Probability explained | Independent and dependent events | Probability and Statistics | Khan Academy

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We give you an introduction to probability through the example of flipping a quarter and rolling a die.
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Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
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Опубликовано:

9 сен 2024

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Комментарии : 1,1 тыс.

@cognitivedissonance7422 8 лет назад

At this point, i dont even know why I bother going to class. Most things are explained exceptionally well on RU-vid, perfect for self-study, on this channel in particular. You have my eternal gratitude for all your work.

@dhruvdust1812 3 года назад

ive dropped out to study better, im using KA and books to pursue in what I want. I'm telling you, no teacher better than the one online, and if you have any questions regarding the subject that's being taught, there are literal physics graduates in discord channels who can help me out.

@bruuxna 2 года назад

tbh I realized why we are learning stuff at school even though we have loads of that stuff on the net. the thing is, if we don't learn some things by heart, meaning so that we can immediately access the information from our brain, we will always have to search things online, through books, ask others, etc. anyways, my point is: if those people from the past didn't know certain information, they wouldn't be able to quickly draw conclusions from there if that makes sense. like if u know something, then you skip it and move on. but if u have a gigantic problem in front of u and u can't break it down into smaller, easier, and more achievable tasks, ur fcked :)

@moyeonkim 2 года назад

@@bruuxna the problem lies with bad teachers that don't have the abilities to teach their students well enough :)) kmn

@severe1878 2 года назад

@@dhruvdust1812 thats such a bad decision

@guyfierimtwi 2 года назад

@@bruuxna also, the social game.

@mollywright7409 5 лет назад

100% probability that I’m failing my exam

@ddh19454 5 лет назад

We'll fail together

@Melkoh02 5 лет назад

Hey, how was it? Did u fail it?

@Ashes2Ashes_Blush2Blush 4 года назад

Same

@elucidated_ 4 года назад

I’m writing tomorrow and same 😔

@IamKayneISO 4 года назад

if your test up to 50 questions the probability of passing is over 1/26?

@matildamaroino8172 3 года назад

this is what happens when a teacher isn’t constrained by time or syllabus. he’s not rushing to get everything finished in time, he’s able to explain the theory behind it without worrying about finishing a syllabus. so refreshing!

@tonibercha7045 2 года назад

Also when the teachers aren’t forced to teach to some unrelated state exam that puts funding at stake

@SarahPrincessMuwema 7 месяцев назад

True

@pixelated_knight 4 года назад

can we just take a second to notice how on point those drawing skills are WITH A MOUSE?! Edit: it’s a pen.

@joana8615 4 года назад

Yeah... that's not a mouse :) it's a pen

@pixelated_knight 4 года назад

Lo Lo oh that’s explains a lot.

@caydidejesus6027 4 года назад

I think its a mouse actually because of the pointer otherwise with a pen that wouldn't happen xD

@joana8615 4 года назад

@@caydidejesus6027 actually with some tablets it does, i used to have one like that :) Like with the tablets that do not have a screen, they need to have this otherwise you don't know where you're writing/drawing Also there's no way he's writing this easily with a mouse😂

@caydidejesus6027 4 года назад

Lo Lo Lol I’m so confused but ok

@BonGrips 8 лет назад

Khan tends to have a high probability of getting head

@michaelawells8559 8 лет назад

+Bon Grips he will if I pass my math test today lol

@BonGrips 8 лет назад

easy there ramagos

@ousslamouchi2542 8 лет назад

+michaela wells LOL hahahahaa

@superroydude 8 лет назад

Bon Grips XD I'm still watching the video and now I can't stop laughing every time he says head "The probability of getting head(s) is 50%"

@Kamalrsm1 7 лет назад

Bon Grips sub to my channel

@incitemylife 9 лет назад

I have always loved the Khan Academy. He has such a simplistic way of conveying the information. So many teachers out there talk, but have no awareness of how they actually sound. It's plain to them, but mystifying to the students. Thanks for posting!

