Coin flipping probability | Probability and Statistics | Khan Academy

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In this video, we' ll explore the probability of getting at least one heads in multiple flips of a fair coin.
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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!
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[@walid562]

I wish I knew what you were talking about, guess I'm just too dumb..

[@carnosinehobs7759]

Hey Sami, first off, no pity comments, for there is none to receive on the internet, and secondly, you're wrong. It will take hard work and dedication to learning content that is difficult for you to understand, but unless you have been diagnosed with a mental handicap by a medical professional, never doubt that you can learn this content. Also, how are you doing nine years later?

[@alderickanthonynolasco1026]

HAHAA ALWAYS BE A DUMB

[@afaqahmed7674]

Same

[@ExplainicatorStudios]

You are not too dumb! The trick is to start with the building blocks first - watch his videos on basic probability first. Then watch a video on compound probability. If you build up to it, this will make sense. He has sooo many videos - it would be great if each video told you what you should have watched before. You can do it 👍🏼

[@alidanish2884]

Attention Seaker Spotted

[@uvitis13]

You can make it even easier. For 10 flips there are 2^10 possible combinations, because we got only 2 outcomes H or T. 2^10 = 1024 and there is only one case where we get all T. So to get at least 1 H in 10 flips: 1024 - 1 / 1024 = 99.9%

[@Ghost-bv1bp]

But where you get the 1024 from

[@dingdong3021]

@@Ghost-bv1bp 2^10

[@dingdong3021]

Yes thats easier. But for beginners what he did is the best.

[@ashwins4776]

That's permutation...

[@あのカワイいちご]

Am i dumb that i dont understand not even a bit of this?

[@kenufak]

Albert Einstein once said: “If I had an hour to save the world I would spend 59 minutes defining the problem and one minute finding solutions” This video is about this attitude.

[@devvanbutler2758]

Mikhail tal once said" I lead my opponents into a deep dark room where 2+2=5 and there is no way out" that is what happens to me when my math teacher tries to teach me math.

[@mehrinimtiaz1537]

SAL YOURE THE BESTTTT watching this the night before my 2nd year genetics midterm tyty

[@1123581314618]

What is the probability of getting head on college?

[@spectre4568]

You’d be better off “tail” chasing

[@smitrib]

WOW "at least" problems are so much easier now. They used to be the hardest thing, but now they seem like a piece of cake! THANK YOU SO MUCH

[@jakegrist8487]

This was a really great video. Thank you!

[@43Cubes]

What if it land on the edge?

[@nothingtralala6491]

You just come straight back here and tell me about it OK x

[@aurora-cc6hk]

thank you! i get it now.

[@rumpelstillkills8036]

I remember this. I learned it from here.

[@jggaming2406]

@Market Gains Bot

[@TheMrlolatu]

99 problems, but getting heads ain't one. Boom.

[@josephkreifelsii6596]

( ͡° ͜ʖ ͡°)

[@KokoBhoneMyat]

gonna ruin the chain.

[@saminm1]

i watch your videos because they are entertaining

[@wedaopps820]

Seriously not that hard. Great video bro. Helped a lot

[@_itsnor_1603]

An even easier way is that there is a 1/1024 probability of having all tails so there are 1023 other probabilities left which will have at least 1 heads. so, its a 1023/1024 chance. In any case there is 1/ total possibility of having all tails so you can just subtract 1 from the total probabilities.

[@Niharikajain72828]

Sal is one of the most hardworking men on this planet..Hats off sal

[@madeleinelavelleericsson5670]

thanks a MILLION, i needed thisssss

[@richieharrinarine475]

Thank you! I finally understand it good :)

[@evanrai2062]

Thank you for helping me out😃

[@leyloomar2983]

Than you 😊

[@blxgaming9359]

Thank you

[@oskarkahar7201]

What if it was Bitcoin instead

[@jubaerad2061]

I was kinda stuck there. You saved my time.

[@andrewdixon7894]

This is super useful to know for blackjack :P

[@cleverresponse3311]

I am a professional equities trader and these same concepts are used for trading probabilities. This is my first time on your channel so if your not already a trader perhaps you should look into it. Trading is all about probabilities and really just a numbers game, seems like you might be quit good at it...

[@mohamedmotaz5194]

Sal khan used to be a hedge fund manager, but he sacrificed it to give free education to the whole world.

[@daniloktz]

Nice math there! Does someone know how to code this probabily in R?

[@johnnygonzales3267]

what if i wanted more the 1 head in 10 flips how would i change the equation.

