The Binomial Distribution: Crash Course Statistics #15

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Today we're going to discuss the Binomial Distribution and a special case of this distribution known as a Bernoulli Distribution. The formulas that define these distributions provide us with shortcuts for calculating the probabilities of all kinds of events that happen in everyday life. They can also be used to help us look at how probabilities are connected! For instance, knowing the chance of getting a flat tire today is useful, but knowing the likelihood of getting one this year, or in the next five years, may be more useful. And heads up, this episode is going to have a lot more equations than normal, but to sweeten the deal, we added zombies!
If you want to try out some of the math from this video here is a great binomial probability calculator: vassarstats.net/textbook/ch5ap...
If you'd like more information on calculating the binomial coefficient (n-choose-k) read this: www.statisticshowto.com/binomi...
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Опубликовано:

8 май 2018

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Комментарии : 200

@saivishnutulugu5014 5 лет назад

If you want to check if a situation is binomial there are 4 conditions: 1.) Each observation can be classified as a success or failure 2.) Fixed number of n observations 3.) n observations are independent of another 4.) p(success) is the same for each observation

@anranzhao1261 4 года назад

feel very relatable when she mentioned 'virus' and 'pandemic‘ lol. watching this because of the lockdown

@enkhbayardambadarjaa7356 4 года назад

who would've thought covid-19 would make classes more interesting.

@malaikadsouza4236 4 года назад

got goosebumps when she said "pandemic level viruses"

@AqashaAhmed 4 года назад

interesting seeing the cold and zombies thing since I am quarantined right now from COVID

@tamisanlatherow3103 6 лет назад

For beginners, it would have been more useful to explain how to enter the factorial in so the math is easier to understand. Math needs formulaic examples, not just verbiage. 5C3 gets entered into the calculator as 5!/3!(5-3)! which gives you 120/(6*2) = 10. Now take 10 and multiply it by the rest of the formula to get the 31%. Not everyone will get this if you do not explicitly state it.

@briansutton5796 4 года назад

I spent 5 minutes pausing going back and forth wondering why I was only getting 3% until this comment. Thank you!

@paulbird2772 4 года назад

Thank you

@xx420xxyolo3 4 года назад

just use the nCr function on your calculator, you dont have to enter the factorials

@rangercarnage 4 года назад

Thank you so much for this! I spent a good 5 minutes trying to figure out what went wrong in my equation!

@ruiqixu4389 4 года назад

Thank you sooo much, I just felt lost and then I saw your comment, which really helped me a lot.

@gian8448 5 лет назад

PEOPLE DID YOU IGNORE AT 0:22 the scary figure in the back??????

@FootLettuce 4 года назад

Go to CC Statistics episode #13 and see the part where they talk about Pareidolia.

@aprilsonline 4 года назад

Honestly didn't even see it till I read your comment😂

@socialcomplexitydinocarpen6372 4 года назад

I'm really creeped out...

@peksn 4 года назад

That's the zombie apocalypse coming as they said, and now covid lol

@rangercarnage 4 года назад

If you look closely, almost every picture has a zombie

@Lucky10279 6 лет назад

OK, now I finally understand at least the gist of the notation for this formula. In my experience tutoring stat 101 students, half of their confusion is because they don't know how to interpret all the new notation. This particular notation was one of few things I think our textbook did a poor job of explaining, so I always had a hard time helping them with it. Your explanation makes perfect sense and makes me wonder why its not always explained that way.

@Improbabilities 6 лет назад

This is why I loved changing schools and getting a mathematician as a statistics teacher. Every time someone asked "why this?" or "why not do this instead?", the teacher would respond "let's find out", and promptly started walking through the mathematics behind the formula/distribution. That usually answered several other questions at the same time.

@HilbertXVI 6 лет назад

Improbabilities That's amazing lol

@Lucky10279 6 лет назад

Improbabilities Sounds like a great teacher!

@springinggrass 4 года назад

the most relevant video in the series so far, as luck would have it. now where to find the probability rate of infection in this country...

