/sci/ - Science & Math

[Anonymous No.2312505]

>>>/g/15240368
Here's something for you to laugh at

[Anonymous No.2312536]

It'd be something to laugh at if I didn't have to see it as often as I do. 1/3, go away.

[Anonymous No.2312545]

>mfw half of /g/ can't math/logic

[Anonymous No.2312551]

>>2312536
Are you retarded, it's 1/2!

[Anonymous No.2312560]

>>2312551
Go away, OP. Stop trying to start an argument about elementary statistics and conditional probability.

[Anonymous No.2312562]

That thread is making me sad, why can't they understand that HT is 25% and that TH is 25% too...

[Krakengineer !!5XY+x7grkpt No.2312565]

Before posting in this thread read this:
http://en.wikipedia.org/wiki/Boy_or_Girl_paradox
>>Many people, including professors of mathematics, argued strongly for both sides with a great deal of confidence, sometimes showing disdain for those who took the opposing view. The paradox stems from whether the problem setup is similar for the two questions[2][7][9]. The intuitive answer is 1/2.[2] This answer is intuitive if the question leads the reader to believe that there are two equally likely possibilities for the sex of the second child (i.e., boy and girl)[2][11], and that the probability of these outcomes is absolute, not conditional.[12]

A paradox is not a question that is difficult to answer. It is a question with multiple correct but contradictory answers. This statement jedi-mind tricks you into not seeing that it is using ambiguous phrasing.

[Anonymous No.2312571]

>>2312536


What is the probability that both are heads, if at least one is heads <span class="math">\longleftrightarrow[/spoiler] What is the probability of flipping heads with a single coin
<span class="math">\displaystyle 50\%[/spoiler]

[Anonymous No.2312577]

>>2312560
>He doesn't understand the difference between statistics and probability.

[Anonymous No.2312590]

[Anonymous No.2312595]

WHAT THE FUCK ARE YOU BLIND?
>>2312551
Not OP
I am OP
the chance of each ahppening is 25%, if we remove TT, that means, since HT can't possible be more probable than TH, goes to HH, this means that HH is 50%, while HT is 25, and TH is 25

[Anonymous No.2312605]

I hate everybody on this board.

>>2312590
Except you, ?rofessor.

[Anonymous No.2312611]

The trick here lies in "at least one is heads." Some people read this "the other flip has 100% chance of being heads" and some people read it "there are two 50% chance flips, of which one was heads"

[Anonymous No.2312615]

>>2312595
>the probability of TT magically goes to HH

0/10

[Anonymous No.2312616]

inb4 200 posts 32 image replies omitted.

[Anonymous No.2312641]

>>2312590

Except that the setting of the question renders TH and HT equal.

[Anonymous No.2312647]

>>2312616
Won't happen, this ends right here and now!
Since ONE is heads, either the first or the second, matters little, and double tails is impossible, which leaves you with a 50% chance of either tails/heads or heads/tails and a 50% chance of heads/heads
Why can't you people into logic

[Anonymous No.2312657]

>>2312641
Try it. Do the experiment. Flip coins, and when one of them comes up heads see how often the other one is heads.

[Anonymous No.2312666]

A. 1.H 2.T
B. 1.T 2.H
C. 1.H. 2.H
1/3?
but still a=b impying order doesnt matter, then 1/2?
and how can the coin surely head?

[Anonymous No.2312676]

>>2312657
Remember not to count the times when neither of them come up heads.

[Anonymous No.2312713]

it's literally a third. you have to take into account the cases and number the coins 1 and 2 as they are discrete.

there are 4 results possible, however we are told that it cannot possibly be TT. 2 ways for it to be HT, one way for it to be HH, so prob of HH given at H = 1/3.

[Anonymous No.2312753]

Thread over. Everyone please go about your normal business.

[MG No.2312774]

>>>/g/15241856
my post

[Anonymous No.2312777]

>>2312565
Someone says this every thread, but I remain unconvinced that \"You flip two coins. One of the coins is chosen at random, and found to be heads. What is the probability both are heads?\" is a sensible interpretation of the question.

[Anonymous No.2312806]

Whoever thought of posing the question like this is master troll
Here goes:
It is 1/2 IF TT is impossible, you should know why
However, it is 1/3, if you have to flip the coins untill you either have HT TH or HH.

Get this?

[Anonymous No.2312819]

>>>/g/15240642

What happens when people read Wikipedia but can\'t actually understand the math the article is talking about.

[Anonymous No.2312824]

You flip two coins onto the floor. The first coin has it's obverse visible to you. What is the probability both coins will have the obverse visible to you after the second coin is flipped?

[Anonymous No.2312828]

>>2312753
No you idiot if coins are flipped simultaneously, then ONE is ALWAYS heads (we know this from the question). Thus, we are only ever dealing with one coin at a a time and the probability is 50%

[Anonymous No.2312831]

>>2312824
What the hell is an obverse?

