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How smart is /b/?
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How smart is /b/?
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>>700852907
1/2.
>>
0.5
>>
1/3
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>>700853085
>>700853242

fuckwits
>>
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Anyone who says 50%, please kill yourselves or at least never have children.

For a 2 coin flip, there are 4 equally likely outomes:

Tails - Tails

If AT LEAST ONE coin landed heads, only
Tails - Tails
is eliminated, leaving 3 equally likely outcomes, each containing AT LEAST ONE heads coin.

is 1 of those 3

1 of 3

1/3

Pic Related
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1 in 3
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>>700853289
im sorry for you and your education
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>>700853458
haha wtf man, do you have this prepared?
>>
Its 50/50, as it it is for everything on this planet.
It either happens or it does not.
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>>700853695

What do you think?
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>>700853499
>you are education
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>>700853458

exactly
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>>700853458
Nice post, man, concise but at the same time completely explains everything. Well done.
>>
19.735% and 96.432%
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>>700853458
You fail to recognize that in fact 2 probabilities are removed. Assume each column is 1 of the coins. If one coin is already declared heads then both tails scenarios from one column would be removed. Thanks for the jnfographic.
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>>700853499

I'm sorry that your mum didn't abort you
>>
>>700853928

Is bait?
Is bait right?
I can never tell anymore.
>>
To everyone saying it's 1/3, it's actualy 50 : 50. Why you ask?

We flip two coins, but one of them is granted to land HEADS, than we actualy flip only one coin, second can lay on the table with HEADS on it.

So possible outcomes are:
H : T
H : H

Why did I substract T : H?
Because it does not matter which coin landed H.

If we know that once coin will always be heads, than our only question is what will the other land on, it can land heads or tails (50:50).

That's why it's 50%

ps. sorry im little high atm
>>
>>700853458
>For a 2 coin flip, there are 4 equally likely outomes:
>Tails - Tails

these are literally the same, therefore there are only 3 original outcomes. a guaranteed outcome of at least one heads removes "tails - tails"

therefore there are only two outcomes. 50%.
>>
It actually depends on why you are saying "at least one of them is heads".

Are you saying that because you already saw both coins or are you saying that because you saw only the first coin and depending on that coin's value were going to say either:

"At least one of them is heads" or "At least one of them is tails".

Without knowing more about what caused the speaker to say the fact you can't know the probability.
>>
I'm close to the right answer but I've fucked up somewhere and can't see where.

Using conditional probability:

=(1/2)/(3/4)

=4/6

=2/3
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>>700854092
it doesnt say "already" anywhere in the post ya fuckin iiiiiiiiddddiiiiiooootttttt (y)
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>>700854529
Donevin?
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>>700854861
>given that at least one of them landed heads

retard
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>>700852907

50/50

It doesnt matter one landed heads or not

What matters it the chances that new coin has to land on heads....

Which is generally 50%
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>>700852907
P(a|b) = p(a and b)/p(b)
= (1/4) / (1/2) = 1/2
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>>700854817

>>
>>700854583

>these are literally the same, therefore there are only 3 original outcomes

But in statistics, heads on coin 1 and tails on coin 2 is a different result to tails on coin 1 and heads on coin 2. If you toss two coins 1000 times, I can estimate that about 500 will be one heads and one tails, about 250 will be two heads and about 250 will be two tails
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>>700853928
>Being this stupid.
Somehow, trying to point out someone is stupid (Even though they aren't) made you look 2x as stupid.
>>
>>700854817
>>
It's 1/3.

The four equally likely possibilities are:
tails-tails

we know it is not T-T, so it must be one of the three others, hence 1/3.

The mistake that people who think it is 1/2 make is they think that you observe one of the coins, let's say coin A. If you know coin A is H, then yes, the p of B being H is 1/2. However you don't know which of the coin is definitely H, so it is 1/3 as described above.
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>>700855132
Ah, of course.

That makes it (1/4)/(3/4)=1/3.

Thanks

It's worrying that I have a first-year uni stats exam on Friday
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>>700854817
2/3, AKA 1/2...
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>>700855496
>>
math is made up so chances are truely imesurable. 1/3 if youre a nerd.
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>>700855602
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>>700855146

Correct.

Simulation confirms 1/3
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>>700852907
the chance will be zero - it wont happen.
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>>700855843
all that proves is that your CS101 skills made a shitty program to output the outcome you wanted

there was no need to flip coin1 as it's given that it's heads. had you programmed it according to the OP's image, it would have output 50%
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I was stoned through most of middle school but

2 variables right? Each has 1/2 chance of being heads. You need to do some maths and shit so its like 1/2 * 1/2 or something, right?

So pic related we have heads and not heads I forgot what the other thing is. Rgjt? So we take 1/2 and 1/2 then tjetez the possibility of 1 coin being heads and the other being bottoms so then its 1/2 plus 1/2 makes 1.

Right?

So we take 2 coins, add another coin for statistical value and recognition and proof, so when the third coin turns around it proves my theorem:

Coins have 1/2 * 1/2 * 1/3 chance of flipping to heads.

So we have a 1% chance of Hilary being president.
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>>700856578
I'm not sure if you're trolling or just retarded
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>>700856840
you just resort to name calling because you're backed into a corner lel

explain to me why you need to flip coin1 when OP says coin1 is given.
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>>700855843

Nice
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Does nobody really thnk of sides?? so it could be like this, the coins are 3D, the have head, tails, and the fucking side

tail - tail
tail - side

So is it 1/7 or what?
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>>700856578
>there was no need to flip coin1 as it's given that it's heads

Incorrect. No coin is specified, therefore EITHER coin could still be tails, just not both.

This is a conditional probability question.

The condition is that "at least one coin landed heads."

I account for this condition in the program.

If you were good at math and were aware of Bayes' theorem, you'd understand that the answer is 1/3.