@e.8927 6 лет назад

crash course I love your videos and all the effort put into it but I don't know why I couldn't understand this very clearly. you made it more complicated instead of simplifying it

@socialcomplexitydinocarpen6372 5 лет назад

CC *Uses quite some math* VIEWERS: Damn! That's too heavy. I feel stupid now... CC *Uses no math* VIEWERS: What the frick? Is this a channel for kids?! CC *Uses some math but not too much* VIEWERS: C'mon guys, you should choose either to use it or not! Don't be scared!

@sam4330 5 лет назад

I mean, the probability that those are the same people commenting is pretty small. :)

@oswaldovzki 5 лет назад

I'm the one who thinks: " Damn! That's too heavy. I feel stupid now..." but instead of complaining I paused the video e studied the math in question to understand ir better :D

@donbrandon2734 4 года назад

CSS: I don't know how to apply Bayes Theorem

@chintangandhi8468 6 лет назад

I've an exam the day after tomorrow. WHAT WERE THE ODDS OF THIS GETTING UPLOADED TODAY? I guess I can calculate now.

@PrattChrisDizzle 4 года назад

How was your exam??

@alexandertownsend3291 4 года назад

That toaster question was shocking.

@harshraojr 4 года назад

This is more relevant now than ever

@ishamathstea9019 4 года назад

Harsh, Jz posted about how to find PROBABILITY using BINOMIAL DISTRIBUTION.... I hope it's helpful..... Would love to hear some feed back too

@rositaroldangan6827 4 года назад

This is so relevant right now

@rahmetovedil 5 лет назад

The quality of the video is better than the quality of my life.

@emenikeanigbogu9368 6 лет назад

Thank you I appreciate this. It really gave me a proper understanding to how this operates and the reasoning behind it.

@JR-ti2ox 4 года назад

Very timely! Covid feels

@alexandertownsend3291 4 года назад

This video was released two years ago and mentions predicting the spread of pandemic. Is this a coincidence? The answer is probably yes (in spite of the COVID age), but it is still interesting.

@michal4593 4 года назад

60 dollar textbook did not captivate in 5 hours what this video did in 15 minutes. Thank you for all that you do!

@love_tammy 6 лет назад

I actually need this for my maths exam next week, that was quite a useful recap for me!

@haeleon654 6 лет назад

The guys at Thought Cafe really should make a graphing calculator that looks like the one in the intro screens that can do all the things described in this lesson. For them: If you do, please share the link; I would love to see something like that from you guys!

@renschuon4992 4 года назад

So what I'm hearing is that my instructor is teaching statistics in a pandemic and didn't use a single pandemic example

@HexerPsy 6 лет назад

DISAGREEING with your first example! Yes, 1 shock per week comes down to 41% - but you have to add the chance for getting No shock, because getting no shock is also happily fine and he/she would gladly eat toast and not get shocked. 0.8^5=0.32768 or 32.8% and so eating toast with acceptable amount of shocks is 32.8+41=72.8% So roughly 3 in 4 or 7 in 10 chance of getting acceptable number of shockes - id have that toast ^^

@burrowowl 6 лет назад

Also disagreeing with the first example but for a different reason. If you simply have toast eat day and stop after receiving the first shock you have a 100% chance of being shocked no more than one time during the week as a result of preparing toast.

@HexerPsy 6 лет назад

I like that reasoning!

@AnaleenAelwyn 6 лет назад

I was thinking this the whole time!

@AnaleenAelwyn 6 лет назад

John Fitzgerald also considered that option, so you'd at least get some toast, even if you got a shock at some point.

@arifodeman5010 6 лет назад

This is great! Thank you guys so much! Jumping off of this, do you think you guys could dive into logistic regression and then count models (e.g., Poisson, Negative Binomial, and Neg. Bin. Zero-Inflated)? I'm a graduate research assistant, and I've found these subjects largely lacking in my department and others, even though they're super useful--not everything fits a normal distribution! I would really appreciate if you guys at some point could tackle these topics.

@Kei-oy9fc 4 года назад

Would it be possible to have a full series of crash course on math?

@sergior.m.5694 5 лет назад

I don't get the 5 C 3 problem, 3 girls out of 5 children, I'm getting 3.1% chance not 31% what am I missing?

@makouras 6 лет назад

I really don't understand how the binom(n,k) formula works. You should explain that more thoroughly. The links in the description only show the factorials equation. And seeing as my math knowledge is below basic, I can't figure out how the numbers fit in your examples. Can somebody explain to me please? What do we multiply with what?

