The Binomial Distribution / Binomial Probability Function

[KSunnySideUp]

I'm taking a statistics course right now, and I just wanted to tell you that I learned more from your videos than I did from a week in lectures (3x a week). Thank you so much for explaining to people who don't do this on a daily basis... my professor just can't seem to remember that. He's a math genius, I'm not! So again, thank you!

[osvideosdojoao]

I have tried to solve the problem without the binomial theorem.Only after I realized that the success and failure events don't have the same probability.

[eforty6318]

you are amazing.

[Anameplsszs]

you have really nice handwriting

[littlekina86]

I've been racking my brains over this for a couple of hours, found your video and it all makes sense now! Thank you! :)

[kanitsethi]

if it wasn't for you i would have failed my exam

[patrickJMT]

@kanitsethi hope it went ok for you : )

[Hogzisking]

Just saved me from more hours of stressing over my impending doom in my January module!

[dfjndsk2008]

you are awesome, making videos to help math students like us. you deserve to be on national television and get recognized by everyone!

[patrickJMT]

@dfjndsk2008 glad you like the vids ; ) i am pretty pleased with the views i get on youtube!

[growABC]

I have a stock pick contest question. An infinite number of people enter the contest, to control the numbers lets say we have a sample of 3000 persons. Each person picks a stock that they believe will be a winner over the next six month. WSJ picks 6 people and their 6 stock picks by throwing a dart at the list. The reader whose stock performs the best between January 1 and June 30 wins.

[The4lbanian]

Thank you Patrick

-with Love, Spongebob

[liamreidy7]

you are getting a thumbs up

[princessbeed]

I LOVE YOU. THANK YOU.

[thesammartin]

I fucking love you, you're my hero

[ColenGroover]

Thanks a lot man

[SMITTYNYY100]

I cannot thank you enough for these videos! It's a great thing you're doing by helping so many people by sharing your knowledge too.

Thanks so much..if you ever need anything just let me know.

[Lilbsilk29]

patrickJMT > silly asian professor that i cannot understand

[Na5iR1]

This guy is awesome.

[jwb4291]

Ah excellent, have an exam in this in about an hour...made it much simpler

[killerbee2k]

why does 10 times 6 factorial cancell out?

[kirollos210993]

Hey, patrick man thanks so much for the videos. Hey I have exams in like 3 weeks and i im really confused with probs, could you please do a video or just write explaining to me how to decide on which type of probability to choose when given a problem, e.g. binomial or normal. I really get confused between them and i need someone to compare several problems and tell me why we chose which one and why not the other. Can you please do that for me man? Thanks. Love your videos btw, theyre awesomne!

[unfavoritemartian]

@patrickJMT, you're left handed, no wonder you're a freaking GENIUS!!! :) :D

[unfavoritemartian]

@patrickJMT, thanks so much, love you man. Really. You should receive an award or recognition of some kind.

[Strawbehrray]

Thanks man I totally get this now!!

[patrickJMT]

@Strawbehrray perfect!

[joaquin174]

10 mins ago i was like... shit shit fuckin test!

now im like... fuckin baus!

[jgoldbergl33]

Very helpful

[xxGkSmasher]

hey how old are you? lol u sound quite young and know alot

[patrickJMT]

@xxGkSmasher 13

[nguyentuan1990]

@patrickJMT there is no way you are 13

[patrickJMT]

@nguyentuan1990 12

[tupacsomething69]

which university do u lecture?

[patrickJMT]

@tupacsomething69 Youtube University.

[TwistedLemniscate]

@patrickJMT i.e. one of the best fucking places to go and learn! seriously, there's even some brilliant junior/senior level stuff on here

[markotany]

Thanks man, you've been getting me through Uni. Very clear and concise explanations, appreciate it!

[whirlydirly]

now that I've seen this, my probability of success in my upcoming exam has increased exponentially :)

[TheImpressionable]

Thank you patrick for your help. As a deaf university student I appreciate the fact you write everything you say. I think that helps non-auditory learners too, even those that can hear. Thanks again.

[PRO73C7OR]

This may sound like a stupid question, but i have to ask it. Why does 10 over 6 factorial cancel and make the numerator 10*9*8*7?

[CrackHeadForLife420]

@PRO73C7OR I can probably take this one.