NOTE: No coin is FIXED as heads. EITHER coin could be tails. This is where you're making your logic/math error.

1/3

Pic related: Washington University Math department

Source: Slide 4
http://courses.cs.washington.edu/courses/cse312/11wi/slides/04cprob.pdf

I'll wait for you to apologize. Be quick though. I have an omelette in the pan.
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>>700852907
1/2.

>coin that landed heads 100% doesn't matter anymore
>1/2 chance to land on heads
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>>700857462
Check >>700857459
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>>700857459

Probability of either coin landing on its side is negligible, anon.
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>>700857020
Coin 1 isn't given. The stipulation isn't "coin 1 has come up heads" (call this scenario 1), it's "one of the coins has come up heads" (scenario 2), which is a very different situation in statistics.

In scenario 1, we can get the following results:
HH
HT

We see that there are two options, one of which is two heads, so the probability is 1/2, BUT only if our stipulation is "coin 1 has landed heads".

Scenario 2: we get the following possibilities:
HH
HT
TH
TT

Out of these four outcomes, one of them (TT) doesn't have either coin come up heads. Since we KNOW that AT LEAST one of the coins has to come up heads (remember our scenario 2 stipulation), we can ignore this result. This narrows down our outcomes to:
HH
HT
TH
We see that we have three possible outcomes, all of them have at least one coin come up heads, and they all have an equal probability of occurring. So our probability of getting two heads, given that at least one of them (not saying *which* coin) is heads, is 1/3

QED
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>>700857691
But still possible, so there is a chance, we donÂ´t know where are we flipping the coins, or gravity, or nothing at all, we are just talking about posibilities, and side is a possibility
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>>700857462
>NOTE: No coin is FIXED as heads. EITHER coin could be tails.

ONE coin is FIXED as heads. It's literally specified.

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>>700857834

good explanation. Also see image here >>700857462
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>>700857459
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>>700858070
Shit you are right, I forgot about side - side
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>>700858007
>ONE coin is FIXED as heads. It's literally specified.

the question states that
>at least one coin landed heads

not to be confused with
>one coin is fixed as heads

Those are two very different things.

If either coin was fixed as heads, the answer would be 1/2.

If at least 1 coin landed heads, and it could be EITHER coin, then the answer is 1/3.

See the pic here >>700857462
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>>700858007

Damn, you're a dumbass. Are you black or something?
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>>700858342
>Those are two very different things.
There is no world where both coins land tails.
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>>700853458

You are a fucking idiot

You cannot discount a T/T occurrence
Therefore the probability is 1/2
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>>700858342
>>700858541
>muh intellectual
>muh niggers
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>>700853341
ur dumb suk a dik
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>>700855116
this here is the real answer
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>>700858342
>i can't explain why the order matters but IT DOES YOU RETARD REEEE: the post

Who gives a shit. At least one coin is heads. Okay. The other coin flip, whether first or last, will be either heads or tails. Two possibilities. 50%.
>>
>
>>700858739
Fuck off back to .reddit you cunt
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If there are four possible combinations, wouldn't it be 1/4?
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>>700859262
No, because there are only two possibilities.
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>>700853458
H, T is the same as T, H, the order is irrelevant

if you dont believe me, you have to list H, H twice, leaving you with 4 possibilities with equal chance for Heads and Tails

its 50%
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>>700858613
>There is no world where both coins land tails.

Yes, but if 1 coin is FIXED as heads, it can't be tails.

The OP question does not FIX a coin, therefore EITHER coin could be tails, just not both.

3 equally likely outcomes

HH
HT
TH

1/3

>>700859139
>Who gives a shit.

Mathematicians

> At least one coin is heads
Correct

>Two possibilities. 50%.

No. 3 possibilities. See above.

1/3

Also, Bayes' theorem, mutherfuckers.

A = "both coins are heads" {(HH)}
B = "at least one coin is heads" {(HH), (HT), (TH)}

P(A|B) = P(Aâˆ©B)/(P(B)) = (1/4)/(3/4) = 1/3

>>700859262
>If there are four possible combinations, wouldn't it be 1/4?

Yes. But there is a condition specified. At least one coin landed heads, therefore 1 of the 4 is no longer possible (Tails - Tails) so that leaves 3 equally likely outcomes, 1 of which is both Heads.

1/3
>>
You need code to remove any result that doesnt have at least one head, original problem says one head is a given. 50% master race.
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>>700859923
>H, T is the same as T, H, the order is irrelevant

Don't be retarded, anon.

Take two different coins. Let's say, a penny, and a quarter. Each coin has a 50% chance of landing either heads or tails. You flip both coins. What are the possible outcomes? Well, let's see:

penny = heads & quarter = tails
penny = tails & quarter = heads
penny = tails & quarter = tails

4 possible outcomes. Each of them equally likely to occur (25% or 1/4)

Now, surely we can all see how the results,
penny = heads & quarter = tails
and
penny = tails & quarter = heads
are different, right? Surely you can see how these are two distinct, separate and equally probable outcomes, yes?

Great, let's continue. Now, it DOES NOT MATTER if you are using two identical coins. HT & TH are two distinct results, and the probability of at least one of them occuring is TWICE the probability of a HH or TT outcome. Remember HT(1/4) + TH(1/4) = 1/2.

So, since we know that TT can't be the result in the OP question, it is discarded, and we are left with the possible outcomes:

HH (1/4)
HT (1/4)
TH (1/4)

Three equally probable outcomes containing at least one heads, hence the answer = 1/3
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>>700860354
yes, this is why I added the second part, according to your theory, you have to list H, H twice, because either coin could be heads

H, H
T, H
H, T
H, H

= 4 possible outcomes, 2 are Heads, still 50%
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>>700860191
Oh yes, sorry misread the question.
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>>700860735

HH is 1 result, you stupid fuck.

HT is a different result to TH

Here, I drew you a diagram.

1/3
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>>700860991
HT and TH are redundant.

