 ай бұрын
  • 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 :)

    @VexWythe@VexWythe10 ай бұрын
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    @HarryHughAndYou@HarryHughAndYou10 ай бұрын
    • I'm abot

      @thekeyboardwarrior1018@thekeyboardwarrior101810 ай бұрын
  • 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!!

    @bogdanbusui5249@bogdanbusui524910 ай бұрын
  • 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.

    @user-db4lk7yg3o@user-db4lk7yg3o10 ай бұрын
  • I’ll keep this in my pocket for when I have my statistics class this autumn

    @christinemeili2398@christinemeili239810 ай бұрын
  • This is quite good. If I still taught Prob and Stats, I'd share this in my class.

    @bassoonatic777@bassoonatic77710 ай бұрын
    • How did you reply to this 1 day ago???

      @loopeater8338@loopeater833810 ай бұрын
    • Hold up how did this comment become 1 day old but the video isn't an hour old

      @thekeyboardwarrior1018@thekeyboardwarrior101810 ай бұрын
    • wtf how did you comment one day ago the video was made 38 seconds ago

      @FriesOnYt@FriesOnYt10 ай бұрын
    • ​@@loopeater8338 Video was unlisted before releasing, and they had the link to view it.

      @AceFaz@AceFaz10 ай бұрын
    • @Don't Read My Profile Picture wasn't planning on it

      @AceFaz@AceFaz10 ай бұрын
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    @ethanpetersen810@ethanpetersen8107 ай бұрын
  • It was amazing to watch the whole content. super high quality, kudos to the amazing team and hard work behind it

    @karansmittal@karansmittal10 ай бұрын
  • *"You miss all the shots you don't take"* - Michael Scott, The Office

    @KevinTan@KevinTan10 ай бұрын
  • The blob at the end is just footage of me trying to play basketball

    @DuchessEvie@DuchessEvie2 ай бұрын
  • Thanks! This was something I studied earlier in the year, was really interesting to see it explained again, and quite well too.

    @midnight4685@midnight468510 ай бұрын
  • 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 😉

    @25thEffect@25thEffect10 ай бұрын
  • Love your videos.Keep up the good work.

    @stanlee268@stanlee26810 ай бұрын
    • I will try. >_

      @PrimerBlobs@PrimerBlobs10 ай бұрын
  • Absolutely love your content. Almost yelled out "BLOB GUY HAS A NEW VIDEO" when I saw this in my feed earlier. I can only assume how much effort goes into these videos, but I sincerely hope you'll keep making them - they are truly awesome.

    @LordHakkera@LordHakkera10 ай бұрын
  • 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!

    @MaskedDeath_@MaskedDeath_10 ай бұрын
  • Thank you for that great video, your videos always make me understand those topics deeper.

    @victor_lu@victor_lu4 ай бұрын
  • If Primer uploads a video, you know it's a good day

    @MaxCubing11@MaxCubing1110 ай бұрын
    • primer

      @molybd3num823@molybd3num82310 ай бұрын
    • @@molybd3num823 sorry, autocorrector

      @MaxCubing11@MaxCubing1110 ай бұрын
  • This isn't overexplained, this is the explanation I wish I'd gotten in school. Thx 👌

    @blacky____05@blacky____0510 ай бұрын
  • The last line really hit me and made me subscribe. Love your videos. Keep going!

    @AzizbekSheripboev@AzizbekSheripboev10 ай бұрын
  • 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!!

    @timnauwelaers6876@timnauwelaers687610 ай бұрын
  • I wish this video came out like 5 years ago when I had to learn this

    @RudyOMP@RudyOMP10 ай бұрын
  • Whenever Primer uploads. It’s a good day.

    @puffer2939@puffer293910 ай бұрын
  • 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.

    @ajtroyer76@ajtroyer7610 ай бұрын
  • Keep up the good work!

    @saram3604@saram360410 ай бұрын
    • Thanks, Sara!

      @PrimerBlobs@PrimerBlobs10 ай бұрын
    • OMG it’s Primer

      @DavidMarketh@DavidMarketh10 ай бұрын
  • A única coisa ruim desse canal é que ele deveria postar vídeos todos os dias. MUITO BOM!

    @MrProfessorFelipe@MrProfessorFelipe10 ай бұрын
  • I really enjoy the style that you present in and would love to see more videos. I love getting your notifications.

    @superson5586@superson558610 ай бұрын
  • A statistics video from Primer right as I am about to start my Stats this semester and I love it!

