Probability (part 6) Khan Academy Czech English (auto-generated)

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Teď budou naše problémy s pravděpodobností

now our probability problems will get a

zajímavější.

little bit more interesting so let's say

Řekněme, že mám měšec plný mincí.

I have a bag full of coins so this is my

Toto je můj měšec s mincemi nebo miska.

bag of coins it's my maybe it's a bowl of coins so a

Tady jsou mince.

bunch of coins in there right I didn't

Takto jsem to nakreslil.

need to draw it but I did anyway and

9 z těchto mincí je normálních.

let's say that I know that nine of these coins nine of them are normal so what do

Co tím myslím?

I mean by normal it's just you know

Řekněme, že jde o čtvrťáky a že

let's say they're quarters and they have

mají hlavu a orla. A mají 50% pravděpodobnost,

a heads and a tails and that there's a

že padne hlava a 50% šanci, že padne orel

50% chance of getting a heads or 50% chance of a tails

u kterékoliv z těchto mincí.

if you flip any of those coins and then

Potom mám jednu minci, která má na obou stranách hlavu.

one of the coins is a two-sided head coin two-sided head so essentially no

Jakkoli ji hodíme, vždycky na ní padne

matter what you flip it it's going to be

hlava. Mám měšec. Poslepu

a heads right so I have this bag what I

do něj vložím roku a vytáhnu

want to do is I'm going to you know blindfold myself take stick my hand in

the bag and pick a coin out and then I'm

Pak tou mincí hodím.

going to flip that coin I don't know I'm

going to flip it five times and my

Jaká je pravděpodobnost,

question to you is what is the

že mi pětkrát za sebou padne hlava?

probability that I get all five to be heads so the probability probability that I get five heads 5 out of 5 heads so

Kdykoliv se potkáte s něčím, co neznáte,

whenever you see something unfamiliar it'll always work it's good to do you

pomůže nakreslit strom či upravený pravděpodobnostní

know maybe we'll do a tree or we'll do a

strom nebo něco podobného.

hybrid of a probability tree or

Na začátku experimentu

something else but you say well at the very beginning of this experiment

se něco stalo.

something happens I'm going to pick a

Vytáhnu minci z měšce.

coin out of this bag and so you could

Takže, kolik máme

say that there is a well how many coins

mincí v měšeci?

are there there's ten coins and I have

V měšci je 10 mincí. Mám stejnou pravděpodobnost, že vyberu

an equal probability of picking any one

jakoukoliv z těchto mincí.

of the coins let's say I can't feel

Řekněme, že poslepu nepoznám hlavy ani orly.

whether it's heads or tails

Dělám to v rukavicích.

so I'm not I'm doing it with gloves on right so I can't feel out the two head

Takže nepoznám minci s dvěma hlavami.

sided coin so you take take my word for

Je stejná pravděpodobnost, že vyberu

it there's an equal probability to take

jednu z 10 mincí.

any one of these ten coins right there's

Máme 9 normálních a 1 zvláštní s dvěma hlavami.

nine normal one weird with only with two

Jaká je pravděpodobnost, že vytáhnu normální minci?

heads on it right so what's the probability that I get a normal coin so the probability of a normal well that's

Máme 9 normálních mincí z 10 mincí se stejnou

there are nine normal coins out of the

pravděpodobností, že je vyndám.

ten equally likely coins I could get so

Takže pravděpodobnost normální je 9 z 10.

the probability of a normal is

Máme šanci 9 z 10, že vyndám normální minci.

nine out of ten so there's a nine out of ten chance that this is a normal coin

Budeme tomu říkat jen 'normální.'

this is called that normal and then

Jaká je pak pravděpodobnost, že vyndám

what's the probability that I get a

dvoustrannou minci.

let's call it a 2's two-sided coin I'll

Říkejme jí 2s.

call it 2s well that's just 1 out of 10

Je to 1 z 10. Takže buď se stane první nebo druhá situace.

I'm either going to get this or that I'm

Předpokládám, že neplatí, že bych nevzal nic. Takže máme 1/10 pravděpodobnost, že vyndám 2s minci.

not going to take nothing out of the bag I assume okay so this is 1/10 side chance that I get a two-sided coin right

A potom, jakoukoli minci vytáhnu,

and then whichever coin I get I'm going

hodím pětkrát za sebou.

to flip it five times in a row and I'm

Nebudu zde kreslit strom, protože

not going to do the tree here because

bych měl 32 vláken na každé straně.

the dru you know tree you know you I'd have thirty two nodes on each side but

Mám-li normální, jakou mám

given this given the normal what is now

pravděpodobnost, že hodím 5 za sebou?

the probability of getting five in a row

Zapíši to tak, že pravděpodobnost 5 hlav

and the way I'm going to write that is the probability of five heads or you

nebo 5 hlav z pěti.