[Anonymous No.2312838]

Since I don't consider TH and HT as the same, and TT is eliminated, then I would come to the conclusion that the answer is 1/3.

[Anonymous No.2312842]

Haha, I was right, how could I have been so stupid before!
Guys, you're not arguing over the right answer, you're all right, you just understood the question difirently

[Anonymous No.2312867]

>>2312838
It doesn\'t matter if you consider TH and HT as \"the same.\" TH and HT, considered separately, each have a probability of 1/4 (without the condition that there is at least one heads). Considered as a single outcome, they have a probability of 1/2.

[Anonymous No.2312880]

>>2312842
Unless your interpretation of the question is
>>2312777
which would be bizarre, you should get 1/3.

[Anonymous No.2312965]

>>2312842
Like somebody said over on /g/, if you believe that a magical force is stopping you from flipping two tails, then the odds are 50%. If, on the other hand, you believe that the flip was fair the odds are 33%.

You have to believe in magic to get 50%. The rest of us only have to believe in math.

[Anonymous No.2312970]

>>2312965
IT WENT TWELVE MINUTES WITHOUT A BUMP. WHY.

[Anonymous No.2312978]

>>2312965
This post made me so mad, I'm seriously considering smothering my own baby..

[Anonymous No.2312985]

>>2312965
I responded to that noob and I will to you saying that Mathematical problems often ahve us make near impossible assumptions, people saying 50% didn't say it because of magic, they said it because they think it is a mathematical problem with strict rules

[Anonymous No.2313004]

I do it a 100 ways and I still get 1/3

[Anonymous No.2313018]

>>2312867
Except that 3/4 of the possibilities contain at least one heads (HH, HT, TH), and 1/4 contains the combination of interest (HH). Therefore, (1/4) / (3/4) = 1/3.

Of course, the question is ambiguous and it may consider excluding TT completely. In that case, it would be 1/2.

[Anonymous No.2313051]

Well at lease /sci got that it could be both ways, would you ming coming over to /g/ just for a second and convincing them too

[Anonymous No.2313052]

>>2313018
It is not possible for TH and HT to be different because it is only ever asking about ONE COIN read the question fucktard

[Anonymous No.2313064]

http://www.liveleak.com/view?i=969_1263249923

[Anonymous No.2313069]

>>2313052
>At least one is heads.

You are not told which coin is heads. You just know that one of the two landed on heads, which means it could be one or another. Therefore, TH and HT are different.

[Anonymous No.2313073]

Ok. I start to play the rules game.

I flip 2 coins. So they are flipped already? Now I have a look at them and see at least one of them is head. If I see these coins there is no probability any more. The coins have been flipped and I see both of them. I know if they are both heads or not.

Or maybe I closed my eyes and asked my friend to tell me if one of these is heads. He said yes. I wonder what he would have done if one weren't a head - would he have said no?

Or maybe I asked my friend to go to another room - take unspecified number of coin pairs and flip all of them. Then discard the ones that resulted in two tails and now I am supposed to calculate what is the probability of double heads among the ones not discarded.

The wording of this problem requires one to make assumptions. Depending on what assumptions you make you get different results.

[Anonymous No.2313082]

>>2313069
>or the other

fix'd

[Anonymous No.2313102]

>>2313069
No they are not, they are both just:
Flipped both and got one head coin, and one tails coin
Flipped both and got one head coin, and one tails coin

You have to be pretty fucking stupid not to see that

[Anonymous No.2313125]

>>2313069
>>2313102
Please see >>2312867

[Anonymous No.2313127]

>>2313102
Say you've got a gold coin and a silver coin. You flip both simultaneously. The gold coin lands on heads, while the silver coin lands on tails. You flip again, this time the gold coin lands on tails while the silver coin lands on heads.

Replace the gold and silver coins with two coins that look the same. You see where I'm getting at?

[Anonymous No.2313138]

>>2313102
0/10

[Anonymous No.2313152]

>>2313125
No, post is wrong you retard
>>2312867

Flipped both and got one head coin, and one tails coin
Flipped both and got one head coin, and one tails coin

does not equal to seperate outcomes that add up to a quarter, such thinking is retarded

[Anonymous No.2313157]

>>2313127
The question has nothing to do with coin A, coin B. The question says nothing that shows one coin distinct from the other. How the fuck are you so stupid?

[Anonymous No.2313158]

>>2313138
fuck off troll

[Anonymous No.2313167]

>>2313157
>At least one is heads.

Read the fucking question!

[Anonymous No.2313177]

>>2313073
THE PROBABILITY OF A SIMPLE COIN FLIP DOES NOT CONSIDER THESE RIDICULOUS THINGS, THAT IS NOT HOW PROBABILITY WORKS!!!!!

[Anonymous No.2313189]

I don't see what the problem is here. The obvious answer is 1/5.

[Anonymous No.2313197]

>>2313152
Did you read the post? It says that the probability of getting one heads and one tails is 1/2, not 1/4. I don't even.