[@11-berkeleyroyyuriahkelly89]

i really cant understand the lesson when it comes to tossing a coin

[@oskarkahar7201]

Cap

[@deanaldridge4277]

One person, one coin, first flip 50/50 chance. What if you change the coin, or the person, or both on the next flip? If both, would that not change the probability back to 50/50?

[@crimsonstrykr]

Nice tutorial - friendo

[@Thecoolconster]

Who is here trying to jam everything in you’re brain😂😂

[@08_benawajavapermadi_xiimi74]

What's the probability of getting 6 of the same sides in a row in 100 coin flips?

[@johndeleonardis901]

This is what I'm trying to find out - the probability of getting X of Tails in a 'run' in Y number of flips.

[@availablehage]

My maths teacher should just play these videos..

[@jennifer86010]

Khan keeps illustrating probabilities based on 3 flips, however his example is using 24 flips, not 3.

[@aashishsah6337]

Sir please See here A fair die is tossed eight times. Probability that on the eight throw a third six is observed is...

[@efrainromero3959]

Does someone has thought that this can be a good betting system for trading? 🤔🤔🤔

[@Sara-ur4mp]

You are amazing!

[@nothingtralala6491]

So are you 😚

[@Niharikajain72828]

Most of the relationships of today have 0.99 probabilty of breaking up one day in future...

[@toxicGD12]

I did it by accident Should've recorded

[@hannahmacintosh1123]

Surely there is a way to do this without writing everything out. There must be formulae for that

[@blognewb]

Salman knows this Title is WAY too suggestive, it's become common knowledge now

[@josephkreifelsii6596]

What are you saying?

[@jean19681]

Good Morning. You said 3 flips where did the 8 counts come from?

[@jnndyx]

bel moun each flip has the probability of 1/2. So (1/2)*(1/2)*(1/2/) is 1/8 because 2*2*2 is 8 >>>> (2*2)=4*2=8

[@jerrytheduck2930]

Most people say that if you flip a coin you have a 50% chance of landing of heads, and a 50% chance of landing on tails. But some peoples say you have a 51:49 chance depending on the side the was upright. Well both of these theory’s are wrong. When flip a coin you have to account for every possible situation that could happen. There are actually 3 possible outcomes of flipping a coin. The first outcome is landing on heads. The second out come is landing of tails. The third outcome of flipping a coin is actually landing on the side, with both head and tails facing sideways. Now as we know this is more rare for this to occur. But how rare? And how does this change the probability of a coin landing on head vs tails.

[@goruloveguy]

😎 loved it

[@observinthelaws]

What if I have 30% of winning, and then in a second separate event, I have 50% chance of winning. What's my probability to win at least once?

[@ashubabbar3322]

What if it is atleast 2 heads in say... 6 flips

[@stevenb4956]

I can't do a flip, so it's impossible.

[@saihemanthpetluri331]

I think 1-p (getting all tails)-p ( getting one head)

[@subb123]

I think it's 57/64

[@bakerworld7310]

Let's say We have a bet I have chance to flip coin #3 times to bet head or tail ( even if it has only 2 sides) How many percent of winning chance I have to bet head or tail?

[@rustyhands5758]

Does anyone know, what's the probability of getting Tails and then Head in a party is???

[@nabman5619]

I am trying to learn this stuff but why do you start talking about it at some advanced level? It would be nice if someone would explain what he is saying.

[@beary605]

First. Nice video!

[@xuanthuy8148]

how many times should a coin land on heads if you flipped it 20 times

[@kuwayt1338]

1/2 x 20 = 10 times

[@Azzucips]

@kenufak sharpening the saw

[@bobhart7067]

Scenario restarts at the beginning each time 50/50

[@nothingtralala6491]

I guessed 19 coins in a row. Kiss my face 😚

[@chessfanaticful]

what is the probability of getting at least 2 heads in 3 flips?

[@islamicreminderswithyahya2585]

William Xu 1/2 or 50%

[@oIdskooI]

8:28

[@brettunger2578]

A lucky friend…..used to wanna see the coin just before flipping…..he’d call the bottom of the coin…if math explained life… why did Einstein mention God….

[@nathuwjohn]

How'd you get that TI-85?

[@imafilipino12]

Consider the probability formula, and explain why it is not possible to have a probability of an event greater than 1. HELP PLS

[@harnoorsodha518]

Because greater than one is over 100%. Let's say flipping a coin. Chance of getting tails cannot be over 100%.