@day7148 6 лет назад

Is anyone else wondering why people "roll" a die? When you "roll" something, its normally spherical, right? But a die is a cube and doesn't really "roll" It, more or less, tumbles.

@WrathofMath 5 лет назад

Interestingly the "tumble" word in relation to dice has been reserved for objects other than hands that are used to shake and then "roll" the dice, called dice tumblers.

@iblanco1 3 года назад

*mind blown*

@cleopatra6792 3 года назад

Isn’t it dice

@dualitygrief576 3 года назад

@@cleopatra6792 they're both correct

@maryamimran3618 3 года назад

Soooo trueee 😅

@1l_ismael304 4 года назад

i love how he can just write perfectly.

@clerpington_the_fifth Месяц назад

your handwriting must not be that great, haha

@naruhinastarr 8 лет назад

You explain it so much better than my professor! I'm barely hanging onto my borderline grade and we have a test tomorrow. Ugh :(

@calenthebard2051 7 лет назад

How'd you do, buddy?

@naruhinastarr 7 лет назад

+CalenTheDestroyer Unfortunately, I will have to take the course over again... I ended up getting a 69.2% in the class... embarrassing. He wouldn't round it up :( I will take it again though, and hopefully I will get an A, which I desperately need! But thank you for asking :) Hopefully second time is the charm.

@amanc9835 7 лет назад

naruhinastarr then why r u watching the introduction to this?! Go and see strategic practices or something!

@zryxii6935 6 лет назад

did u do better? may the math spirits be with you. Also im a boi

@ethanmccoochie2082 6 лет назад

Profecer im in 7th grade

@darianmonsefan5167 9 лет назад

i have a math test coming up in math class about probability and i just want to say " THANK YOU" because that helped me a lot

@ignacy5509 3 года назад

Well that was six years ago. How did it go?

@asmamanzoor393 3 года назад

@@ignacy5509 Heyy you’re here too u have a test? Cuz I have mine tomorrow and I’m gonna fail 😄

@ignacy5509 3 года назад

@@asmamanzoor393 yup I had that test…

@SandeepM0ttan 11 месяцев назад

So it's Been 8 Years ,How did your Test Go? It's 2024 in 3 months

@joshm8256 3 года назад

In 8 minutes, you just taught me what my stats teacher couldn't teach me in 6 weeks. Thank you.

@thabangnkopane4626 4 года назад

Probabillity Chain effect -Rolling a dice after another dice -I can predict how many possibillity By re-running the following eqquation A=current possibillities D=How many outcomes you'll explore A1×D=A2 A2×D=A3 A3×D=A4 Combination -Rolling 2 dice at the same time -Apply the following formula -N=Number of points and outlying factors in A(B) -N+(N-1)(1/2(N-1)+1/2)=All possible outcomes

@Tirthankar17 6 лет назад

"Probability, a word that you have probably heard a lot."

@mangakhoon4517go 5 месяцев назад

yo are u indian

@ynrlock9315 5 лет назад

I'm in the tenth grade and i have been watching ever since 5th grade.

@iiAngelic 10 лет назад

The more popular KhanAcademy gets the more trolls it brings in.

@lorainesanchez9199 6 лет назад

IKR

@ugh.anyways1361 4 года назад

RoomWithAView Woah 6 years ago?

@theskeptic7713 4 года назад

Well that is one of the main problems of being famous. The more famous you get the more people you get to hate on for no reason.

@kennyMcCormick602 4 года назад

@@theskeptic7713 tru dat

@theo.g1462 4 года назад

@@ugh.anyways1361 Woah 6 months?

@thestandarddeviant7932 3 года назад

It seems so simple after you explain it like that. Sometimes it's nice to go back to the basics.

@basiceric88 8 лет назад

Thanks! I'm going to have to do this tomorrow at school but I had no idea what probability was but this video helped me a ton! I now understand it and it's actually really easy.

@chanelclipston1557 8 лет назад

what grade are you in?