know I could have written 5 out of 5

Tato čára nahoru znamená 'při'

heads or whatever and then this upward line this means given given that I have

normální minci.

a normal coin so if I can assume that I

Mám-li normální minci, jaká je pravděpodobnost, že

had a normal coin what are the

pět dalších hodů

probability that my next 5 so I'll say

pět hodů z pěti budou hlavy?

this is 5 out of 5 heads well we figure

Toto je řešení.

that out each time there's a 1/2

Pokaždé je poloviční pravděpodobnost,

probability and and I'm going to do it

že to dokážu 5 krát za sebou v řadě. Takže to bude 1/2 na pátou, to jest 1/32.

five in a row so it's 1/2 to the fifth which equals one over 32

Takže pravděpodobnost, že hodím pět z pěti hlav

so the probability that I get 5 out of 5

na normální minci je 1 ze 32.

heads given a normal coin is 1 out of 32

OK. Jaká je pravděpobonost, že hodím 5 hlav z 5

fair enough well what's the probability what's the probability of 5 out of 5 heads 5 out of 5 heads given the

při oboustranné minci?

two-sided coin and I'm just a just

Teď používám náhodná označení

random notation I'm coming with the

pro tu dvoustrannou minci.

two-sided but this this upward and

Tato vertikální čára

downwards line this vertical line that

znamená 'při.'

means given well that's I'm definitely

Takže mohu hodit minci milionkrát a ve všech

going to get ome I could accurate I could flip this coin a million times and

případech to mohou být hlavy.

all of them are going to be heads so the

pravděpodobnost je 1 z 1.

probability here is 1 out of 1 right I'm

Tady budou vždy hlavy. Na začátku jsem se zeptal,

definitely going to get a heads here so what is the possible what it what are the probabilities of so all I asked initially is what are the what is the

jaká je pravděpodobnost 5 hlav z 5? To se bude rovnat

probability that I get 5 out of 5 heads well this is going to be equal to

--vyměním barvy--

and I will switch colors arbitrarily here just to keep things interested this

To se bude rovnat pravděpodobnosti s jakou získám 5 hlav z 5

is going to be equal to the probability that you get 5 out of 5 heads given let's call that a normal coin give it a

'při' normální minci krát pravděpodobnost,

normal coin times the probability that

že vytáhnu normální minci. Krát pravděpodobnost

you had a normal coin times the

řekněme 'normální.'

probability of let's say normal right

Plus--a tady nemám dost místa--pravděpodobnost,

plus and I'm running a little bit of space the probability that you get 5 out

že vytáhnu 5 hlav z 5 'při' dvouhlavé minci

of 5 heads given the two-sided coin

krát pravděpodobnost, že si vytáhnu dvouhlavou minci.

times the probability that you had the two-sided coin hopefully that makes

Doufám, že o tom přemýšlíte tímto způsobem.

sense and you can kind of think of it in

Jaká je pravděpodobnost tohoto výsledku?

this way you know what is what is the probability of getting to this outcome

Je to pravděpodobnost, že si vyberu normální minci a pak

it is the probability that you picked a normal coin and then given the normal

u normální mince je šance 1 ku 32,

coin there's a 1 in 32 chance that you

a jsem tam. Takže to bude 1 z 32 krát možnost

got there so it'd be 132 times the

že mám normální minci,

chance you get the normal coin so 9 out

což je 9 z 10.

of 10 and what's the probability of

Jaká je pravděpodobnost, že se dostanu sem?

getting here what's the probability that

Jaká je pravděpodobnost, a obecně,

you you you had to and in general in a

ve stromu stačí násobit všechna vlákna, abychom

tree you just have to multiply all of

se dostali k pravděpodobnosti, jak se dostat sem.

the nodes to get to that point to figure

Předchozí videa obsahují vysvětlení

out what's the property of getting there and I think you if you watch the first

tohoto postupu.

few videos it makes sense why that

Jaká je pravděpodobnost tohoto?

happens so what's the probability of

Máme 1/10 šanci, že jsme si vybrali

this well there's a one-tenth chance

dvoustrannou minci.

that you picked the two-sided coin and

Pak je samozřejmě jisté, že všechny hody budou hlava.

then of course then you're guaranteed to get all heads so then this is this is 1

Je to 1 krát 1/10.

