What I want to do in

this video is give you at least a basic

overview of probability. Probability, a word that

you’ve probably heard a lot of, and you are probably a

little bit familiar with it. But hopefully,

this will give you a little deeper understanding. Let’s say that I have

a fair coin over here. And so when I talk

about a fair coin, I mean that it has

an equal chance of landing on one

side or another. So you can maybe view it

as the sides are equal, their weight is the

same on either side. If I flip it in

the air, it’s not more likely to land on

one side or the other. It’s equally likely. And so you have one

side of this coin. So this would be

the heads I guess. Try to draw George Washington. I’ll assume it’s a

quarter of some kind. And the other side, of

course, is the tails. So that is heads. The other side right

over there is tails. And so if I were

to ask you, what is the probability– I’m

going to flip a coin. And I want to know what is the

probability of getting heads. And I could write

that like this– the probability

of getting heads. And you probably, just

based on that question, have a sense of what

probability is asking. It’s asking for some

type of way of getting your hands around an event

that’s fundamentally random. We don’t know whether

it’s heads or tails, but we can start to

describe the chances of it being heads or tails. And we’ll talk about different

ways of describing that. So one way to think

about it, and this is the way that

probability tends to be introduced in textbooks,

is you say, well, look, how many different, equally

likely possibilities are there? So how many equally

likely possibilities. So number of equally–

let me write equally– of equally likely possibilities. And of the number of

equally possibilities, I care about the number that

contain my event right here. So the number of possibilities

that meet my constraint, that meet my conditions. So in the case of the

probability of figuring out heads, what is the number of

equally likely possibilities? Well, there’s only

two possibilities. We’re assuming that the coin

can’t land on its corner and just stand straight up. We’re assuming

that it lands flat. So there’s two

possibilities here, two equally likely

possibilities. You could either get heads,

or you could get tails. And what’s the number

of possibilities that meet my conditions? Well, there’s only one,

the condition of heads. So it’ll be 1/2. So one way to think about it

is the probability of getting heads is equal to 1/2. If I wanted to write

that as a percentage, we know that 1/2 is

the same thing as 50%. Now, another way to think about

or conceptualize probability that will give you

this exact same answer is to say, well, if I were to

run the experiment of flipping a coin– so this flip, you

view this as an experiment. I know this isn’t the kind of

experiment that you’re used to. You know, you normally think an

experiment is doing something in chemistry or physics

or all the rest. But an experiment

is every time you do, you run this random event. So one way to think

about probability is if I were to do this

experiment, an experiment many, many, many times– if

I were to do it 1,000 times or a million times or a billion

times or a trillion times– and the more the better–

what percentage of those would give me

what I care about? What percentage of those

would give me heads? And so another way to think

about this 50% probability of getting heads is if I

were to run this experiment tons of times, if I were

to run this forever, an infinite number of times,

what percentage of those would be heads? You would get this 50%. And you can run that simulation. You can flip a coin. And it’s actually

a fun thing to do. I encourage you to do it. If you take 100 or 200

quarters or pennies, stick them in a big

box, shake the box so you’re kind of simultaneously

flipping all of the coins, and then count how many of

those are going to be heads. And you’re going to see that the

larger the number that you are doing, the more

likely you’re going to get something

really close to 50%. And there’s always some

chance– even if you flipped a coin a million times, there’s

some super-duper small chance that you would get all tails. But the more you

do, the more likely that things are going to

trend towards 50% of them are going to be heads. Now, let’s just apply

these same ideas. And while we’re starting with

probability, at least kind of the basic, this is

probably an easier thing to conceptualize. But a lot of times, this is

actually a helpful one, too, this idea that if you run the

experiment many, many, many, many times, what

percentage of those trials are going to give you

what you’re asking for. In this case, it was heads. Now, let’s do another

very typical example when you first

learn probability. And this is the idea

of rolling a die. So here’s my die

right over here. And of course, you have, you

know, the different sides of the die. So that’s the 1. That’s the 2. And that’s the 3. And what I want to do–

and we know, of course, that there are– and I’m

assuming this is a fair die. And so there are six equally

likely possibilities. When you roll this, you could

get a 1, a 2, a 3, a 4, a 5, or a 6. And they’re all equally likely. So if I were to ask you,

