Probability (part 1)

[Essencedx]

He gets heads 50% of the time... lucky guy

[corderomichelle]

ur so smart it's ridiculous. ur head it prob to heavy to carry. lmao thank you for all your help - if i pass the GMAT, you're the reason.

[alipaf2002]

V Good.



[tehboxface]

too basic gah..

[flyleb]

I cant believe I havnt subscribed to you yet!

[16professor]

nice



[MrVayden]

240p, we meet again.

[7Adelheid]

You sound like the weather man not a teacher!

[xxelaine952xx]

Thank you so much! I understand it now, compared to my double-class algebra at school.

[DPx111]

probablity of getting heads with a dice =/ ... 0?

[MrCarsandstuff]

In a cool accent yeah baby (if I was American I would make whooping nosies)

[MrCarsandstuff]

Right

[rami1ify]

hey don't make fun of people from the middle east

that is not cool racist bitch

[Alnasrlina]

@rami1ify Stop being such an uptight fool!

[ubentu]

@rami1ify He wasn't making fun of the middle east. He was making fun of public perception.. You have to catch his humor in all of this.. I mean.. the weather.. THE POSITION OF THE MOON?

[MrDaBBaS]

I don't understand this very much, yet I never get them wrong ;)

[vertexgo]

One question about those dices - the points on the sides of a die - all the same volume is being carved out - since there are six carvings on one side while one side only has one carving. This means that every point on the six-side would have to be way flatter so that they all together have the same volume as the carving with the "1". And how does the shape manipulate the fall of the dice - since 6 holes create a different airflow pattern as one does. A dice is everything but symmetrical.

[treefangers]

@ 7:53 I would have thought that the probability of flipping heads with a dice would be 0.

[vi0lat0r84]

@treefangers he is talking about a coin not a dice .. he said it wrong g-money

[Lettime1]

Guys you are not forced to watch the video.For that reason ,I you dont want to watch this ,go ahead and watch what you feel like watching.Do not discourage those who understand this type of teaching...Keep it up Proff ,you are my God of Math !!

[MaraimH]

great example with WMDs :) thanks for posting these!

[TheUnknownFactor]

I just wanted to comment on this. You state that "if the probability of result [x] is 50% and you did this experiment 100 times, the result would be [x] 50 times"- this is incorrect. It's essentially like saying, if I flip a coin twice- one will be head and one will be tails- which simply won't hold true. What is true is that if you did this test an infinite number of times, half would be result [x].

That said, I love this stuff- keep it up.

[roarmaster2]

can i request you do a video or a tutorial on bearings please and fast

[Dalwanaage]

But sadamm Hussien had no Mass destruction weapon. USA government is evil.

[4u2nvdfx]

You said the said "if I'm flipping a dice" then you said "what the probability of flipping heads"... At this point I thought it was a simple mistake anyone could make but then you kept going and called it "a completely fair dice"... I'm not sure what type of dice you have in America but in Australia the probability of flipping a head only occurs when you flip a COIN!

[Dalwanaage]

@4u2nvdfx

Man u don't get it. He is talking about not a dice it self but has got 6 numbers from 1,2,3,4,5 and 6. And these 6 numbers can be divided into two groups namely even and odd numbers 1, 3,5 and 2,4,6. Ok . Look carefully at it now . You have 6 numbers where three of them are even while the other three are odd numbers. So what is the chance of getting and odd or even number after rolling the dice. 50%, so Salman is right.

THanks khanacademy.

[askshbni]

i used to detest probability...i could just not figure out the answer to any question however much i worked hard.....it seemed so ambiguous...but now thanx to ur detailed & lucid explanation...i'm able to catch up...:)

[Examiner86]

Wouldn't 0% probability mean it would not rain, not he is not sure there would be rain?

[MrAlix777]

calmdown

[StealTeal]

I looooooooooooooooooooooove this. SO professional/concise yet approachable. PERFECTION.