@amanc9835 7 лет назад

Chanel Clipston why does that sound so stalker-like? XD

@Malicio. 6 лет назад

Lol ur done

@ntoiyt 13 лет назад

Thank you so much for all those wonderful lessons. You're definitively a teacher at heart. Great lessons!

@justinlewtp 8 лет назад

What is the probability my exam has a probability question?

@animew2animew435 8 лет назад

99.10000000000000 percent lol jk

@tman400gyki3 8 лет назад

I subed so sub back

@vinikode97 8 лет назад

why you say that? i got curious hahaha

@allanahnoel6870 8 лет назад

how many questions on the test XD

@deeksha611 6 лет назад

Justin Lew less than likely

@zeyadaltair9133 5 лет назад

3) Bello plays cricket for his school team. Last season they won 5 games, lost 7 and drew 4. a) What was his team’s chance of winning a game last year? He says that this year they have a better chance of winning. He estimates that they should have at least a 40% chance of winning their matches. b) If they play the same number of matches this season, how many would you expect Bello’s team to win? c) Halfway through the season Bello’s team has won 4 games, lost 1 and drawn 3. He adds these values to last years results and calculates a new probability of the team winning. win=9 lose=8 draw=7 What did Bello calculate the new probability to be? d) Bello uses this value to estimate the number of matches he will win in the second half of the season. What value did Bello get?

@YVLmolly Месяц назад

Bro knows mathematics, biology, chemistry, and physics😮

@katrrivera 2 года назад

I have a test tomorrow and i've just been staring at the problems hoping I would get it. NOW I DO THANK YOU. Why do we even need math class when we could just watch khan academy???

@stop_simping7845 2 года назад

We all here because of a exam

@Adventurine-yz2qy 4 месяца назад

@HeindsAG 2 месяца назад

I’m actually studying for next year, it’s the summer btw

@Martinmr07 4 года назад

I just donated $20.00 and I wish I could donate more. This channel has helped me so much with math. Thank you!

@nonametoname5974 6 лет назад

Tommorow we have the explanation of this lesson, and i feel that i caught it very easily it opens for me new roads for playing chess diy...etc LIKED IT!

@AKAwafan 7 лет назад

Watching this right before my final lol I think I've got it though, thanks!

@sarbjitdhillon7332 2 года назад

0% chance I will do good on my test

@aroshamustafa6937 3 года назад

him: makes a perfect coin in literally one try, with a proper drawing of the president- me: can't even make a good circle-

@bellacamria2118 6 лет назад

I know I'm certain about one thing... *I'm failing my exam.*

@harshavardhanchaudhari9830 5 лет назад

@moon8546 5 лет назад

Same

@janethtorrez872 5 лет назад

What is the probability of passing your exam? 0%

@kevinceniceros1690 5 лет назад

You had it lucky. I'm the guy taking a fast track course in statistics.

@mibkle 4 года назад

Dis guy is better than my own teacher

@chloef5115 3 года назад

the way he write is immaculate

@cyan1294 5 лет назад

Well, I've seen a person land a quarter on the rim. It's very improbable due to bounce, gravity, wind, or vibrations on the surface if whatever you are throwing the coin on. Its density as well, but if the conditions are right. It's probable.

@lonecolamarine 2 года назад

My motto as of late has been "Thank God, Khan Academy has a video on it."

@frankgarcia423 2 года назад

"What is the probability of getting head?"-Khan Academy

@mangarmathiang4432 4 года назад

Thank you for lessons you given

@meloneylartey6809 Год назад

Great explanation. My facilitator introduced me to Khan Academy and i am loving it. So easy to understand and to reproduce. Thanks for the channel.

@KhalidCantBuild Год назад

wow I have a test tomorrow and this is gonna help a lot

@cutiepew5815 10 лет назад

I understood absolutely everything he said :D

@muddasirahmad 5 лет назад

hey

@yugiohisthebest2819 Год назад

thanks for this my school uses this rarely but i use it a lot

@dunamathcalculadoradeproba1835 6 лет назад

Well done. Probabilities many times are computed based on a data sample, and collecting a sample with high quality data might be the most difficult part.