what is the probability given that I’m rolling a fair

die– so the experiment is rolling this fair die, what is

the probability of getting a 1? Well, what are the number of

equally likely possibilities? Well, I have six equally

likely possibilities. And how many of those

meet my conditions? Well, only one of them meets

my condition, that right there. So there is a 1/6

probability of rolling a 1. What is the probability

of rolling a 1 or a 6? Well, once again, there are six

equally likely possibilities for what I can get. There are now two possibilities

that meet my conditions. I could roll a 1 or

I could roll a 6. So now there are

two possibilities that meet my constraints,

my conditions. There is a 1/3 probability

of rolling a 1 or a 6. Now, what is the

probability– and this might seem a little silly

to even ask this question, but I’ll ask it just

to make it clear. What is the probability

of rolling a 2 and a 3? And I’m just talking

about one roll of the die. Well, in any roll of the die,

I can only get a 2 or a 3. I’m not talking about taking

two rolls of this die. So in this situation,

there’s six possibilities, but none of these

possibilities are 2 and a 3. None of these are 2 and a 3. 2 and a 3 cannot exist. On one trial, you cannot get a 2

and a 3 in the same experiment. Getting a 2 and a 3 are

mutually exclusive events. They cannot happen

at the same time. So the probability of

this is actually 0. There’s no way to roll this

normal die and all of a sudden, you get a 2 and a 3, in fact. And I don’t want to confuse

you with that, because it’s kind of abstract and impossible. So let’s cross this

out right over here. Now, what is the probability

of getting an even number? So once again, you have six

equally likely possibilities when I roll that die. And which of these possibilities

meet my conditions, the condition of being even? Well, 2 is even, 4 is

even, and 6 is even. So 3 of the possibilities

meet my conditions, meet my constraints. So this is 1/2. If I roll a die, I

have a 1/2 chance of getting an even number.

I appreciate the laughter that I have gotten from some of these comments. I am so not a math person. Do not understand why things should ever be explained by numbers.

Your a good drawer

8th grade anyone or 7 advanced

1/6 is the probability of getting 2 and 3, because 2 and 3 is 5 lol

When I get out I'm hitting a casino

Independent and dependent events????

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

I've got a question what would be the probability of rolling a die twice, and expecting that I'll get 1 and 3 will the answer still be 2 over 6??

how did he get 50%? =D

All the topics are very interesting and expainned in a simple way thank you so much

예쓰~

I have my GCSE Exams and I suck at physics and maths. Ooohh boy why didn't my teachers teach me the good way. 🙁

Hate to see if you are looking for a while back and forth between the hours I was wondering if you are a couple days ago and I have been a while ago by the way you want to be able to get to see the place of the most important thing to remember to bring the kids to the new York and I have been working on a regular basis and the other side effects.. lol

Wasted 8 minutes waiting for "Independent and dependent events". Probability that Mr.Khan messed up with the video title is equal to 1

at 7.30ish, (where you write 0 over 6), you say "probability" where you are still working out the "possibility". Sure it will result in 0% possibility, but in syntax you where still working on the "possibility".

other then that, nice clean explanation.

What’s the probably taking AP Stats was a terrible idea

You are a great drawer!

basically it result a percent. what chance with statistic we have.

Topic: Newton pepys

Pepys asked Newton Roll a fair dice which is most likely from the following?

A. At least one 6 if you roll it 6 times.

B. At least two 6's if you roll it 12 times.

C. At least three 6's if you roll it 18 times.

In answering this question Great Newton did the calculation right but his intuition was wrong (intuition "C").

His calculation gave the result like P(A)~.66; P(B)~.619;P(C)~.597.

So most likely is A. You said in this video if you flip the coin more and more you will get the (nearly)50% of Head or Tail. but the example I mentioned is also true. But it sounds contradictory to me!

What program did you use to draw?

Math teachers should really watch these videos 😂

Did he say die instaid of dice?

100% probability that I’m failing my exam

thanks mahn😍

never study probability if your exam is tomorrow

meanwhile: here i am

Hi

ill give you a question

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?

please solve it

8:10

Who’s here cause they failed a probability test.

i wish it were 50%, i really do.

watches 1 hour before the quiz1:03 "the probability of getting heads" You mean in high school or college?

I am confusion

The probability of me getting heads (Yes plural) this weekend is 100% (͡ ͡° ͜ つ ͡͡°)

Hey at lest I have an idea

im gonna failEverything is still confusing Q u Q

this helped me soo much! thank youuu khan academy

Hi,

I am trying to build my own youtube channel with my video tutorials, in a different subject than the one you present here.

Could you share with me any suggestions on the hardware & software setup you use to record these videos?

Do you use an E-drawing tablet plugged into your PC?

Do you use an independent mic (eg an USB one)?

Do you then record the whole screen session from your PC, or do you have a specific software that lets you record only the vide itself from the E-drawer?

I like the colour effects you use; could you share the model of the E-drawer tablet you use?

Thanks!