If only you had office hours as well! :)

[Iritisaring]

Hey, you must be talking about COIN when you said/wrote P(H-head) not a DIE/DICE.

[pyVlad]

Heh... third in my honors math class, going to AP next year, and I don't get probability. Or at least, it didn't interest me as much... *watches and learns*. I succesfully learned and applied the binomial theorem using khanacdemy, so, awesome :D.

[angie1239218]

Sal , you're just fabulous! The way you teach Math , makes people want to learn more!! God Bless ya Sal!

[FallofDarkness55]

can you please make a playlist on lie groups? thanks.

[malikjunaid1]

at 1:05 I think Your statement is wrong.

I think it should be 100% means he is sure that it will rain tomorrow and 0% means He is sure it will not rain tomorrow.

[jessemaurais]

There's at least one more way to define probability; as a feature of a model conforming to the Kolmogorov axioms.

Also there's a old joke about Bayesians and frequentists. In a coin toss experiment, the Bayesian will sooner expect an unfair coin.

[DawnBreaker1100]

"Let's do a playlist on probability."

[iamdwtf]

P.S. KhanAcademy Rules.

[iamdwtf]

Could anyone help with this problem?

If I flip a coin 'x' times, and alternate between predicting Heads and Tails, is there a way to get the probability that I will guess right/wrong every time. and is it possibly to know how many times something has to be flipped on average to get the prediction. Like if we did an experiment on average how many times would someone have to flip a coin to predict correctly?

If anyone know's how to figure this out would be awesome, if not thanks for your time.

[cuzimaog8]

@iamdwtf the chances of predicting right and wrong is always gonna be 50 percent.No matter how many time u flip a coin the chances of predicting heads or tails is will always result in 50 percent.

[iamdwtf]

@cuzimaog8 Cheers guy, but as you continuing tossing the coin, to correctly predict 'x' many correct in a row the probability decreases, someone explained it to me. basically to get one is a 1 in 2 chance (1/2), but to get two in a row is 1/4, and this continues. See i wanted to know how to predict , getting 5 right in a row and the chances there are 1/32.

[cuzimaog8]

@iamdwtf the chances of predicting right and wrong is always gonna be 50 percent.No matter how many time u flip a coin the chances of predicting heads or tails is will always result in 50 percent.Asumming that person is not a fortune teller than there no possible way of predicting the outcome in a 100 percent manner.

[amusagete]

flav666, the butterfly effect was simply to illustrate the point that it's extremely hard to get two cased in nature that are exactly the same (b/c even one little difference in the environment can affect the case)--so he was actually ON topic the whole time. Maybe to some people, this obvious connection is not obvious?

[flavs666]

Thanks for the effort, but my god this guy lost its focus so fast !!, in a sec can be talking about percentages and then "The butterfly effect ??" haha is hard to pay attention to the actual good info he provides ...

[3333sweetie]

Good teacher. Has a cute, sexy voice too.

[elevin901]

woooh darth vader

[lindorchocolate]

P(people hating on Sal are douches) = 1

[Mogrodu3]

Hah this kind of problem was on the open ended of hspa thank God I saw this before I took the test, thank you

[kiddyflo]

loooooooool dungeonns and dragons dice...

[KillaNaz1]

equally probable, equally probable..Gosfaba, Gosfaba

[KillaNaz1]

equally probable

[Tralmirall]

GREAT movie!!!



[Tralmirall]

GREAT movie!!!

[Manoj4874]

Irritating

[novatodeguitarra]

So every time you get head you reduce your chance of getting head again by half?? Shit, that's a fucked up world we live in, I hope it's not hte same for scoring.

[anticorncob6]

@novatodeguitarra No. The probability of getting heads on a coin 5 times in a row is 1/32. The chances of getting it 6 times is 1/64. The chances of getting heads the sixth time isn't 1/64. It's 1/2; when working out the chances of it happening the sixth time you also have to know that there is a 100% chance of it happening 5 times; it already did. For the sixth time you ignore the first five flips of the coin, and get the answer 1/2, which is the correct answer.