If you think otherwise you're literally room temperature IQ. Did you go to a University?
>>
Should we also make the assumption that the coins can land on their side?
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>>700855843
This code is bad and you should feel bad. Its some good trolling though, if thats what you were going for
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>>700861241
>HT and TH are redundant.

This is what retards actually believe.

Explain to me why you think they are redundant, and I will tell you how you are wrong.
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>>700861332

Sure think, m8.

I get 33% too. Let's see your code, faggot.
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>>700861241
There are two coins. One outcome is that the first coin is head and the second is tails. The other outcome is that the first coin is tails and the other is heads.
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>>700852907
1 in 3
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>>700861743
>There are two coins. One outcome is that the first coin is head and the second is tails. The other outcome is that the first coin is tails and the other is heads.

Correct.

And the final outcome is that the first coin is heads and the second coin is heads.

3 outcomes.

All equally likely.

1 of them is both heads.

1/3
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>>700861241
His math is solid, HT and TH are both different outcomes, better go back to statistics 101
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>>700852907
known as "boy or girl paradox""
>>
>>700860735
>>700859923
this guy knows what he's talking about. all you 1/3ers are fucking retarded.

coin 1 tails, coin 2 tails
coin 2 tails, coin 1 tails
coin 1 heads, coin 2 tails
coin 2 heads, coin 1 tails

6 possible outcomes, the two TT results are removed. Thus, you are left with two HH possibilities out of four total, which is 50%
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>>700862240

This is b8. Don't respond to it.
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>>700853458
You fucking retarded? There are only two available outcomes:

H - H
H - T

One coin is already on heads, so the probability now only remains that the second coin has a 50% chance of heads or tails.
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>>700862721
>assuming a first coin

first coin could be tails and second heads.

HH
HT
TH

1/3

Stay in school.
>>
>>700853458

You're fucking retarded mate. There are more than 3 possible outcomes.

T + H
H + T
H + H
S + H
H + S

S being where the coin lands on its side.
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>>700861466
>>700861743
You see, this is where your retarded minds go wrong. The order does not matter and is not stated as an objective of the problem.

Whether you get H-T or T-H, you have achieved literally the same outcome. One heads, one tails. You cannot and have not been able to explain why it matters. It's because it doesn't.
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>>700862240
lets try to explain this with no maths for the less inteligent among us

the given is that atleast 1 coin landed on head, not knowing the result yet this means it could be either 1 of 3 things
- coin 1 head, coin 2 tails
- coin 1 tails, coin 2 head

all of the above options are equally likely, you just don't know yet

now given this info, what is the chance it will be both heads, well easy math from here, 1 out of 3, 1/3
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>>700862482
This is b8. Don't respond to it.
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>>700863026
>Whether you get H-T or T-H, you have achieved literally the same outcome.

2 coin flip

HT has a probability of 1/4
TH has a probability of 1/4
HH has a probability of 1/4
TT has a probability of 1/4

At least 1 coin landed heads.

TT no longer a possible outcome, leaving

HT
TH
HH

1/3

>Whether you get H-T or T-H, you have achieved literally the same outcome. One heads, one tails. You cannot and have not been able to explain why it matters.

Point 1:
They are not the same outcome, just because they look the same to retards. Imagine one coin is blue and the other is red.

Do you think
red = Heads & blue = Tails
is the same as
red = Tails & blue = Heads

If you think they are the same, congratulations, you're retarded.

Point 2:
It matters because they are 2 distinct results and are equally likely to occur. So you have

likelihood of HT = 1/3
likelihood of TH = 1/3
likelihood of HH = 1/3

Do you understand now?
>>
>>700863847

Refer to

>>700862993
>>
>>700863847
You keep saying the same thing over and over again and you STILL sound retarded. Was there even an attempt at explaining why the order matters? Get it together man lol.
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>>700862951
there is no "first" or "second" coin, they are thrown at the same time.
All this question sais is that the result set contains at least one Heads

so we have (and pay close attention to the notation, because it is scientifically accurate):
{ {H, H}, {H, T} }

you cannot list {T, H} in there, because it is equivalent to {H, T}. If you disrespect that, you may as well list {H, H} multiple times, because you are not following a rule to eliminate duplicate items in the result set.
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>>700863128
>coin 1 heads, coin 2 tails
>coin 1 tails, coin 2 heads

these two are the same thing. you can already assume that one has fallen heads, since it says it in the problem. so you are left with HH and HT
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>>700864257

>This

H + H
H + H
H + T
T + H
T + T
T + T

T + Ts are eliminated, leaving a 50% chance it's H + H, 2/4
>>
>>700863847
You are a fucking retards.
>>
Well lets do the math.

There is a 50% chance for either outcome, so lets look at the possibility of 'tails'.

A 50% chance the first coin lands on tails, and a 50% chance the second coin also lands on tails.

Add the two 50%s together and we receive a 100% chance that OP is a faggot.
>>
>>700863847
I didn't know people could be this stubborn in their ignorance.
>>
>>700864257
you are right that sets must not contain duplicates, you're mistake is what you put in your set, the coins themself are unique, they are thrown at the same time, it has nothing to do with order, just with which coins lands on what side

your set should thus include a coin identifier
{ {C1H, C2T}, {C1T, C2H}, {C1H, C2H} }
now they are unique, and no longer equivalent

another anon gave a good alternative way too look at it, imagine one coin is blue and the other one is red, indepentend of order TH and HT would still be different outcomes (with colored coins this would be more visible, but i think we can both agree that color does not affect chances do they ;) )
>>
>>700864892
>let me change the experiment so my wrong result remains "correct" despite this new evidence
>>
>>700863847
they ARE the same you ass
>>
>>700855602
what are you? retarded?
>>
>>700853804
haaaaa
>>
>>700865270
nothing is changed, do you really think coloring the coins affects the outcome (assuming you don't use lead paint lol to make the coins havier)

if you are that naive then there is no point in continuing this discussion, please don't take a job in anything to do with statistics
>>
>>700865270
>let me get BTFO
>and whine
LOL
>>
>>700854529
this tbqhfampaisu
>>
Threadly reminder that giving consideration to ORDER is effectively altering the problem in OP's picture and incorrect.