[@availablehage]

Because probability us given in fraction..1 is the highest that can be since the numerator cannot be more than denominator since it includes total outcome

[@logandef1993]

What about edge?

[@anjnamittal4869]

Have you any answer

[@new-knowledge8040]

What are the odds of correctly predicting the outcome of coin flipping 27 times in a row? I was with a friend and his cousin, and I started flipping a coin, slapping the coin on the counter, and then predicting the outcome before removing my hand from covering the coin. I got it right about 12 times in a row. So the cousin said that I must be cheating. So I gave the coin to him and turned around while he did the flipping. When he was ready, I turned around and predicted the outcome. I kept on winning. When the total of correct predictions in a row reached 27, I stopped. The reason I had stopped was because the cousin was making bets and doubling his bet each time. By the time I had reached 27, he owed me a ton of money. So I just laughed it off and said forget about the money. My guess is that it is 1 in 134,217,728 times.

[@aS9dxf869sd]

Not sure if you're gonna read this, but when you're dealing with such an unlikely probability, it's fair to assume a possible cause. Maybe there was a cue that you didn't conciously pick up on, but your intuition did, like the coin having a slightly different noise when dropped on each face, or someone's subtle reactions to the flip. This intuition could've aided you in predicting correctly that much, or maybe it was just pure chance after all. People manage to win the lottery, it's not impossible.

[@obesegaming5964]

Having a hard time in stats trying to find the probability of getting a head.

[@TheUnworthy]

Aaaaaand, it is once again demonstrated that my mind is filthy.

[@TeamJella]

So Gavin is right

[@meshmuhammad6927]

Why you don't write (1/2)^10 instead of writing it 10 times :p

[@geraldcollins7103]

I'm just trying to get either 5 heads or tails in a row. Seems impossible lol

[@Anotherrnumber]

anyone wishing to test themselves on this, work out the probability of not getting a 6 in 3 rolls of a fair 6 sided dice

[@victor_peral]

It’s easier to solve for getting a no 6 in each event and then X 3 . Which is getting any single number except 6 In each event which is 1-p(any number )/ total out come X 3

[@shilatz9341]

Why does he multiply 0.5 *0,5*0,5? It doesnt make sense in my head, why isnt it 2 when there is two posibilyties each time?

[@sergiom3988]

Very simple question: I flip a Coin twice, what's the chance to get the same result twice?

[@jdoe7674]

Do it 3 times it takes a second longer and you know if you get two out of three heads then the answer is unequivocally yes

[@zmonkey111]

50%

[@heybro2305]

Heads or tails, a tossed coin, a metaphor for the uncertainties of life. Of course, the wise player, always cheats

[@axmatra]

0.5*0.5=0.25

[@KevinFrost]

Okay but I'm not going to write 1/2 * 1/2 * 1/2... 5184 times. Is there not a way to write that in a simpler way?

[@sehd3031]

Kevin Frost (1/2)^5184

[@Hannah-du4yg]

Can someone explain to me why the answer to this question is 4? Apple got coins from his pocket which accidentally rolled on the floor. If there were 16 probable outcomes, how many coins fell on the floor? The answer is 4. Just wonder how the answer was gotten.

[@amanjha5916]

considering the coins are similar they can have only two distinct values on both the faces, therefore for each coin tossed we have a total of 2 possible outcomes. Now the tossing of 4 such coins is an independent event therefore the probability = 2 X 2 X 2 X 2 = 16 alternatively you could try mapping the sample space.

[@Ibahz]

salman khan doesn't need to make this video. he has 100% of getting heads

[@MrPickardt]

So what if something has a 18% chance of happening, and you try 2 times, what would your chance of succes be?

[@SNOWBALLGOLH]

baskemtball

[@yasharora3200]

what is the sample space for 10 coins tossed together??

[@saihemanthpetluri331]

2^10 possible outcomes

[@josephkreifelsii6596]

1 - ((1/2)^2)

[@Puh539]

Anyone watching this before exam2020 Thumb up 👍👍👍👍

[@jestbraine4076]

B

[@Elixir_JPGG]

Bills studying this next year

[@oskarkahar7201]

Ratio

[@sheistranquil2913]

my head hurts.

[@just1294]

So if a roulette wheel has hit red 9 times in a row; bet black right? lol. i had a professor tell me every spin/coin flip is independent and the odds are always the same as the first. For example: if you flipped a fair coin 10 times and it landed on tails the first 9 flips then the odds of it landing on heads the 10th flip is still 50%. That is still hard for me to buy, and i'd like to think this video disputes that theory. But maybe not...