[Romeowasbleeding1]

You're a good man. I would love to know how you profit from this

[MegaGabby15]

good video this is why im so smart.

[MegaMattcar]

question, probability-p(heads of a coin,5 on a die. what is the probability

[anticorncob6]

@MegaMattcar probability = (1/2)*(1/6) = 1/12

doesn't matter whether you flip the coin first or roll the die, it will still be 1/12

[Mawz11]

Quick question. What is the probability of an event with a 50% chance of happening, happening seven times in a row.

[jonjonjon1370]

@Mawz11 I think it's 14%?

[anticorncob6]

@Mawz11 The probability of heads seven times is (50%)^7 = 0.78125%, not 14%

[Mawz11]

@anticorncob6 Yeah, it is. I use that probability in gambling quite often.

[MajorNourhaghighi]

Hi, please let me know, what is the probability of event that: Among 2629 lockers, in 50 rows "one particular locker -number 2134" be targeted by a thief? The other factors that may be considered is that locker 2134 is located in more safe area than others. Thank You

[anticorncob6]

@MajorNourhaghighi Suppose there is a 1/4268 chance of getting locker 2134 (2134*2 = 4268). If 2134 thieves strike, the chances at least one will hit it is:

1 - (4267/4268)^2134 = 39.4%

That's not something to take chances about, so you should either have more lockers or make this one more secure.

[sdrulz]

A truth serum has the property that 90% of the guilty suspects are properly judged while of course 10% guilty suspects are improperly. On the other hand, innocent suspects are misjudged 1% of the time. A suspect was elected from a group of suspects of which only 5% committed a crime and the serum indicates he is guilty. What is the propbability that is he is innocent?

Can someone help please

[Ceonsamea]

@sdrulz 95%. Regardless of what the serum indicated, you said yourself that only 5% are guilty, meaning the other 95% are innocent.

It was a trick question right? :D

[gameofdeath19991]

@sdrulz your question is related to conditional probability wich is coverd in other videos of khan....

the answer is:

1st= 0.95*0.01=0.0095 ( which is just the probability of choosing an innocent person out of the pool and then multiplying the prob of judging him wrongly (guilty))

P( Innocent but judged guilty)= 0.0095 P( guilty and judged guilty)= .05*.90=.0405

P( Guilty)= .05*.90 + 0.0095 =.0545

Now that we know that hes charged guilty, the prob that he is innocent = 0.0095/0.0545= .1743

[TheAkizo]

"If I were conduct this experiment 100 TIMES! What are the chances of me getting head? .. 50%" 8:18 LMAO. I'm so sorry.. I just thought it was funny.. its youtube c'mon.

[TheAkizo]

your voice reminds me so much of charles trippy. OMG.

[HeyyHuda]

" i dont do videos on spelling"

hahah

love this guy!!!!

[gitarania]

Its not opening

says

An error occurred, please try again later.

Same with Probability 3 also.

Can you please fix it?

[bstereopsis]

Dear Sal

Thanks so much for this excellent lessons.

I am writing to request a few video tutorials on programming in Matlab and C++.

I was graduated from medical school and we never used probability, statistics and programming in medical school. But I happened to do research in phsychophysics and I have to learn all of these. You may not imagine how these tutorials were helpful.

Your simple explanation of complicated problems caused me request a play list in programming.

Sincerely

Mohamad



[3s3guero916]

you are that MIT GUY RIGHT?

[korathiren14]

@3s3guero916 Yes Sal graduated from MIT, BS in mathematics and his MBA from Harvard Business School.

[gennkill]

@3s3guero916 ????

[Rawrlor]

I didn't understand the 50%-25% transition.

[vrolok4768]

May God give you serious donations to your bank account for all the trouble you have teaching people worldwide. Thanks!

[jessecax]

amazin

[gennkill]

@jessecax yes i know

[Tenzinpelha]

i fucking hate statistics. i don't get it at all! worst math subject of all time.