Chances of landing heads vs tails is 50% and will always be 50%.

Posters giving 1/3 as an answer are 1+1=0 hurr I have proofs xDD tier
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>>700854995

the names donovan, jackass.
>>
trick question, there are no heads on those coins
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>>700864892

>Has nothing to do with order
>Puts order to them to prove point
>>
Its 1/4...
>>
>>700865743
Dumbass detected. It's a conditional problem. You're getting tricked because you are thinking in terms of actually throwing real coins, rather than solving the hypothetical.

stop being such a nigger
>>
>>700865892
>nothing to do with order
>at least 1
>out of 2
>not specified
>>
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>>700852907
If it is Euro, like in your picture, then there don't existing a for every nation a head on the other side
>>
>>700865937
>My outcome doesn't match a real life outcome! You're a retard!

listen to you'reself
>>
>>700866070
there's no actual tails on any coin either
>>
Friendly reminder that anyone saying 50% is either genuinely retarded or trolling.

For those who want to know the answer, see all the solutions posted ITT

>Bayes' theorem
>Punnet squares
>Venn diagrams
>probability trees
>computer simulations

All giving the correct answer 1/3

Pic related if you're still confused.
>>
>>700865743
ask a friend to throw two coins, don't let him show them to you

when he throws atleast 1 heads, let him ask you to predict if there are double heads (you still can't see the coins, only he can)

do this 20 times and always pick double heads, i can garantee you that you will be wrong more then 50% of the time
>>
>>700866243
Again, you're acting like a low IQ nigger. The coins in the problem are not real. You are not throwing coins to solve this problem. It's a conditional problem.

Apply yourself.
>>
>>700865892
since when is order equal to unique coins

i can have 2 unique coins, that i throw at the same time, thus no order
>>
>>700866421
I threw coins to solve the problem and I got 50%.

So you're saying math isn't real?

>>700866370
I literally did that. I got 50%. One coin heads, other coin heads/tails. 50%.
>>
You're all a bunch of fucktards. The answer is 0% because it's 50/50 chance. If one lands heads, statistically speaking, the other must be tails.

Source: I am right
>>
>>700866597
You're not actually solving the problem in the OP.

>>
>>700866355
How can you be this retarded?
>>
>>700866597
then either you did not follow my rules or you just did it twice, that's no valid sample size
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>>700866796
Why? because you changed the problem to suit your needs.
>>
>>700866950
seriously?

either /b/ is full of tards or full of trolls, don't know which one is worse actually, in both cases it shows what direction society is going
>>
>>700866950
Projection is some non-nonsensical trolling at this point.
>>
Question is deliberately ambiguous in how it can be interpreted. Such bait.
>>
>>700867312
No it's not, people just confuse flipping coins themselves with solving the actual scenario.
>>
>>700852907
50/50. Unless you add weird shit like landing on it's side.
>>
>>700853695
This is basic statistics.
>>
You faggots truly will argue about the most simple things. :^)

1/3 though guys
>>
>>700853458
Oh right kek, I will go get dat sweet sweet helium.
>>
Everybody who says the chance is either 1/2 or 1/3 is a retarded faggot.
Everybody knows it's actually 9/11
>>
>>700867553
HH - 25%
TH - 25%
HT - 25%
TT - 25%

these are the possible outcomes when just throwing 2 coins, do you agree?
>>
>>700868031
TH and HT are the same fucking thing
>>
>>700867964
Fuck you Bush! I won't let you blame statistics for what you've done
>>
>>700868144
No because it applies to 2 distinct coins. This HT and TH are 2 independent outcomes.
>>
>>700861739
If one coin is always heads, as stated in the original problem, why does atLeastOneHeads not come back as 100000 or however many iterations you decide on. Does that not jump out at you?
>>
>>700868031
now the given component of the questions state we are just looking at the cases where there is atleast one heads

HH - 25%
TH - 25%
HT - 25%

a probability distribution has to sum up to 100%, so we need to rescale them

HH - 33%
TH - 33%
HT - 33%

this is the new probability distribution for the question which includes the given component

HH = 1/3
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>>700868295
I do realise they are distinct,both outcomes are the same anyway.
>>
>>700868031

break it down:
3. Two Tails

three possibilities. one is eliminated. 50%
>>
>>700852907
>>
>>700868144
okey, if you want to see them as one thing be my guest, here comes the example again

HH - 25%
HT - 50%
TT - 25%

now the given component of the questions state we are just looking at the cases where there is atleast one heads

HH - 25%
HT - 50%

a probability distribution has to sum up to 100%, so we need to rescale them

HH - 33%
HT - 66%

this is the new probability distribution for the question which includes the given component

HH = 1/3
>>
>>
>>700868625
>HT - 50%
you just added them together, there's nothing to add up, there is only ONE OF THEM
>>
>>700855231
>taking the bait
You fucking moron
>>
>>700868625
You don't get the whole idea behind OP's problem.
If there is already a fixed H then the other coin is going to be:
H-50%
T-50%
Hence:
HH-50%
>>
>>700868610
You're thinking about the probability as if one has already been flipped and you're about to flip the next one.

But the question is asking what the distribution is after both have already been flipped. So you're counting HT, TH and HH but discounting only TT.