@danharte6645 3 года назад

Probably the best video explaining probability theory ive listened to so far

@OhLorex 7 лет назад

I used this for my project

@TopCrypto787 2 года назад

Just got the clear idea of probabiliy. I was confused during taking the class on this topic. Thank you so much !! Love you !💓💝

@christophermoran2943 7 лет назад

Thanks Man, I have a test coming up, and this has really helped.

@Tankaddict-6098 Месяц назад

one thing is that, heads and tails are not exacly 50/50. According to standford research, it is known that it is 49/51, this is where 51 is for the side the coin is faced upward.

@Imuetinyanosa 8 лет назад

Thank you soooooo much!! This is FINALLY making sense!! :)

@artistheart9844 8 месяцев назад

your voice. It is so much like the voice of a young man I see in videos on Facebook that are usually about how awesome certain animals are. For instance there was one about wolverines... are you the same guy?

@sophiajuliette612 8 лет назад

Helpful but doesn't explain the difference between dependent and independent events. I would suggest fixing the title.

@bjerk1881 7 лет назад

kimberlyy022 lmfao

@andrewshati1564 6 лет назад

Independent events were events that fit the constraint (flipping a heads or rolling a 1). Dependent events were the total number of equally likely occurring events (two equal sides on the coin or 6 sides for a die). He actually did explain this, however didn't use words like dependent and independent because they're confusing, and also the reason why most students ended up watching his videos. He simplified the theory that's badly taught in schools so more people can learn.

@terris. 6 лет назад

I agree

@al-tahatutorials2499 10 лет назад

thanks a lot you a good teacher i hope your my teacher so i can understand coz i can't understand from my teachers

@ousslamouchi2542 8 лет назад

For those who are Grade 8 and are Asked to simplify their answers after finding the Probability, It's easy.. Let's me give you an Example. Q1 : A person threw a dice, What is the Probability of getting an Even Number? A Dice has 6 total sides/Numbers, How many even Numbers are there from 1 to 6? 3.. Why? (2,4,6 are even) Which means the answer is : 3 ----- 6 TO Simplify it.. Divide 3 and 6 By 3.. Why? Because they both can be divided by 3. So.. 3 Divided by 3 = 1 ------- 6 Divided by 3 = 2 Final answer : 1 -- 2 And that's how you Simplify. xDD

@deeksha611 6 лет назад

Its the day if my math exam and im over here studying for the first time since last year

@keepitjazzy7349 5 лет назад

1:03 "the probability of getting heads" You mean in high school or college? I am confusion

@anonymustypist125 4 года назад

OMGHOSH IMAOOO

@TheAbdallahalmassri 5 лет назад

all respect it is perfect

@MacKenzieDarcey 8 лет назад

yo, this dude is so the voice from the spotify ads. Stop. I can't

@razaepicheese487 8 лет назад

No it's not...?

@jaredsmith1314 6 лет назад

@isabellamufaramu442 6 лет назад

Your wet

@tenzjorden6678 5 лет назад

Bruhghhbh

@davialbuquerque4964 5 лет назад

Are you from Chicago?

@Jdc.3_ 12 лет назад

You're a very smart man, you should be proud of yourself, it help me.

@RobertoAHenderson 9 лет назад

great video

@Hero_of_Recovery 4 месяца назад

I calculated my probability of me subscribing to this channel and it turns out to be 100%!

@amaanpatel9889 5 лет назад

The probability of me getting an A in my test: 0.1/100😥

@krithinjay9377 3 года назад

If probability is in your test there are more chances

@queenbee7786 7 лет назад

Thanks. It was very helpful.

@shashidharshettar3846 3 года назад

Your teaching skills are so easy to follow, thank you

@oliviajordan055G 11 лет назад

this video has helped me so much keep up the videos

@GreighThunda 13 лет назад

Thanks you made this so simple! Just wanted to request if you can make a video on how to predict numbers. Example: 64,16,4,1,__,__. 3,-6,12,-24,__,__. Problems like the two above always stump me on test and quizzes. I would appreciate it if you can explain this your a great teacher!