[discharmingman]

He said

"So, If I'm flipping a dice and I say, What's the probability of heads" lol

I say things like that too when I'm teaching and the kids correct me. I guess our minds mean one thing but we say other things. At least there's someone listening!

[darkmannin]

"This is a normal die not a Dungeons & Dragons die."

NEEERD. =)

[kprabhakar975]

The examples are correct with different assumptions.

[coremaster22]

quit your bxtchin and let the man teach. if you dont like the examples then dont watch the video you pussies.

[meschool]

@coremaster22 yeah...

[rarchimedes]

The primary example here is just wrong. When a weather man talks about a 50% chance of rain, he means that there is a 50% probability of rain at any point in a designated area, but an almost 100% probability that there will be rain at some point in that same area, regardless of the probability at any given point. They seldom talk about the more general probability of any rain in a given area except in the most general and non-specific terms.

[2CSST2]

I live in Montreal and it happens often that when the wheater man says there is 50% of rain/snow(winter) tomorrow, there is no rain/snow at all in all Montreal. in fact, close to 50% of the times. Maybe if you think about a very large regionbut then what's the point to say the example is wrong, he didn't specify it was for a very large region you're just making it up for, I don't know.. the pleasure of saying he's wrong... no point...don't do that unless it's a real mistake we can care about

[sparkloweb]

@rarchimedes By the NOAA method, IF the reporter is 100% confident it will rain somewhere within an area (e.g., it's already raining), then "50% chance of rain" means he expects 50% of the area to receive rain.

If he's 80% confident (similar to probability) that it will rain somewhere in the area--and, supposing it rains, he expects 62.5% of the whole area to receive rain--then any discrete point in the area also has .8*.625 = 50% chance of rain.

[rarchimedes]

- @sparkloweb The NOAA method aside, weather stations seldom follow such a methodology, giving a single probability that is the likelihood that a particular person in their viewing area will see a drop of rain. Of course, you could interpret it as the probability that it will rain for that percent of the time, though you would probably be wrong. None that I know have given a formula for what they put in their weather casts.

[rarchimedes]

- @sparkloweb The NOAA method aside, weather stations seldom follow such a methodology, giving a single probability that is the likelihood that a particular person in their viewing area will see a drop of rain. Of course, you could interpret it as the probability that it will rain for that percent of the time, though you would probably be wrong. None that I know have given a formula for what they put in their weather casts.

[sergio1020881]

Try to put more complex examples, for eaxmple tom wants to go to the beach and jerry to the mountain in order to figure out where they go they decided that jerry throws the dice twice and sums the numbers, if the sum is greter than the last lotary number they go to the beach if smaller to the mountain, what is the prbability thay go to the beach. na d the mountain.

[anthonychemistry]

I dont think that flipping a coin is affected on the second flip. Flipping a coin is not a conditional probability.. There is no relation on the probability on the second coin from the first coin...Flipping A coin is not a conditional probability....You should at least introduce conditional probability...

[psychodriveskip]

@anthonychemistry

The individual events are independent. The first flip and the second flip have the same 50% chance to land on heads.

However, when taken as a sequence of events, the calculations are correct.

In Khan's words, the experiment hasn't ended until after the second flip.

If it helps, you can count the number of (equally probable) events. In two flips, the set of events is { TT, TH, HT, HH }. From this, you can see that HH only appears once out of 4. That is, 25% of the time.

[366lizar]

no 0¼ of raining chance means that the weather man is sure is not gonna rain. well he belives that

[knighttango]

i took me quite a while couple years ago to understand that the mathematical probability is different from the english probability....

gotta interpret differently

[toxicfreddiemercury]

I believe that the probability if event a happening over the total number of events accounts for biased events.

Thus I believe that the "equally probable events" is the wrong way of thinking of it.

btw: maths is not an opinion ;P

[sliverx78]

i forgot my science txt book, this is my last hope....

[Caymos]

it makes me weak...... why?!