@jazminaguilar9714 5 лет назад

makouras Maybe this will help but n and k will always add up to one and if there’s a percentage in the question it’s usually n and you just have to find k that makes it add up to 1 or 100% or the total amount bc sometimes it’s not always going to be 100% sometimes it can be out of 40 like at 8:55

@ericklestrange6255 4 года назад

I haven’t found many videos that are better than StatQuest. However this video is amazing, the production value is really nice, everything just adds up really nicely even the shelves in the background and the colors, I’m very grateful for your video thank you very much

@janjoy10 6 лет назад

I was just procrastinating studying for my statistics midterm... And then this video was in my feed so here we go!

@davidsweeney111 6 лет назад

I love the bin distribution, thanks Adrian!

@mikeharrison1868 4 года назад

April 2020 - Ouch!

@pastelsparadox 5 лет назад

"To make up for it, we added some zombies" I, known Maggot Boy fan: _Oh hell yes_

@xsaberfaye 6 лет назад

Crash Course Linguistics?

@betostunt 4 года назад

Zombie's article from 2009, mentioned during video, had modelled the best actions against COVID-19...

@BlueyMcPhluey 6 лет назад

More maths! More maths! More maths!

@ElliotRuddy 6 лет назад

Perfect timing for my statistics test tomorrow !

@d.harrison1570 5 лет назад

At 6:52, the only answer of mine that matches theirs is for the first one. For the second one, I multiply (.05) x (0.3774) and get 0.01887. For the third one, I multiply (0.0025) x ( 0.397) and I get 0.00099. What am I doing wrong?

@akshayabalakrishnan8701 6 лет назад

I defo needed this!!! Thx u 🌟🌟🌟

@Kingofmolotov 6 лет назад

Hands down the best series in the whole CrashCourse catalog!

@shreyalahiry3900 6 лет назад

This got posted THE DAY AFTER MY STATS FINAL 😭😭😫

@verdatum 6 лет назад

Mr. Stark...Mr. Stark, I don't feel so good. I don't know what's happening...I..I haven't covered binomial distribution in STAT yet...I don't wanna go...Please, I don't wanna go...I'm sorry...

@NeoGee 6 лет назад

Too soon! *sob*

@ps374249 6 лет назад

Screw you! I'm already crying over taking the AP Stat test today, I don't need your help!

@obalolaNig 6 лет назад

hahahahahaha! don't worry.'the snap' will hopefully affect your Maths professor.

@ShiiFT12 5 лет назад

Oh no! Someone, quickly! What's the probability that everything will turn out alright?!?!?!

@mwinsanerocka 6 лет назад

Thx, helped a lot. Will you guys do a video about the Normal Distribution too?

@rchuso 6 лет назад

Spend more time with equations, not less. Remember the intelligent people who've spent so much time determining what equations properly represent the data.

@Khether0001 6 лет назад

when you showed the zombicide minis I'd hoped you would tackle which weapon has the better chance of hitting (throwing 3 dice that hit on 4 or more or 5 dice on 5+), which would be a wonderful and insanely fun example on statistics... ow man...

@cameronzulu7064 6 лет назад

Thanks for this!

@colorblindphotographer 4 года назад

Ironic learning about binomial distribution during the Covid-19 pandemic. Crazy

@ishamathstea9019 4 года назад

Hye Mark, Jz posted about how to find PROBABILITY using BINOMIAL DISTRIBUTION.... I hope it's helpful..... Would love to hear some feed back too

@HorzaPanda 6 лет назад

Toast problem. You forgot to factor in the chance of receiving 0 shocks, 0.8^5, or 33%, so there is a ~74% chance of being shocked 1 time or less. Much better odds You did specify once and only once, but I feel one or less is what you'd actually be interested in XD (Edit: Ah, it's for illustration of the later content. Fair)

@HorzaPanda 6 лет назад

I would also assume if there were 1 zombie in that crowd of 20 outside the window then there would quickly be 20, or 1 zombie and all the people fled >_> But nice example XD

@georgekutubidze3316 5 лет назад

wonderful! thank you so much

@maxberre 6 лет назад

Brilliant!

@greyareaRK1 6 лет назад

The probability of getting a flat during a zombie apocalypse?