Vitus

At minute 4:30 in the video you concede there is a small, unlikely chance of you flipping heads 100% of the time…how do we calculate that rarity? What are the chances I flipped the coin 5 times and out of those 5, I landed on heads 100% of those 5 times?

They need a video with more difficult examples…

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.

The probalitiy of me failing my state test is 100% but according to khan I have a probaliity of getting head (I’ll admit stolen comment)

What does he use???

Teach me how to draw that perfect coin

I did that I am not kidding

Heh "probability for getting heads"…….

The probability is 16.6666666% times 6 equals 1. How can an infinite number find closure when it meets it's other half?

hehe I have a test about this next week 🥴

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

I’m probability gonna fail my math test tomorrow 😂 Jk thanks for the help

I AM HERE BECAUSE OF THE HOMEWORK

i was studying for my math test and in my head I was like this guy is better than my teacher.

nice

Thank you for this, it was timely and helpful

Dang this was from 2011

thanks Sam L Jackson

Comment

lol……..what?

I have an exam on this and it really helped thanks!

new studys show tht ure 51% percet more likely to get a heads on a cent…

Yeah This Helps A lot 💯

I got a question that many seem to not be able to solve.

I play on a minecraft server where they have a sort of "lottery" called Vote Crates. You can vote for the server and get keys to open. The highest donator rank on the server is available in the crate for 0,2% chance.

Essentially people think that the chance of getting the rank will increase the more times you do it, as a total chance they might not be completely wrong usually. Except they all do the math without considering a very important aspect. The max amount of keys one can get is infinite. How would you do the maths for how many keys would be needed to most likely get the rank. Keep in mind that this is basically a lottery between infinite amount of "lottery numbers". Also this is a computer programmed lottery where the crate resets every try.

independent is not mutually exclusive. Change the title, you're explaining what mutually exclusive is and not what independence is in prob.

The probability to get the head par is 50% because it's totally 100% and 100 divided by 2 is 50. And 50 times 2 is a 100.

The head is not easier or harder probability to get when you throw a coin.

Probably is my favorite math

Guy: 0:59

Girl: 0%

good

If everyday I have a 5% chance of finding a silver coin under my pillow, how likely is it I'd find a coin within 25 days?

How did he draw that quarter so well though?

why 1/3?

What's the probability of me about to fail

Khan Academy: 90% sadly.

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

I used less than 0.0001% of my mind to understand this

Wow!!! I am in 9th grade… Since 6th grade I never understood proablity and I lost interest… Not even math antics can help me…. But you did pretty good and now I recognize How easy proablity is…. All my math teacher's mistake….😁😊

In the forth demension, rolling a 1, 2,3,4,5, and 6 (at the same time) is a 100% possibility…. Think about that for a moment

P = no. Favorable outcomes over total no. Outcomes you could explain that too

I randomly asked a co-worker of mine that I worked with for the 1st time to think of a number between 1 and 100. I said 17, his number was 16. Granted I was off but was close in comparison to how inaccurate I could have been.

What site or channel can I learn more about probability and statistics??? Help me plssss this is my last chance to pass this sem 😭

all respect

it is perfect

Ok lets be real if you stydy math P(Tail) is not even close to 1/2 in any given date. Also realistically P(Head) is very close to zero.

I like your optimism though.

I understand…thank you

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

thank you Khan. I have a test tomorrow and my math teacher doesn't know how to properly educate us

“whats the probability of getting head” lmaoo i laugh way to hard smh got a dirty mind

never knew that Samuel L. Jackson teaches math in YouTube

I don't get ''it''.

"Probability, a word that you PROBABLY have heard a lot of and you are PROBABLY a little bit familiar with…"

What a great teaching style 👍

I scrolled down here just to look for "probability of getting head" jokes

Khan is the best teacher

my teacher taught it to me but

I didn't understand so I consulted it!

Thank U Khan!

2:13 "That meet by conaitions"

I could up my probability by tossing the dice a certain way. Lol 😂😉😉 hahaha

From past experience it is known that a machine if set up correctly 90% of the time, then 95% of good parts are expected but if the machine is not set up correctly then the probability of a good part is only 30%. On a given day the machine is set up and the first component produced was found to be good. What is the probability that the machine is set up correctly?

Solution

it is currently 5:13am on a tuesday. i have school in 3 hours. i have a test on probability in second period. did i postpone actually learning the material in favor of browsing tumblr and drawing? absolutely. am i going to fail? absolutely.

wish me luck.

Ill update what i get on my exam:

Stay tuned

GG

Also his voice is 😻😻👌🏾🙌🏽

this dudes art is so good