Thus 1/3
>>
>>700868790
so let me get this straight, you're saying that if you throw 2 coins you have 1/3 chance for both HH, HT and TT? because that is what you're telling me now

if you think that is the case you're even dumber then i expected
>>
>>700852907
Everyone forgets the third possible out come of a coin flip.
>>
>>700868790
When you flip two coins it's actually
TH-50%
HH-25%
TT-25%
>>
>>700852907
50%
>>
>>700868144
Yeah, just like your balls are the same fucking thing.
>>
>>700869158
It rolls under the couch?
>>
>>700854291
>bait
>b8
>b-eight
>>
>>700861332
His code is fine, you're just a faggot.
>>
>>700869400
anon, i think you mean ball (as in singular) because it's 1 thing
>>
>>700866538

You're putting order to it by saying you check one first Everytime.

There are only two options without putting an order to them. One is heads, one is tails. Both are heads.
>>
>>700868405
BECAUSE he's flipping two coins, and only comparing "double heads" versus "at least one heads"

It's much easier to just simulate the flip a set number of times, and throw out the unnecessary data.

Goddamn you're fucking dense.
>>
Not usually do I flip my balls.
>>
You fucking idiots. He said one lands on heads no matter what. Its 50% did you not get reading skills in middle school
>>
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>>700869631
My nigga.
>>
>>700868433

>they are distinct
>they are the same

gr8 b8, m8. Either that, or you're buttfuck retarded and beyond helping.
>>
25%
>>
>>700869780
It's not saying one will ALWAYS be heads it's saying only count the throws where one of them is heads.
So you only get to discount TT.
HH out of TH and HT is 1/3......
>>
>>700869634
for the Nth time in this thread,

ORDER =/= OBJECT UNIQUENESS

both coins have an outcome, unrelated to which order they were thrown in they stay unique

the fact that i write HT does not mean heads first and then tails, no it just means that coin a landed on H and coin b landed on T, whether a was thrown before b, or b before a does not matter
>>
>>
>>700868447

HT/TH is twice as likely as HH, you simpleton.

HT/TH = 1/2
HH = 1/4

(1/4) / (3/4) = 1/3
>>
>>700870050
>given at least one will land heads. Fuckin read the pic mate
>>
>>700853458
This is troll math... Those that said 1/2 are right actually.
If u have coin A land heads then B can be heads or tails. So 1/2 chances. If u have coin B land heads then coin A can be 1 of the 2_ so 1/2 chances again.
I mean heads - tails and tails - heads are the same, if u take them separate then you should also take coin A heads - coin B heads; coin A heads - coin B heads...
>>
>>700869634
>One is heads, one is tails.

there are 2 ways to get that

1/3
>>
>>700870508
How did you even get this result?
>>
Maybe this will be simpler.

You have a Dime (D) and a Quarter (Q).

Assuming one always lands heads, what's the probability they both land heads?

Because the D and the Q both have unique 1/2 probability of being heads and tails

so the conditions are

DQ
HH
HT
TH
TT

Since we don't care about the condition of TT, we strike it, and have three conditions.

Thus, any probability of any one condition is 1/3rd.
>>
>>700870173
>two regular coins WERE flipped
>given that one of them LANDED heads
Landed, not WILL land.
>>
>>700852907
depends on what side you flipped the coins.
>>
>>700870725
True.What's the difference either way though.
>>
>>700870065

Still putting order to them. Nothing in the question is specified and you're specifying coins. The only way to take this question is to look at both coins at the same time. You do not get to set a uniqueness to them.

So when you look at both you see either one is tails and one is heads or both are heads.
>>
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>>700870188

>Bayes' theorem
>troll math

Kill yourself.

Solution:
A = "both coins are heads" {(HH)}
B = "at least one coin is heads" {(HH), (HT), (TH)}

P(A|B) = P(Aâˆ©B)/(P(B)) = (1/4)/(3/4) = 1/3
>>
>>700870860
That probability doesn't work the way you think it does you fucktard.

You don't have a 50/50 chance of winning the lottery just because there are two outcomes for you (win/lose)
>>
>>700870725
landed yes, but do remember the other coin also already has landed, thus this knowledge affects our knowledge about the other coin
>>
>>700870923
You only look at ONE coin since the other one is fixed in the question itself.
>>
>>700852907
TREE FIDDY! Goddammit.
>>
>>700870667

2 coins. 4 possible outcomes equally likely

HH
HT
TH
TT

At least 1 coin landed heads, so TT eliminated

HH
HT
TH

3 equally likely outcomes remain

HH is 1 of those 3

1/3
>>
>>700870860
One sounds like a guarantee that one of the coins will always land on heads.
The other (correct) way to read it is that both already landed and you're only going to count the times when at least one landed as heads. So you only get to discount TT. Giving 1/3.
>>
I get where you people with 1/3 come from, but what you have to understand is that althouh there is a HT state and a TH state, both posibilites cant and dont exist at the same time. We do not have to know if coin a or coin b lands heads, all we need to know is that one of them does land head, and whichever that coin is, the combination where that coin landed tails and the other one heads cannot exist for that particular "throw", hence 50%.
>>
>>700858635
you literally can because it's impossible given the rules of the question. one HAS to be heads.
>>
>>700871131
TH and HT are the same you fucktard
>>
>>700870923
No, nigger, he is not putting order to it. But they are unique fucking objects, and regardless of the fact that we're only looking at all conditions where one coin is heads, one heads one tails is more probable, as shown in previous simulations
>>
>>700871040

>Only look at one coin
>The next coin is fixed

What is it fixed as? Heads or tails?
>>
>>700871231
No nigger, they are not.
>>
>>700871231

>hurr durr they're the same

You need better b8.
>>
>>700870923
haha, okey, i give up, i might as well try explaining this to 4 year olds

i highly suggest you look up Bayes Theorem and conditional probability distributions if you're serious about this and don't want to believe me
>>
>>700871470
Please explain how are they not the same you shitwit.
>>
>>700871040
Fuckin hell. No they are not fixed. We're just only concerned with the situations that follow the rule of "at least one head"
>>
>>700871470
>>700870671
>>
>>
>>700871581

Anyone saying 50% is too retarded for Bayes' or else trolling.