1 times 1/10 and all I did here and here

A to, co jsem udělat zde a zde jsou stejné věci jako nahoře.

is the same thing that I wrote up here

Změním barvy. Co je toto? Jaká je pravděpodobnost 5 hlav z 5

let me switch colors so what is so what is this the probability of 5 out of 5

'při' normální minci krát pravděpodobnost normální mince?

heads given a normal coin times the

probability of a normal coin well that's

Toto je pravděpodobnost 5 hlav z 5

just this this is the probability of 5

u normální mince krát pravděpodobnost normální mince.

out of 5 heads given the normal coin times the probability of a normal coin

A to se rovná? 9/320 A pak toto, pravděpodobnost 5 hlav z 5

and this is equal to what 9 over 329 over 320 and then this the probability of 5 out of 5 heads given the two-sided

u dvoustranné mince krát pravděpodobnost

coin times the probability the two-sided

dvoustranné mince.

coin well this is the probability of 5

Toto je pravděpodobnost 5 hlav z 5

out of 5 heads given the two-sided coin

'při' dvoustranné minci, u které je vždy 5 hlav z 5.

you're guaranteed to get 5 out of 5

A pravděpodobnost, že vytáhnu dvoustrannou

and the probability of getting a

minci je 1 z 10.

two-sided coin is 1 out of 10 so 1 out

of 10 this is this so this is equal to

To se rovná 1/10. Takže pravděpodobnost, že vložím ruku do měšce,

110 so my probability of you know just putting my hand in the bag taking out a

vyberu náhodnou minci a hodím ji pět krát

random coin and then flipping it five

a hodím 5 hlav bude rovna toto plus toto.

times and getting all five heads is going to be equal to this Plus this so

Je to 9/320 plus 1/10.

it's nine over 320 plus one over ten but

Převeďme to na 320.

let's make that as a 300 so it's 320

Takže je to 32/320

that's thirty-two over 320 so nine plus

9 plus 32 je 41/320.

32 is 40 1 over 320 so that's

To je zajímavé.

interesting but I'll let me ask you even

Teď se zeptám zajímavější otázku.

a even a more interesting question and and this is something that you know this

Proto je užitečné to, co jsme se již naučili.

this is why I think what we've learned so far is useful what let's let's say

Řekněme, že jsem hodil 5 hlav z 5.

that I do get five out of my minutes so

Takže vím, že mám 5 hlav z 5.

I know that I got 5 out of 5 heads so

Trochu to tady vyčistím.

let me let me clear this up a little bit

Řekněme, že jsem vytáhl

just because I think it's getting over good so let's say that I do get 5 out of

5 heads what is the probability that I

Jaká je pravděpodobnost, že jsem si vytáhl dvoustrannou minci?

picked the two-sided coin so what we're

Takže se ptám, jaká je pravděpodobnost, že

asking is what is the probability that I

jsem si vytáhl dvoustrannou minci

picked the two-sided coin given that I

'při' 5 hlavách z 5?

got 5 out of 5 heads and I hope you

Doufám, že rozumíte otázce.

understand what this what what I'm what

Například se podívejme na

I mean here before we said oh you know like for example I hope you see the

rozdíl mezi tímto a jaká je pravděpodobnost,

different this and what is the

že hodím 5 hlav z 5 u dvoustranné mince.

probability of getting 5 out of 5 heads 5 out of 5 heads given the two-sided coin well this is you know if I know I

Vím-li, že mám-li dvoustrannou minci,

have a two-sided coin I know that the

vím, že pravděpodobnost je 1.

probability is equal to 1 I know that

Vím, že budu mít vždy 5 hlav.

I'm guaranteed to get 5 heads but this

Toto je ale zajímavější.

is a little bit more interesting if I

Jestliže hodím minci pětkrát za sebou a budu mít hlavy,

flip a coin five times in a row and I

řekněme, že mám štěstí

get a bunch of heads I'll say well I either got you know maybe really lucky

s normální minci, nebo jsem házel dvoustrannou mincí.

with a normal coin or I picked the

two-sided coin and I don't know which

Jaká je pravděpodobnost?

one I happened so there's a probability I have to and so and of course the more

Samozřejmě, čím víc hodím hlav,

times you get a heads just intuitively

tím intuitivně vím, řekněme, že mám 100 hlav za sebou.

if I got a hundred heads in a row I'll

Pravděpodobně jsem si vytáhl dvouhlavou minci,

say well I probably picked the two-sided coin or if I you know without actually

a nemusím se na ní ani dívat.

just looking at the coin

Řekněme, že to není přijatelné.

assuming that that's not acceptable you

jestliže mám milion hlav za sebou, pak jsem si docela jist,

know if I got a million heads in a row

že jsem vytáhl dvoustrannou minci, ale nejsem si

we'd be really really sure that we pick

the two-sided coin but we're not

Je určitá pravděpodobnost, že jsem si vybral férovou minci,

completely sure there's some probability that I picked the fair coin and it just

a že prostě hodila milionkrát hlavu za sebou.

happened to get heads a million times in

Takže, jak to vyřešíme?

a row so how do we think about this well

Uděláme to analyticky a já to nakreslím.

I'll do it analytically and I'll draw it

Oba způsoby pak budou pochopitelné.

out and hopefully both of them will make

A udělám to zřejmě v dalším videu.

sense to you and I'll probably have to do it in the next video I'll see you

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