[Fangornmmc]

I deem probability to be: "The likelyhood of a certain event to occur"

[masterchief527]

I hate probability,bcuz I sucked at it,but thx to you I can understand!

[valeagrl1]

dice (two or more dye)

dye (only one dye)

[watts618]

dye noun

1. a colouring material or matter.

2. a liquid containing colouring matter, for imparting a particular hue to cloth, paper, etc.

3. colour or hue, esp. as produced by dyeing.

verb (used with object)

4. to colour or stain; treat with a dye; colour (cloth, hair, etc.) with a substance containing coloring matter: to dye a dress green.

5. to impart (colour) by means of a dye.

The singular of dice is die.

Glass houses? Stones?

[valeagrl1]

I think Khan is an AMAZING teacher. He asked which one is singular/plural. It's how it sounds anyway. Die is singular. You really went to a lot of work; getting a dictionary account & writing this all out just to accuse me of throwing stones instead of seeing that I was just trying to be helpful. Shame on you for being so angry and accusatory. Khan would not have thought of my comment the way you do, so you are just defensive and angry.

[micpax1]

Man... your videos are PERFECT. I wish I had them when I was at school..

[blacksilkblacksilk]

I know perfectly well what you mean, dude. The man`s a life saver. Would have saved me hunderds of hours of frustration. Just GREAT.

have a nice day

silk

;-))

[etraderx11]

just a thought, when they talk about rain they could also refer to a larger area 50% of which WILL get rain and the other 50% WON'T, but they don't know which one WILL and which WON'T

[robertwc82]

what if i rolled the dice for infinity, then the chance of me rolling a 6 is 100% but it becomes a matter of how regularly it occurs.

the chance of life emerging in the universe is 100% because time, matter and energy are infinite and as we know it is a possible event though improbable

[raxxrulez021]

what is the probability of winning in a 6/42 Lottery? hope you can help. thanx

[rimtech]

With a random play your chances are

1 in 42^6

or 1 in 5,489,031,744

However, there are several ways to *select* lottery numbers that will increase your chances of winning. This is done using data from past drawings, and these systems are called "lottery wheels".

[seldemitria]

yay probability is my favorite!!!

[Jackies1979]

you could have mentioned the propensity theory of probability (my favourite): the prob of a die to show 6 is a physical propensity/property of the die just as is its mass, density etc. it solves

almost all the problems of frequentism at least...

what in frequentism would be the probability of the truth of the statements "there are tachyons" or "all ravens are black"....

probability of events only once occurring? 1??

[archangel11b]

flipping a dice? lol u r too smart for your own good

[lumel666]

wow bash the guy who is taking time out of his life to try and pass his knowledge on to you without any obligations..

you sure are smart

[jceja24]

"a guy with a big mustache" . . . Sal is hilarious, great examples.

[starlost1957]

It works when you let it work!!!!!

[MellyJelly14]

i dont get it, someone please help me, im retarded

[dayvandal]

Why don't you get it? Are you deaf?

[pageysLP]

hahaha

[galwholovespie]

(\__/)

(=_=) Z Z Z Z

[buckethead111]

you sound like obama

[gerdie2011]

No he doesn't.

[monimstarfox]

LAMO lol

[nabeelmerchant]

Probablity Sadam Hussain has Wepons of Mass Distruction lol nice phrase.

Anyway you video helped me to understand probablity well thank you

[heyyouwhatever]

datz useless!!!!

[ImTestingSleeping]

Cracked me up too

[5tmatb]

Thank you for your lessons. My kids ages 10 & 12 love listening to your voice. You keep their attention! You are a blessing to our homeschooliing day! Thank you so much!

[akeeva89]

if you "flip a dice" P(H)=0

[Euniceiscool]

xD lol

[santacharlie]

I am a manufacturer & expecting to receive parts from the vendors.

IF the first of the two orders of parts is delivered late by the vendors, I will not be able to deliver the product to the customer on time. My historical record shows all vendors have failed to deliver on time 10 percent of the time. I am using two vendors in hope that at least one of them will deliver parts on time.