Either way, don't waste your time.

It's already been explained multiple times in this thread for anyone who cares to know the correct answer.

>>
>>700871746
that's for
>>700871620
not myself
>>
>>700852907
probability that both landed heads given that at least one of them landed head so one lands on heads no matter what... 50/50 for other coin to land on heads.
>>
>>700871620

Read this you dumb cunt >>700860354
>>
>>700871231
If you don't count order (which is fine), then the "one head one tail" outcome has twice the probability of two heads (get two coins, you can test this and see it to be true).

Easier IMO to see it as four separate outcomes of equal probability though.
>>
This depends entirely on your interpretation of the question. if the first flip has already landed when considering the odds, if the first land is heads, it's 1:2, if it's landed tails, it's 0, and if you're considering the odds before the toss, knowing at least one will land heads, which the question almost certainly intends , the odds are 1:3, as a tails-tails circumstance is impossible.
>>
>>700852907
0% I accidentally swallowed the coin
>>
I really hate to jump in here, but let's do some basic math here.

Say the coins are actually two-sided dice. Heads is 1 and tails is 0.

There is one (1) way to get 2 (H+H).

There are two (2) ways to get 1 (H+T, T+H)

There is one (1) way to get 0 (T+T).

Now, what is the likelyhood you will get two (2), if you are guaranteed a result of at least 1 (1) on a roll?

So we aren't to count zero (0) rolls (T+T) so we are only left with 3 options.

Hence, we have a one (1) in three (3) chance (1/3) of getting a 2 (H+H)

Stop thinking one coin is set. When you roll 2 six-sided dice, there's only one way to get 12, not fucking 2, or 3, or what other number you're fucking thinking of.

So in this case, since 2 (H+H) is the maximum of this combination of dice (coins), there is only one way. There is also only one way to make 0 (T+T), and two ways to make 1 (H+T, T+H). Because the coins are discrete objects, and your limitation is that at least one (1) coin is heads.
>>
>>700871821
Lets assume your retarded logic is correct.The only options would be HH and HT anyway so it's 50%.
>>
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Depends where OP is based...
>>
>>700871885
you're considering after the toss of both coins, you only have the knowledge that atleast one coin is heads (this is what the questions literally says), also leads to 1/3 though
>>
>>700872041
>The only options would be HH and HT anyway so it's 50%.

You're retarded. One of those is twice as likely as the other, dumbass.

>2 options: win the lottery or don't win the lottery
>so it's 50%

^That's how retarded you are.

You are twice as likely to get HT/TH as you are to get HH

HT or TH = 2/3
HH = 1/3
>>
>>700872041
Nigger there're two chances of getting HT. That's why it's 1/3.

Go suck the business end of a shotgun.
>>
>>700852907
op is an asshole for making me read for 5 minutes before realizing he just posted the monty hall problem. Why do people always get so heated about these kinds of things in statistics?
>>
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>Bayes' Theorem

or simply

>Conditional Probability

Now go study.
>>
>>700872463
There is only ONE fucking coin to toss since the first one is fixes as H.Can you please explain to me how are there three different options on a two-sided coin?
>>
>>700864216
He's not saying order matters man, just showing you that there are two instances where you get Heads and Tails, thus it's twice as likely
>>
>>700872615
because you have 2 - 2 sides coins, which makes 4 option, out of which one is excluded by the given information the the question, 3 remain.....
>>
>>700853458
the problem is that you're wrong from something so simple its worded in the question. its only asking about 1 coin because it removed 1 coin from the equation. you're retarded kiddo. 50%

reading comprehension is a lost skill.
>>
It is nearly impossible to know due to factors such as wind, gravity, dimensions & weight of coin, height & force of flip and in what direction, etc, etc.
>>
>>700872615
>since the first one is fixes

No, it isn't. You are retarded. Reread the question, dumbass.

>At least one coin landed heads

No coin is fixed. EITHER coin could be tails, just not both, giving 3 equally likely outcomes:

HH
HT
TH

1/3

Pic related

Source
http://courses.cs.washington.edu/courses/cse312/11wi/slides/04cprob.pdf
>>
>>700872527
"monty hall problem"? one coin is removed from the equation. its 50%. this is basic shit. are you retarded?
>>
>>700872791
Excluding one coin excludes two options,not one.
>>
>>700872615
No fuckface, that is not how this works. By fixing one of them you've changed the problem. It clearly states "two were flipped". That means you have to take all considerations, which is that there are two distinct coins with two distinct outcomes. Two different outcomes with two distinct coins = 4 distinct outcomes. Since we've removed one distinct outcome (two tails), there's 3 distinct outcomes. Then, since there's only one outcome that is equal to two heads, that probability is 1 out of the total (3) outcomes. Or one third.

Go die in a fire.
>>
>>700872795
>what is the probability that BOTH coins landed heads

nice try, m8.

1/3
>>
>>700872795
>>
>>700864257
see this is why it's troll/bait, it's never specified in the question and left open.
both 1/2 and 1/3 are right, it's just that they use two different assumptions.
To get 1/2 you're applying the 1 Heads rule 1st, then calculating the resulting odds.
To get 1/3 you calculate the odds of coin flips and then remove the TT to comply with the 1 Heads rule.
>>
>>700872961
Yes, it does. But that is absolutely not the problem. Reading comprehension.
>>
I got some brain damage a few years ago, so I have a hard time with numbers and math.
>>
this thread gave me extra chromosome
>>
>>700872898
sequence doesnt matter. it doesnt matter if its the first coin or the second coin. it doesnt matter fi its the left coin or the right coin. or however you want to differentiate them. the RESULT is fixed with 1 heads, so you've removed it from the equation. stop trying to sound smart, you're an idiot. its 50%

through whatever magic of the universal wave function or whatever, one coin's result is fixed, leaving only one coin ambiguous. as such, 50%.
>>
>>700873096
No, you blistering cow, there are NOT two correct answers. The problem EXPLICITLY SAYS two fucking coins were flipped.