10!=10*9*8*7*6*5*4*3*2*1

6!=6*5*4*3*2*1

the 6,5,4,3,2,1 (the one is optional, do with it what you will) all cancel out, just via simple algebra theory. You're left with nothing (a one) in the denominator and the 10*9*8*7 in the numerator. Just look up factorials.

[derekagamboa]

thanks for the video man, it really helped!

[FXIX]

I should use 3D TV to watch this

[BelialMadHatter]

4 Class periods.

We spent 4 class periods on this...

I understood NONE of it.

Less then 7 minutes of video and I understand it all now.

Really?

Love you. Much thanks.

[rockboy679]

I got a little lost when you started to plug in the numbers for n!/(n-r)!r!

What does the *** r *** represent in the equation?

[LolitaLaces]

@rockboy679 This might be a bit late, but r represents the number of "successes" you want.

For example, the question wanted 4 correct answers (4 successes) and so,

10!/(10 - 4)!4!

But for me, I just use my calculator and key in 10C4 (given that you have a scientific calculator).

So yeah. =)

[dizzychicken1]

Up all night trying reading through my lecture slide print out on this makes no sense. But 6:45 of good explanation now i do. Some lecturers are just shit...

[venonat7]

You are awesome!

[michaelreina2007]

You, my friend, just saved my grade!!!!

Thank you!

[tylertrippy]

r is the same as x?

[awesdaws]

Thank you soooo much! This has helped me see where I'm going wrong.

[Marksman230591]

Those 6-and-a-half minutes helped me learn about binomial distributions better than the 40 minutes I was given in college. You know what? Fuck it, I'm just gonna use YouTube as my teacher now :)

[patrickJMT]

@Marksman230591 youtube is not a person. patrickjmt is though.

[Stavzilla125]

weird watching a lefty

[happy2bebuddylee]

Your videos are a tremendous help! I have taken statistics classes about 4 different times and this is the first time I actually "GET" it. Please keep up this amazing public service!

[Blindedinchains1]

your amazing i understand things immediately here you leave me staring at the pc... what is the magic formula you use to make people understand... you should go in politics hehehe.. Great keep it up really appreciate your work thanks

[patrickJMT]

@Blindedinchains1 hahah, politics: never! plus, my checkered past would come out to haunt me

[fabscorer]

You Are The Best !!!

I Do Additional Maths In Year 11 (Because I Did My GCSE A Year Early)

You Are Maths !!!

[drunkfro187]

im so confused...

[redrextj]

What happened to the (10-4)! on the denominator?

[staind2523]

@redrextj It got canceled with the 10! in the numerator. 10!/6! is just 10*9*8*7, which is what he was doing. Hope that helps!

[LadyTomiko]

This video is very helpful for the final exam Im studying for. Thank you so much. But I'm having trouble understanding why you crossed out the 9 and it become a 3 and crossed out the other numbers has well, why did the answer to that step become 210.

[ActSciBlink]

Thank you patrick for your help. As a blind university student I appreciate the fact you read everything you write. I think that helps non-visual learners too, even those that can see. Thanks again.

[patrickJMT]

@ActSciBlink never thought about that... but i do try to read it all i guess. thanks for pointing that out, this is something i will keep in mind when i make future videos!

[kiddo108]

thank you so much .tomorrow is our final exaam for Stat and you video helped me a lot : D

[chiva94]

gracias

[neiche146]

thank you!

[samiirsaad]

Thanks man, that was really helpful.

[MegaMcSpicyyy]

i have a qn.. why is 10 factorial only 10 x 9 x 8 x 7?

[drummerrrpb]

@MegaMcSpicyyy its because the 6! cancels out the rest so it is actually:

10x9x8x7x6x5x4x3x2x1 over 6x5x4x3x2x1 so he just cancelled out the 6! and got left with what you have shown

[MegaMcSpicyyy]

@drummerrrpb i see .thanks man :)

[patrickJMT]

@drummerrrpb thanks for answering!

[RandomDirectors]

What do I do when they ask me things like... what is the probability of getting at least 4 correct.

Which would include 45678910 do I work out all of them and add them up?

Is their a quicker way?

[Xanthosis012]

Question: what if they ask to find P(failures) and P(success) when they given the probability of the outcome and the 'x' ?

[MarcusClayman]

Thank you good sir, videos like this make me wish there were independent studies for lower level classes. I could learn so much so much faster.