    @beb6c2a@beb6c2a10 ай бұрын
  • I litteraly just learnt this exact thing for the first time in my maths lesson yesterday!! What are the chances!?

    @ilikeplanes5292@ilikeplanes529210 ай бұрын
    • 100%

      @PrimerBlobs@PrimerBlobs10 ай бұрын
    • @@PrimerBlobs Did you use the formula to get to that conclusion 😅

      @ilikeplanes5292@ilikeplanes529210 ай бұрын
  • My teams yasuo being good is always 0%

    @randy3222@randy322210 ай бұрын
    • I'm a bot

      @thekeyboardwarrior1018@thekeyboardwarrior101810 ай бұрын
  • This is so amazing! The graphics are super well done too. Thank you Primer!

    @navalshah5999@navalshah599910 ай бұрын
  • It really makes sense now why you subtract in the parentheses before the factorial. Thanks for the video!

    @MattTrevett@MattTrevett4 ай бұрын
  • 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!

    @jrodartec@jrodartec10 ай бұрын
  • Very Few Times I have seen someone explaining such concepts with such clarity.Thanks, A lot

    @samjam1992feb@samjam1992feb8 ай бұрын
  • 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!

    @Eggmanlover@Eggmanlover10 ай бұрын
  • 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.

    @hellopeoples8@hellopeoples810 ай бұрын
  • Always glad to see another Primer vid!

    @erinkarp@erinkarp10 ай бұрын
  • 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 👏🏼👏🏼👏🏼

    @Matheusramoss17@Matheusramoss174 ай бұрын
  • Exactly the explanation I was looking for! Great video!

    @vkn3682@vkn368210 ай бұрын
  • Thank you for this, I always struggled with binomial distribution but this video makes it very easy to understand

    @sajinth2006@sajinth200610 ай бұрын
  • 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.

    @streambotnt2095@streambotnt209510 ай бұрын
  • I love these videos you make, they are instructive with a fun way to learn.

    @TheWizardsOfOz@TheWizardsOfOz10 ай бұрын
  • 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. :)

    @laughsingay@laughsingay10 ай бұрын
  • You make this so understandable and clear! Keep up the good work man

    @pimderijke4560@pimderijke456010 ай бұрын
  • Just had a test about this last week, awesome video, would have loved to see it back then.

    @matthijsperabo7282@matthijsperabo728210 ай бұрын
  • 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 :)

    @atlas4733@atlas473310 ай бұрын
  • Perfect timing for my A-level Stats paper in two days time!!!

    @flipgalaxy711@flipgalaxy71110 ай бұрын
  • I absolutely loved this! You should do one on geometric distribution and normal distribution!!

    @antwidavid389@antwidavid38910 ай бұрын
  • 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!

    @dsfmdiya7500@dsfmdiya750010 ай бұрын
  • 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.

    @petermoras6893@petermoras689310 ай бұрын
  • Thanks for that! I am huge fan of your videos and the binomial distribution :)

    @brightsideofmaths@brightsideofmaths10 ай бұрын
  • Brooo... It's Primer! He's back! Jokes aside I love your videos man, hope to see more of you soon 👊

    @hollowshiningami3080@hollowshiningami308010 ай бұрын
  • so great. and the blobs made it fun to learn. well done sir !

    @Ma-pz5kl@Ma-pz5kl4 ай бұрын
  • 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

    @memesalldayjack3267@memesalldayjack326710 ай бұрын
  • It’s always a great day for a Primer video!!!

    @B0NES48@B0NES4810 ай бұрын
  • a primer vid on my math curriculum just in time for exams, literally what could be better

    @chazhovnanian6897@chazhovnanian689710 ай бұрын
  • Fantastic video! The quality has really gone up recently!

    @marcomonti5758@marcomonti575810 ай бұрын
  • Yay I’ve been waiting for a video from you!!!

    @c3cris2@c3cris210 ай бұрын
  • It’s a good year when primer upload ❤

    @lycanlycan1802@lycanlycan180210 ай бұрын
  • Great video. Really well explained!

    @Skeffles@Skeffles9 ай бұрын
  • I was really missing these videos!!

    @Thiago100Zwetsch@Thiago100Zwetsch10 ай бұрын
  • So glad to see your video after sooooo long

    @vighneshraman1784@vighneshraman178410 ай бұрын
  • 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.

    @rokushou@rokushou10 ай бұрын
  • 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!

    @gabrielgs7925@gabrielgs792510 ай бұрын
  • the info may not be sticking in my brain but it is still fun to watch! thx man :)

    @DolphinLearner@DolphinLearner29 күн бұрын
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