THAT MEANS there are FOUR FUCKING outcomes.

THEN it says assuming ONE is heads - which removes ONE outcome, leaving THREE - what is the probability of double heads, which is ONE outcome. ONE / THREE = you're a fucking faggot.
>>
>>700873096
>both 1/2 and 1/3 are right

No, there is 1 correct answer to the OP question and that answer is 1/3.

It's a basic conditional probability question taught in beginners stats modules in every university.

See image here >>700872898
>>
>>700872961
No, no coins can be excluded, both were already thrown, either one of them could be the heads given in the question
>>
>>700873433
But if one coin is heads already then you are only flipping 1 coin really so its 50/50
>>
>>700873043
reading comprehension is hard, i know. i hope you can learn to live with your disability some day.
>>
>>700873269
You're right. It doesn't matter if it's the left or right coin. But it does matter that they are distinct fucking outcomes you cocksucking carpet bagger
>>
>>700873554
Yes but that's not the goddamn problem you assbag.
>>
>>700873509
What is the difference which one of them is heads?
>>
>>700873643
it actually is
>>
>>700873580
Faggot its clearly 25% because both coins could be were tails
>>
>>700873646
The difference is that they are two distinct objects with distinct probabilities of being heads or tails.

>>
>you flip 2 coins
>You know at least 1 is heads
>What's the possibility both are heads
>2 outcomes

What you guys are saying:

>3 possiblities

You have 1 guaranteed heads. Take that coin, remove it. It's guaranteed. Flip the next coin 10000000000 times.
Report findings.

Go ahead and say flip both coins like you guys are doing. You will get T + T which isn't allowed in the problem. You have to remove one and flip the other, or else you allow the T + T one to come to fruition.
>>
>>700873715
No it actually isn't
>>
>>700873643
But it says one is heads so that makes only 1 coin get flipped in reality
>>
>>700872898
and tails tails?
>>
>>700873779
No.One of them has no possibility of being tails.
>>
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>>700873269

>I'm right and Washington university Math professors are wrong hurr durr

Kill yourself.

For a 2 coin flip, there are 4 equally likely outomes:

Tails - Tails

If AT LEAST ONE coin landed heads, only
Tails - Tails
is eliminated, leaving 3 equally likely outcomes, each containing AT LEAST ONE heads coin.

is 1 of those 3

1 of 3

1/3

I'm just going to copy and paste now, because you're either retarded or a troll, so replying to you is a waste of time.

Pic Related: Punnett square. Can you say 'punnett,' faggot?
>>
>>700873646
https://en.wikipedia.org/wiki/Conditional_probability
>>
>>700873878
realised immediately after that im an idiot
>>
>>700873840
That's absolutely a separate problem.
>>
>>700873043
there are two people before you; frank and his neighbor. you do not know which one is which. frank and his neighbor drive him in separate cars every day. 50% of the time, frank makes it home without an accident, but his neighbor always arrives home perfectly fine. what are the chances they both arrive home without any accidents today?

>>
>>700852907
There are two kinds of people in this thread.

1. People who say it's 1/3
2. People who have never taken math after high school
>>
>>700873903
Amerifag fuck off with your poon-eeeit squares. Clearly 50%
>>
>>700873872
>Two regular coins were flipped

Nope.
>>
>>700873580
no, they arent. learn to independent variable.
>>
>>700873840

ERRRRR

Incorrect. Would you like to try again?
>>
>>700873580
Jesus man calm your shit. I think that the main problem here is taht this example inst particulary illustrative since there is no reason that 1 of the coinst must hit head other than divine intervention, so i guess that confuses some folks. But yea 1/3
>>
>>
>>700873884
No, you're ignoring the outcome that is both of them being tails, that's why the probability is 1/3 and not 1/4.
>>
>>700874133
Well if they aren't regular coins what are they? Chocolate coins?
>>
>>700874198
The only way for a guaranteed heads is if it is fixed, therefore it is 50/50
>>
>>700873903
>>
>>700874298
>Testing
>>
You know what the best (or worst actually) thing is? After reading this thread I actually think most of the people here arguing for the 1/2 answer are actually not trolling, but serious about their answer...

The direction this world is heading in...
>>
>>700874329
The nope is to (you) you faggot, not the greentext. The greentext is to prove you're wrong.
>>
>>700874062

Let's rephrase that.

Both have a 50% accident rate (like two fucking coins). Assuming one of them makes it home safe, what is the chance the other makes it home safe too?

SC
CS
SS

Loser.
>>
>>700874198
>there is no reason that 1 of the coinst must hit head other than divine intervention

It simply landed heads by chance. No Gods or magic required.

1/3
>>
>>700874504
It's why we have so many people play the lottery.
>>
>>700874435
>If one coin is fixed to land heads

1/3
>>
TFW every answer is wrong because the problem is shitty and vague, made by faggot professors a long time ago
>>
>>700874546
They're fucking horrible drivers if they have a 50% chance of being in an accident.
>>
>>700873903
was this the question they were asked? were they asked these exact words? because anyone with a fucking brain can read these words and discern that its only asking about 1 coin, which is a 50% chance, and knows that sequence doesnt matter. if you throw 2 coins a million fucking times and one of them is rigged or enchanted to always land heads up, you'll actually get numbers to match 50% in an actual physical fucking experiment. your theoretical bullshit is misplaced because thats not what the question is asking.
>>
>>700874703
It's not vague at all.
>>
>>700874703
>basic conditional probability math question
>shitty and vague

>>
>>700874514
The only way for it to be %33.3r chance would be if you were flipping a bottlecap instead of a coin idiot
>>
>>700874650
>given that at least one of them landed heads

>>
>>700874850
>simple problem

retard
>>
>>700874546
no, we arent rephrasing anything. i asked you a specific question, but you refused to answer because you know it shows you as wrong about the other answer, dipshit.
>>
>>700874732

Yes they are. Thankfully, their shitty driving makes a good metaphor for this problem.
>>
>>700874064

Look at this fucktard.
>>
>>700874749

hmm, let's see.