[retry4581]

thanks a million. big stats cram sesh. these will help.

[LateAgainGerald]

what about if it was AT LEAST 4 correct answers? =(

[LateAgainGerald]

what about if it was AT LEAST 4 correct answers? =(

[jamesbalboa24]

Cheers from UCLA. Your helping me out tons. My professor has a crazy accent and in don't understand her. Thanks for the help!

[kmringel63]

you explain things very well but you need to move your hand a little while you're writing.i can't see

[gooseaford]

how do you change it if the question is at least 4 correct?

[Zackwithamy]

@patrickJMT You are my hero! A god amongst men! You're helping me all the way down in South Africa!

[patrickJMT]

@Zackwithamy nice! that is a ways away from here

[Alnasrlina]

@Zackwithamy May blessings fall upon your name patrickJMT.. From Malaysia!

[roozterchick]

Omg! Thank you for posting this :D

I have a test tmrrow and my TI-83 Plus calc broke :(

Able to borrowed TI 85 but it doesnt have the VARS/ distribution function .. huhu!

Thank you really cause our teacher didnt go over doing this since everyone can just do it thru VARS..

[muzammilali007]

Lol this reminded me of my engineering exam in which I used probability to answer my Integrated Circuit MCQ.

[jwmcmac]

If Permutation is simply the Multiplication Property of probability . . . then what is Combinatinos in this regard ? . . . and thoughts that would be as simple ?

Thanks for all you do . . . GOD Bless you.

[pokkagossip]

your videos just save my life ! ... Thanks so much ! ;)

[zlatanwb]

good video mehn really helps

[calicollege10]

Viewing this video has helped me with my binomial distribution problems. Where was this site when I was in Trig.

[patrickJMT]

@calicollege10 probably sitting here like it is now

[sjsawyer]

I love you ~ * <3 * ~

[shanequilly]

@sjsawyer i'm nervous about my test monday but i'm gonna eat sleep and shit his videos till i pass this class and when i pass i am going to have a drink in your honor!!!

[norhayla]

thanks a lot for this..i hope u also posted a gamma distribution,exponential and chi-square..it seems so hard w/ all the parameters and whatsoever..haha..pls...i want to learn those..thanks!!

[norhayla]

thanks a lot for this..i hope u also posted a gamma distribution,exponential and chi-square..it seems so hard w/ all the parameters and whatsoever..haha..pls...i want to learn those..thanks!!

[TonySRF]

thankyou so much for this!! i have my stats exam tomorrow, and now i can feel confident about this chapter :)

[TonySRF]

thankyou so much for this!! i have my stats exam tomorrow, and now i can feel confident about this chapter :)

[xSebas6089x]

u are the man , thank you so much

[iGlompsh]

I have my stats paper in two hours time, and to not know anything about these distributions I'm doomed T.T Thanks for showing me the basis of it though, I'm sure I'll work out the rest.

[yabangulum]

i love your way of teaching.... THANK YOU SO MUCH....

[Rolexkamei]

how does (1/5)= .0016

[MrJesterr]

@Rolexkamei (1/5)^4 = 1.6 x 10 ^-3 which is 0.0016.

He just combined the steps instead of finding 1/5, then raising it to the fourth.

[fascist27]

MR Patrick can you please tell me when do we approximate binomial to normal and poisson to normal.i mean what are the conditions do switch over these distributions

[midotheboss1]

the q in the general formula should be p complement because there can be more than 2 possible out come .like in the dice the probability of getting a 3 two times in tossing the dice four times would be =4c2 (1/6)^2 *(5/6)^2

[bmacdonal21]

You break everything down and make much more sense of things than my professor does. Thank you!

[Ulquiorrapwns]

thank you. this is very helpful for my upcoming AP stats exam. Thank you!

[trisky1234]

I dont understand why 10! would be 10x9x8x7 and not 10x9x8x7x6x5x4x3x2x1..?

[trisky1234]

@trisky1234 Nevermind, I confused this with the (X = k) = (n! k!) p^k (1-P)^n-k function!

[nifsprite]

that's because he canceled everything in mind and right down! that's simple and u can try urself on the paper

[OdyOwnz]

because 10! is divided by 6! and 6! is 6x5x4x3x2x1 and that cancels out so you're left with 10x9x8x7

[trisky1234]

Thank you :)

[macrory07]

Absolute Legend sir!!!!