[@just1294]

At the end of this video we find that if a fair coin is flipped 10 times there is a 99.9% chance of getting one heads. So are you saying that if 9 flips in a row are tails the 10th flip still only has a 50% chance of being heads? Take it further, what if I had flipped the coin and received 99 tails in a row...the probability goes up astronomically of me receiving a heads in the near future. That's why it is hard for me to wrap my head around the every spin/flip is independent theory.

[@just1294]

For me personally, no that really doesn't clear it up. You say that it is statistacally unlikely to land on heads or tails 10 times in a row....that is exactly what I am saying. If it is statistacally unlikely then why would the 10th flip be a 50/50 chance, I would think if you keep flipping tails every time then the chances go up to land on heads eventually. Why? Because eventually we need to balance back out to 50% of the flips being heads and 50% being tails. Or something close to that. I understand the coin has no idea what i it has been landing on but we can't flip heads forever. I just don't get how you can say something is statistacally unlikely but then say the 10th flip is 50/50 of achieving something statistacally unlikely. Not trying to be hard headed or confuse anyone. Just saying that doesn't seem like a logical statement.

[@just1294]

Finally talked out and have better analyzed the every flip is independent statement. Now have a better understanding of why that is.

[@josephkreifelsii6596]

essentially, you could have done: (1 - (1/2)^10)*100

[@blakerwalk]

@Spyez I'd much rather get tail than head.

[@jeffciaccio2463]

Here is where i start going wrong: What is the the prob of at least 1 H if we flip a coin 3 times? P(1H) + P(2H) + P(3H). 1/2 * 1/2 * 1/2 (Prob of H on 1st * Prob of tails on next 2) + 1/2 * 1/2 * 1/2 (Prob of H on 1st 2 * Prob of tails on next 1) + 1/2 * 1/2 * 1/2. (Prob of all H's) I know I'm missing a combination or permutation somewhere. :(

[@joesimmons90]

Head ON a college? Slim.

[@Mark_Red]

V1

[@funhax7597]

What is the probability of getting a girlfriend?

[@alinapostol2230]

isn't it 0.99% ?

[@josephkreifelsii6596]

No. To make a percent, you move the decimal 2 places to the right. 0.99 becomes 99% 0.5673 becomes 56.7%. 0.6835 becomes 68.4% 0.1648 becomes 16.5%

[@brescalofrio1]

ged prep

[@pauljamieson4409]

Anyone else here because of Achievement Hunter?

[@OfficialSilverMoon]

Turns out both were right

[@mrcv1999]

No because Epic Five Tv who was best prankster in universe

[@Plaincitysims]

My kid doesn’t understand anything about this. Make probability easier

[@thomasp1482]

So why is there an 1-

[@Nobody-Nowhere-Nothing]

Thomas P 100% in decimal is equal to 1. For example, if I say I will give you 100% of 200 dollars that's the same as 200•1. If I say I will give you 108% of 200 dollars, that is the same as 200•1.08. So when we say the probability of getting not all tails is equal to 1-P(TTT), that is the same as 100%- P(TTT)% because there is only one scenario where we get no heads and that is when we have all tails. So 100% minus whatever percentage the probability getting 3 tails is , which is the same as 1-P(TTT), will leave us left with the rest of scenarios. All of them having at least one head.

[@1ns939]

+GreenDemon125 TLDR

[@Nobody-Nowhere-Nothing]

Lucid Abyss Lol alright, it's 1-P(TTT) because the one represents all the scenarios that could happen and the -P(TTT) are all the scenarios where you don't get at least 1 heads which happens only once :P

[@pawanjadhav1108]

Find the probability that it took exactly 10 flips.

[@cantthinkofnameyeah7249]

You have a 1 in million chance. You try a million times. My math says 64 percent chance of winning. Is that correct?

[@obesegaming5964]

What is the probability of me getting a head on youtube Sal?

[@PInk77W1]

What are the odds probability that Computer glitches only help Biden ?

[@stavik96]

Well I guess I must be really unlucky because i failed something with a 33% chance, and then afterwards failed something with a 50% chance 14 times in a row. gg me

[@mightyredstallion]

Remake the video when you're not drunk.

[@laxmikanth8111]

I dont understand iam 6th class my name is A.pranav

[@j_5244]

So can you tell me if this is right? Say I want to know the prob. of having at least one boy if I have __ kids. For one kid, the poss. are b g so 50% For two kids gb bb gg bg so 3/4 For three kids bgb bgg gbg ggb bbg gbb ggg bbb so 7/8