>what is the probability that BOTH coins landed heads

nope.jpg

1/3
>>
>>700874830
>>700874850
The question cannot have a definite answer due to basic physics fuckshits
>>
>>700874749
Yes, that was actually the question asked.

>Two regular coins were flipped
4 total outcomes

>What is the probability that both landed heads
1 outcome / total outcome

>Given that at least one of them landed heads
remove 1 total outcome; P=1/T = 1/3
>>
1/4
>>
>>700874982

>basic conditional probability

So you really ARE retarded.
>>
>>700874984

Yeah but you were wrong about the question. It's "AT LEAST ONE COIN" not "ONE COIN IS HEADS. FLIP ANOTHER COIN."
>>
Its a 100% chance for the end outcome to be what it is. No way of knowing until it happens, ez
>>
>>700875071
It's not vague.

see
>>700875093
>>
>>700875170
underrated post
>>
>>700875156
compared to choosing wether a single coin lands heads or tails it is advanced math
>>
>>700875215
It tells you nothing about the conditions surrounding the coin, which will influence it more than mere chance
>>
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I have a masters in engineering, and I drew up a Finite State Automata diagram to settle this

{H,T} and {T,H} are the same state, there are only 2 possible outcomes, its 50%
>>
>>700875381
finally anon with brain
>>
>>700875161
But if one coin is heads that means that that coin is already heads no matter what so its as good as not being flipped. 1/2
>>
>>700874582
Yea but we know that inm this problem at least 1 will land on head 100% of the trials, which in real life scenarios doesn't happen, so I think that is what is confusing people who claim its 50%.
>>
>>700874954
>given that at least one of them landed heads

means something different to

>one coin is fixed at heads

Do you understand that?

If one coin is fixed at heads, then it can't be tails, and the answer to that would be 1/2.

In the OP, no coin is fixed. At least one coin landed heads. It could be EITHER coin, meaing EITHER coin could still be tails, just not both, and that gives us 3 equally probable outcomes:

or
coin1 = Heads and coin2 = Tails
or
coin 1 = Tails and coin2 = Heads

1 of those 3 is a hit

1/3
>>
>>700875381
>>
>>700875381

You're ignoring the fact that the two coins are discrete objects, hence HT is different than TH.

I think that's where the problem is here. The problem never states whether or not the coins are discrete.
>>
>>700875590
>Guaranteed to be
>fixed
Same thing
>>
>>700875590
I means exactly that you nigger.
>>
1/1
>>
>>700875381
your FSA is good, however, you must realise that there are 2 ways to go to {H,T} and 1 way to go to {H,H}, thus {H,T} is twice as likely giving

{H,T} = 2/3
{H,H} = 1/3

if you really did a masters in engineering, just must agree with me here
>>
>>700875678
masters engineer
>B T F O
>T
>F
>O
>>
>>700869661
If youre throwing out the junk data why not throw out the junk logic with it. Set one coin to 1 and run only the second if staatement, then divide by the total runs. 50 percent
>>
>>700875733

Nah man. We're simply ignoring outcomes of TT here. the H could be other coins.
>>
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>>700875381

TH line is 1 outcome
HT line is 1 outcome
HH line is 1 outcome

3 outcomes

1/3
>>
>>700875050
P( A | B) = P( AB) / P(B)

'In english dude'

That's read as 'The probability of event A happening given that B has happened, is the same as the probability of both A and B happening divided by the probability of B happening.

Applied to our example:

B = At least one is heads

AB = Both are heads and at least one is heads -> same as A, because A is contained by B.

so P(AB) = P(A) = 1/4
and
P(B) = 3/4 #only one outcome without a head present, so take the complement.

And finally, (1/4) / (3/4) = 1/3
>>
>>700875809
>The stories and information posted here are artistic works of fiction and falsehood.
Only a fool would take anything posted here as fact.
>>
>>700875823
If we threw out junk logic you wouldn't be here anymore.
>>
>>700875789
there is only one fucking way to go HT since one of coins is already fixed as H
>>
>>700875854
But he never said what type of coin it is. What if its a chocolate coin and it melts before you get to see what side it landed on? If you already know that it is guaranteed to be heads then that makes it 50/50
>>
>>700875942
i still see 2 ways to get there if atleast one of them (which one does not matter) is H xD
>>
>>700875733
>>700875738

Retards detected

protip: to answer this question, you first need a basic grasp of the English language.
>>
>>700876083

You only know that one coin is heads. It's never stated to be "THIS COIN" is the point here. It could be either coin.
>>
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>>700875942
>>
No.The only way to get to HT is for the other coin to be T.
>>
>>700875590
>coin1 = Heads and coin2 = Tails
or
coin 1 = Tails and coin2 = Heads

Same outcome, only reversed, counts as one outcome.

Coupled with

Is two possible outcomes.

1/2
>>
>>700875942
all lines do include atleast one H don't they :)
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>>700876302

But it's not though. They're separate coins, and are being treated as discrete objects. Hence, HT is not TH because they are discrete results.
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>>700876205
But what if you get hungry and eat the other coin? Then that coin cannot be heads no matter what as it is destroyed, making the melted one guaranteed to be heads. Its a 100% chance to be a 50% chance
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>>700875678
i am not ignoring that, I am proving that they ARE THE SAME

a result set cannot contain two items of the same components
{ {H, H}, {H, T}, {T, H} } IS INVALID because
{H, T} = {T, H}
they are the same items, and a result set cannot contain two items that are equivalent

order them alphabetically.
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>>700875905

You're trying to explain bayes' theorem to actual retards and trolls.

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