@TheSpacePlaceYT 2 года назад

Ik it's 10 years later but... this is best done finding the common attribute. In the first problem, it's dividing by 4, and the second one, multiplying by -2.

@mslizzardroscoe9051 9 месяцев назад

@@TheSpacePlaceYTSo what comes after 1 in the first example and what comes after the -24?

@megaidiot95 6 лет назад

i know this is old but thanks. I passed one of my university exams by watching your playlist. Subbed for life.

@rockingamingwiththesahit2145 3 года назад

@@akie1326 Who wanted

@champagnesupernova4081 8 лет назад

i hate my life.

@therealb888 8 лет назад

I am with you here don't worry, we are not alone.

@MrCrashDavi 8 лет назад

+Circus Girl I hate all life. Anyone who doesn't is deluded.

@Khalid_913 8 лет назад

+Living In A Fantasy why

@ivyy11 8 лет назад

+Khalid Abdulkadir Cuz math is cancer \(-.-)/

@LiamsFc 8 лет назад

+Tips 4 Pets yeah fuck u

@azazaelmaher6468 2 года назад

That coin drawing was sick

@triple7marc 8 лет назад

2:15 says "my" but writes "by"

@carolynpotts3846 2 года назад

I hate probability!! Thanks khan academy for trying to help me 😔

@cr4shu 9 лет назад

3:45 I didnt expect to watch a video about getting and giving heads :B

@diddy1971pj 6 лет назад

cr4shu lml

@harryprigg1021 8 лет назад

THIS HELPS ALOT

@jinhoscheeto8830 5 лет назад

I came here to find out the probability of me pulling JUST the bts vocal line if I have 8 more albums to go (from LY series), AND I AM LOST

@jaiden2982 2 года назад

@tagreedghalib6272 Год назад

Khan academy is the best at explaining things. At first i had a problem with this lesson but then i saw his video the best and the most simplistic way of explaining Thank you khan academy

@sophiecoates9122 8 лет назад

Omg this is amazing helped me so much

@davialbuquerque4964 5 лет назад

You`re welcome, Ashley

@axelpinkstone2154 3 года назад

Jesus Loves you and He died on the cross for your sins! He also rose again! Repent and follow the Lord and Saviour Jesus who washes away all sin!

@ferdsmand_ 6 лет назад

This saved my life Thank you :)

@brianknox8439 5 лет назад

When I get out I'm hitting a casino

@SarahPrincessMuwema 7 месяцев назад

I will definitely pass biostatistics with Gods help

@x-xw3fx 6 месяцев назад

you can

@gamergunk2 2 года назад

My coin landed on its side

@sirotan9672 4 месяца назад

Bruh 😂

@vamsikrishnakolli1886 7 лет назад

Thank you for posting this video...

@_PurplePhoenix 6 лет назад

What Is The Probability Khan Will Say Tails?

@78anurag 3 года назад

50% because he will either say Heads or tails

@georgechannyeinlwin6743 3 года назад

POV: You never care about your exam but this is the night before your exam and you are watching this and saying Thanks to Khan Academy for saving your life

@DANKAF 4 года назад

0:59 , its 0 in real life

@rsgandrb 5 лет назад

Khan's handwriting and drawing are so neat, and his explanation of a topic like probability is first class!!!

@aksharaarrepu8780 Год назад

😂

@SaysWhoGaming 8 лет назад

wow crosshair config?

@julia-id3wz 4 года назад

anyone watching this in quarantine?

@soonyoungpark1830 4 года назад

Yep

@justro7839 10 лет назад

i'm in sixth grade and i'm already learning surface area and volume ratio which btw is for HIGH SCHOOL

@justro7839 9 лет назад

i'm sorry but what i mean is that this is pretty difficult for ME i didn't mean to show off

@justro7839 9 лет назад

***** Actually I live in another country and we learn that later soooo just keep your comments to yourself.

@vitinhoguida 9 лет назад

***** Cala a boca seu lixo, fica ai falando mal dos outros achando que é esperto...

@christelleofcourse5180 9 лет назад

Um my sister is in a normal fifth grade class and she's learning surface area and stuff like that too

@justro7839 9 лет назад

Yea but i'm in a foreign country so here it's different

@robinfell 11 лет назад

Khan you are a master we are all so lucky to have you teaching us math!