[ajetha786]

why don't you just use NcR function?

[IglooGirl1]

because some people (like myself) aren't allowed scientific calculators in our exams :(. Cruel isn't it?

[patrickJMT]

it is good for you!

[IglooGirl1]

lol, you're funny ;) Seriously though, i've never gotten better than a C+ in high school math & after watching this video a few times, i GOT it :) it clicked! TY SOOO MUCH!!!

[xxveskoxxbg]

@patrickJMT not good for the final grade

[fazekaslaszlo]

@IglooGirl1 at my university we are not allowed to use calculators at all during maths exams!

[IglooGirl1]

@fazekaslaszlo i think that's just horrible!  ;) but I am of a non-math mind, so i'm a bit bias ;)

[fazekaslaszlo]

@IglooGirl1

At my university we are not allowed to use calculators at all during maths exams!

Great videos, I really appreciate the effort!

[funkflexstar]

Great video, thanks a ton!!!!

[katydo1]

I learned more from him than my math professor!

[TonySRF]

@katydo1

same!!! our teacher was new this year, straight out of uni...

not very helpful lol

[uhohhoe]

how do you type all that into a calculator?

[nikola1tesla]

awesome

[mccuesharon]

I have a simple calculator and there is a " x!" key that I use.

[mariajrn]

this is great

[mycelthedudex]

You roooock dude.....tnx a lot

[jars121]

Great video! Quick question, if you wanted to know the probability of getting AT LEAST 4 out of 10 questions correct, do you have to do P(4) + P(5) + P(6) + ... + P(10)? That seems like a pretty long process?

Cheers

[patrickJMT]

yes, or you could do:

1 - [ P(0) + ... + P(3)]

but still tedious!

many stats books have tables in the back so that you do not have to compute them, but rather just read the values off so that it all goes a bit faster

[jars121]

Ahhh no worries. Cheers mate!

[mahlerite]

If there are 10 questions, and X denotes the number of questions you get correct, another way of saying P(X ≥ 4) is P(X = 4) or P(X = 5) or . . . or P(X = 10). Hence, there is a union, as opposed to an intersection, of 7 outcomes that compose the single event that you will get between 4 and 10 questions correct, inclusively.

CONTINUED . . .

[mahlerite]

. . . CONTINUED

Events that include the word "or," such as this one, tend to imply that you must add the probabilities of the outcomes, whereas events that include the word "and" tend to suggest that you must multiply the probabilities of the outcomes, hence the multiplication rule.

[MrRiemannCalculator]

ARGGGHHH! I wish I was as awesome as you.

P.S Does the success, failure thing mean that there can only be two outcomes or can there be multiple ones?

Mr. RiemannCalculator

[patrickJMT]

yes, for a binomial distribution, there can only be two outcomes

[anonymous2431]

you are awsome

[FunkMynkey]

Thanks soooo much, Ive just begun to brick it about my Add Maths exam tomorrow, this help me a lot

[love4piano82]

Wow, I use this formula for coin flip probabilities, but had no idea you can use for mulitple choice exam probabilities. Thanks a lot for sharing your insight!

[3CROWNS1991]

thanks, explained quite nicelty :)

[balahura1182]

thanks for ur video it really hekped me a lot! Im taking up my master's degree and i have a report on this... thanks.

do u have a video about pearson correlation? it would be a big help for me too.

[mfnjc]

Could you use this to calculate the probability that a basketball player will make a certain number of free throws in succession.

[patrickJMT]

yes

[murray4life57]

thanks :) studying for CST may 18

[patrickJMT]

good luck! : )

[1234funsies]

go math!!! i watch these videos and think i get cleverer. is it true? probably not. But yay for your math genius

[patrickJMT]

hopefully they do not make you less clever at least : )

[pabloMTv]

:) thanks

[patrickJMT]

no problem!! : )

[Scampern]

Nice video. I love em. I use them to frequently in my economics studying, cause math is not my strongest skill.. How about likelyhood for 4 or more correct answers? How is that computed?

[patrickJMT]

you could either find: the probability of getting exactly 4 + the probability of getting exactly 5 + the probability..... etc..

or you can use P(A) + P(Not A) = 1

so you could instead find: 1 - P( getting 3 or less correct)

which would be easier to compute