@ruthhh.m 6 лет назад

This video is actually so helpful and clarifying, but it would have been lifesaving last semester when I was struggling through Prob and Stats😭 why me...

@JahDale 6 лет назад

great talk

@lorir1143 6 лет назад

welp, I just took a hard math test today. . .and this just uploaded?

@brookeamm7655 6 лет назад

same here!

@lorir1143 6 лет назад

WildernessCraft what for, mine was algebra, it was the end of coarse or eoc test.

@anti_MATT_er 6 лет назад

I literally had my Data Analysis final today and Binomial Distribution was one of the problems.

@brookeamm7655 6 лет назад

mine was Algebra 2 Honors, it was on binomial distribution and some other statistics stuff

@roneyandrade6287 6 лет назад

calc 3?

@florentinosanchez3969 4 месяца назад

BEST VIDEO EVER!!!

@sumayya4587 4 года назад

never been a better time to study this 8:22

@gloystar 4 года назад

Well, I must say I liked the zombies example.

@diegofernandorueda9160 6 лет назад

I doing a study analyzing some variables how they change in time. but I wanted to ask. how can you calculate the probability of a failure of a car based on the temperature in the crease if its motor, or the water or the oil?

@helenalilianavaquera5599 6 лет назад

I'm lovin' the series,but could you hurry it up a little? I have my AP Statistics exam next week

@nandaveerum4399 6 лет назад

Please make videos on Mechanical engineering related topics too.

@kathyh8047 6 лет назад

For the purpose of checking the probability of getting shocked only once, it might also be worth taking into account the probability of _not_ getting shocked - that is, how likely am I to get shocked one time *at most*?

@APaleDot 6 лет назад

Wait, I'm confused about the Bernoulli Distributions. If the exponents are either 0 or 1, and the probabilities are just the failure and success rate, how are this different from just multiplying normal probabilities? If you already have the rate of failure and the rate of success, why not just use those? Are there cases where the exponents can be fractional? Or where having more than two outcomes somehow makes the Bernoulli Distribution more effective?

@michaelbrynda1603 5 лет назад

6:57 It seems like the math is wrong for the zombie prob. Shouldn't Binom(20,1)=.01887 not .3774 and Binom(20,2)=.00099 not .1887?

@ArbJunkAgeG 5 лет назад

5:30 should've continued to finish the example with the toaster problem; instead of introducing another problem.

@Ensorcle 6 лет назад

b-b-b-b-bayes! Gotta cover that prior!

@Gemoron 6 лет назад

Your toaster example sadly has one logic error. It shoul mean "Only one shock or less" so the chance of not beeing shocked should be added as well (0.8^5 =~32%) which would leave the chance of one or less shocks at ~74%

@ramonsimms3553 6 лет назад

don't forget to calculate the value of the binomial coefficient (n-choose-k) in your binomial distribution formula!! for example the coefficient (5C3 or 5-choose-3) is 5!/3!*(5-3)! = 5!/3!*2! = 5*4*3*2*1/(3*2*1)*(2*1) = 10 in the problem about getting 3 girls when you have 5 kids.

@Danilego 5 лет назад

Idk why so many zombies but combinatorics is pretty fun!

@markelmy5933 6 лет назад

Wheres #16? Watched number 15 .. above but then skip/jump to 17? Can you provide a link please?

@alexschalk5439 4 года назад

You should have mentioned the odds of not getting shocked at all

@jasestrel89 4 года назад

Can anyone please tell me why when I run the numbers on my TI-83, is shows that 0.1887 (18%) is the result for the probability of encountering 1 zombie instead of the aforementioned 37%? Or am I plugging the numbers in wrong? Are my calculator setting off? I plugged it in this format for probability of 0 zombies like this and got the right answer: (0.05)^0 * (0.95)^20 = 0.3584 or 36%....PLEASE ADVISE!

@yiyiyao7165 4 года назад

more likely to become a zombie than to get coronavirus - woohoo!

@ransom4734 6 лет назад

Hey guys do video on Economy. Love you guys

@lowenzahn3976 6 лет назад

Crash Course Economics does exist. Even with the same host.

@timeaesnyx 6 лет назад

And the economics course made me mad by treating non zero sum games dismissively.