What is the PROBABILITY at least one of them will deliver parts on time?

Can someone answer this?

[peacedudepeace]

99%

10%x10%=1% of being late (sorry for the writing i'm french) you have to claculate the probablilety of being unable to do it like if you have 1/3 of having good answer and you do it again and again you have to do 2/3x2/3x2/3... so you will never have a 100% so alwais have it Thx

Have a nice eavning or whaterver it is when you read this

[qingshuione]

thank you ,i like your vedio very much,i found them for a long time ,thank you ,extremly

[floopy312]

Dude im speak spanish and im learning english.. if you could speak more slowly sometimes i could understand you much better and easier... Thanks anyway for all your video posts.. they are excellent...

Remember that your videos can reach any spot in the world and reach most of the 6billion people that live in earth and most of the time this people can just understand plain english.. like me :)

PD: i really love ur explanations about the financial crysis.. i learned a lot

[Mattprole]

Why did people mark this comment down? he has a legitimate request and wasn't malicious at all.

[baynetrain88]

could you tell me the probability of using a 1982 chevrolet camaro car key to unlock a 90's model camaro car door?...to help out, a car lock usually has 6 tumblers which can be arranganged in some number of different ways...I need to figure that part out!

[mgunar]

I second that. How about a video series on Real Analysis or Abstract Algebra? The amount of resources available for "elementary" math is overwhelming. By elementary I mean the math that say, a typical engineer would take: Calculus (I, II,II), ODE, and Linear Algebra. However, beyond this, starting with PDE, and continuing to Analysis and beyond, resources become scarce. These are not "popular" subjects; however, there are those of us who would love to see video lectures of these topics.

[Nanumir]

is there any way you could do a series of videos on abstract algebra? analysis? number theory? etc...?

[volintine]

yup probability

[markerat]

time index 7:58 i am flipping a fair dice whats the probability of getting a heads. I tried flipping a fair dice 100 times and i never got heads or tails. Please explain what i am doing wrong ? Good video series, i love your stuff.

[Blarg247]

The results for any probability experiment depend on the definitions given for each possible result. When flipping a coin, the outcomes of any experiment are generally called either "heads" or "tails." If one were to define the event "heads" as a specific side of a six sided die facing upwards, then, applied to a specific side of a die, the probability for "heads" is 1/6. This is also valid if "tails" were applied in the same way to trials involving a die.

[Blarg247]

It seems that you are simply applying incorrect definitions to the possible outcomes for the type of experiment you are performing.

[LickMyAssWhole]

I roll a die and there is a 1/6 chance for the die to land on 6! Now that is probability.

[CogitoErgoCogitoSum]

Say, hypothetically, I initiated an experiment in which I flipped a coin ten times, and it landed heads up all ten times. Based on your frequentist perspective, in which you analyze historical occurrences, the chances of another head on the eleventh flip is 100%. But that is called a Gambler Fallacy and we all know it isn't true. So where is the problem? The frequentist perspective is obviously incorrect.

[khanacademy]

A "frequentist" wouldn't say that if they have a history of all heads, that the next toss would be heads. A frequentist would say that any toss has a 50% chance of being heads. The wikipedia entry on probability explains this further.

[bean2594]

The frequentist perspective also requires a hypothetically infinite number of trials.

[baybook123]

wow! your a good explainer!

[SumRandomRem]

@CogitoErgoCogitoSum Schooled.

[Shazaaming]

@CogitoErgoCogitoSum

I think the frequentists are able to dodge this circumstance by saying the probability of an event a approaches its true probability as the number of times you perform the experiment approaches infinity. I think they are able to get away with this because we have a pretty intuitive idea of what probability a fair coin should give, so that if you got 1000 head and 0 tails, you would say the coin is not fair...

[panda00303]

Thanks, probability got confusing after a while in school. I think the teacher got lazy, it was near the end of the year.

[beornborg]

Ditto. Yaaay!

[Max11551]

Probability!! Yay! :)