@KristenPratt-ny6xg Год назад

Never let them know your next move *the coin lands on its side*

@T-Storm Год назад

I never realised i could laugh so hard at a joke, thankyou for making my entire day

@tamimmuftah7250 9 месяцев назад

Bro you made my day

@guyintophat9438 2 года назад

Bro I got a test tomorrow thank you 🙏

@gahgi 8 лет назад

Did anyone else notice in the very beginning he put the dot of the "i" in probability in the wrong place? lol sorry that bugged me....

@tman400gyki3 8 лет назад

poo

@Chinese-tutor 7 месяцев назад

I like this teacher's teaching, very good, I am going to enroll Khan Academy for me and my son.

@j_spa_ic1821 7 лет назад

What are u using to draw on (Software)?

@shamsrahman9980 6 лет назад

Paint

@pranpriwo8347 4 года назад

Undoubtedly, it was such a helpful video on this puzzled probability.Could you please make some videos for finding the probability of a disc ???Since it is so tricky and mazy..

@lokimoki9626 7 лет назад

..... Stop reading the comments, ! Do your math!

@elliottbrice281 7 лет назад

savage

@callmeishmael_S 4 года назад

OMG

@thatloner2831 3 года назад

I'm looking at videos on this subject because my online math class is too boring and I got test tomorrow and the day after. Wish me luck because I'm gonna wing it with basic understanding and zero practice.

@DennisAllums 9 лет назад

At 04:30 You said "If you flip a coin a million times there is at least some chance you get all tales." WTF?

@Mexisio22 9 лет назад

That is 100% correct. There iS SOME chance, for that to happen. Its possibilities are VERY low but there is still a small chance for that to happen. So says the theory of probability.

@DennisAllums 9 лет назад

***** so a million times in a row?

@dbfr2017 9 лет назад

Dennis B The exact chance is (1/2)^1,000,000, which is, a very, very, VERY small chance. So small that it might as well be zero. But it isn't zero.

@DennisAllums 9 лет назад

DBIYBIMWBIU If some give me a 100 billion dollars if I could flip a coin and get 1 million heads or tails in a row, even if they gave me eternal life to do it, it would lose. If they repeated the experiment on every planet in the universe, it still would not happen for even after ten out of ten tails, the probability of the 11th tail in a row would be worse than a heads and the odds would get progressively worst per flip. thus although I know there is still a possibility based on probability; the odds of probability are also repudiating its own law or at least that's how it seems.

@renanbrazparente449 9 лет назад

Dennis B To have an apreciable chance of getting it you would have to try 10000000000000000.....000(three hundred thousand zeros) times. If you get a computer to do it he would take the age of the universe to do this many tries (and still would not get it done). So as you can see there is nothing wrong with probability theory, is just that we humans find it hard to wrap our minds around really small numbers.

@sarahburchfield9379 10 месяцев назад

You sound like my math tutor from Sylvan learning center back in the day! Hope you are doing well, you helped me so much

@chrisgaming9567 3 года назад

Who else is here because of Dream

@stratum7634 3 года назад

My brain hurts help

@happysplash3133 3 года назад

DREAM, YEAH I AM NOW DEAD

@ayalol8 3 года назад

omg...

@user-hz3lg1wf2n 3 года назад

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@zakiyaqub2151 8 лет назад

He didn't talk about the independent and dependent

@davialbuquerque4964 5 лет назад

Yes, he did. Pay attention

@Ak-ib7vb 6 лет назад

Thank you!! You are lifesaver… 2moro was my test of probability and I didn’t even know how to solve probability... again, thank you! Thank you so much!!!