@ShuvamNayak 4 года назад

How did you calculate the 91% figure?

@cosmoinstant 5 лет назад

Is that a good-sized joint he is holding at 1:31

@zanehawkins3457 Год назад

The material is presented in a way that is easily understandable, but the pace is too much. I realize that there is a goal to condense and keep the videos short, but I would prefer the information a little slower. There was a lot of pausing to absorb what was being said with the text on the screen because I was trying to introduce myself to the equations while she was moving on to the next bit. It felt like she was talking very fast. Still well done, just it jumps along so fast

@justicar347 6 лет назад

Did anyone else check the math on the possibility of a zombie in the crowd? I kept getting the answer for the second equation ( possible zombies) for the third equation (2 possible zombies). I entered it every way I could think into my calculator and it would not match up.

@matthewmortimer8251 6 лет назад

how do you use the bionomial distribution when it says you may use: p^3+ 3p^2q+ 3pq^2+ q^3. rely asap have exam tomorrow

@unodinoi9478 4 года назад

Good stuff to know considering the coronavirus spreading around

@AJoe-ze6go 5 лет назад

Doesn't the chance that one of your friends at 11:00 are infected, but asymptomatic depend on BOTH the infection rate AND the percentage of infected who are asymptomatic? Sounds to me like a conditional probability calculation is needed.

@raw.musician 5 лет назад

It can be explained in much easier way.

@DuluthTW 6 лет назад

I admit, you hadn't piqued my interest until I heard the word Zombies. Great lesson!

@Lolfire 6 лет назад

Last ditch effort for this Statistics 1 A level next Thursday.

@aaronmarks9366 5 лет назад

The Brave Little Toaster!! Omg :,(

@mattabesta 6 лет назад

I feel like you spend way too much effort in this series avoiding numbers and math, anyone voluntarily watching a math series probably isn't so afraid of numbers.

@jazminaguilar9714 5 лет назад

Goldmattress Agreed.

@stereotype3329 5 лет назад

Nah, I'm watching this BECAUSE I'm deathly afraid of numbers.

@rynthorn1551 5 лет назад

That's not true at all. This is a 101-style series so it seems more likely that people are watching because they want to learn to not be "so afraid of numbers" (read: actually learn the basics of this field), not because they are already familiar with it.

@MsAmalie99 5 лет назад

Yes! I would really like some numerical examples! :D Really love this series!

@williamkibler592 4 года назад

Most people learn better if you dont just plug and chug

@asterdan712 5 лет назад

What's that thing at the back at 0:22?

@skoockum 6 лет назад

You had me at equations, then you lost me at zombies. This series seems like it's aimed at the Dora the Explora crowd. I was reeeally hoping to learn some probability, but nearly all you give out are teases to the uninterested.

@jsal7666 4 года назад

is anyone just thinking about how the part at 8:44 has aged badly because of miss rona

@robertofontiglia4148 5 лет назад

1) This has been bugging me for a while now : PUT. PLANT. IN. BOX. PLOT. SHELF. 2) MORE MATHS !

@themonkeymoo 6 лет назад

What about the 30% probability that you are yourself a latent carrier and therefore immune? In that case you would also survive even if all 3 of your friends were also latent carriers

@ps374249 6 лет назад

I just realized her shelves are a bell curve and whisker plots

@DuranmanX 6 лет назад

Except that one zombie can infect other humans, so it may not be just one or two for long

@tessat338 6 лет назад

About Binomial theorem she is teaming with a lot of news.

@HarperGamble 6 лет назад

Is this going to be last video in crash course statistics?

@SteelCheeks 6 лет назад

hey its zombicide models! fun game.

@DarkLink606 7 месяцев назад

Once I fully grasped the concept of binomial distribution, I decided never to vote again.

@joewilson3393 6 лет назад

There is another consideration for the zombie examples, just as a little mental puzzle to consider, not a critique. You used the population as a whole for your sample size on infection rate. However, the population as a whole might not be a good representation for the data. For example, in your blood transfusion. If your friends have been actively fighting zombies a better sample might be all those with frequent exposure to zombies. Using the population as a whole would include people with much less risky exposure. Like you said with the pandemics. The odds of a doctor being exposed during a pandemic would certainly be higher than a more average person.