[Anonymous No.2313213]

>>2313197
>Completly ignore post to point out something tedious because i have already realised i am a massive retard for ever believing it could be a third and as a result can no longer make actual arguments


bravo sir!

[Anonymous No.2313233]

>>2313213
At this point, you've got me for completely misunderstanding whatever point it was you were trying to make. It was either so confusing or nonsensical that I couldn't get it, or I am as dumb as you say I am. You can see this as a "win" if you want.

You can restate it in a way such that I can follow your train of thought, or you can ignore me and deem me as unworthy of your flawless arguments. Your choice. I'm not going to continue making assumptions about the point you are trying to make, since I apparently don't know.

[pascal !n5Z3VuZapw No.2313244]

There are 4 possible outcomes for flipping 2 coines
tails tails
head tails
tails head
head head

however because we define at least 1 coin to be heads we have 4 different outcomes

head head
head tails
tails head
head head

This means the probability is 50%

[Anonymous No.2313260]

TT, HT, TH, HH
The last three fit the "at least one is heads" condition. The odds that both are heads is therefore 1/3.

[Anonymous No.2313263]

>>2313244
Pascal confirmed for retired tier.

[Anonymous No.2313266]

>>2313244
I think you derped. Might want to fix that second part.

[EK !D96TK2PSsI No.2313270]

0/10
>heads:heads twice

...

>realises post is from pascal
>likes pascal
>changes pic from obvioustrollisobvious.jpg to wtfman.jpg

[pascal !n5Z3VuZapw No.2313272]

>>2313263
Let me graph it

We are given 2 possible scenarios. Scenario 1 coin A is heads

Hx
hthh

Scenario 2 coin B is heads
xH
thhh

4 possible outcomes, 2 of which are head/head

[Anonymous No.2313276]

A single coin has a 50% chance of being either heads or tails.
Two coins have a 25% chance of being both heads or both tails and a 50% chance of being mixed.

Two coins are flipped. At least one of them is heads removing the 25% chance that both coins are tails.
There is now a 33.3% chance of both being heads, 66.6% chance of being mixed, and 0% chance both of them are tails.

[Anonymous No.2313277]

-.-

[Anonymous No.2313279]

>>2313244
You see that second list? Check for redundancies.

[EK !D96TK2PSsI No.2313281]

>>2313263
>retired

[Anonymous No.2313282]

Does Pascal normally troll?

[Anonymous No.2313288]

>>2313281
thats hilarious

[Anonymous No.2313289]

>>2312571
>>2312551

> Doesn't understand that the coin you're flipping might be the 'AT LEAST 1 HEAD'

[EK !D96TK2PSsI No.2313291]

>>2313276
>>2313277

this.

also, this is very similar, and is related http://en.wikipedia.org/wiki/Boy_or_Girl_paradox

[Anonymous No.2313292]

>>2313272
>if we can't go right, we can go left, forwards, backwards, or left. 50% it's left.

[EK !D96TK2PSsI No.2313298]

>>2313282
I don't think so...

[Anonymous No.2313307]

there is always the possibility the coin will land on it's edge.

Thus far, i have seen no evidence that this almost insignificant detail has been calculated into the probabilities.

i haven't looked for one either though, so idk

[Anonymous No.2313309]

>>2312551
>>2312571

> You flip 2 coins

Derrrr, you flip 2, not one and then another. When you flip it's not certain which coin is heads which means both coins are variable.

Before they land you a guaranteed that one coin land heads you don't know which one it is thus there is 1/3 chance

[Anonymous No.2313311]

BUT HOW DO YOU KNOW ONE WAS HEADS?

[Anonymous No.2313314]

>>2313311
Your friend saw it and is making you geuss but giving you a hint.

[Anonymous No.2313318]

>>2313314
What would my friend have given as a hint if both had been tails?

[Anonymous No.2313323]

>>2313307
That's because in this scenario the coins don't actually exist.
They have no weight. They have no shape. They are thrown and land simultaneously. There is no order in which they are checked ("at least one is heads").

[Anonymous No.2313331]

You are introduced to the possibility of two Gods existing. You know at least one exists. What's the possibility atheists are wrong?

[EK !D96TK2PSsI No.2313338]

>>2313307
coin flipped properly, and by a human, CANNOT land on edge. physically impossible. 0.0 probability.
if it spins laterally, it will not find balance.
(it has to also land on a flat surface, cant land leaning against something, or it is not a valid flip)
(coin must be a standard coin, not artificially thickened)

[Anonymous No.2313342]

The statement "At least one is heads" is fucking stupid, pointless, and ambiguous. The probability of flipping 2 coins and both being heads is 25%. Period. If you were to say that 1 coin that was flipped already turned up heads and asked for the probability of the second one being heads then it would be 50%.

[EK !D96TK2PSsI No.2313347]

>>2313318
question would change

"at least 1 is tails"

perhaps.

[EK !D96TK2PSsI No.2313352]

>>2313342
correct, but that is slightly different to OP's question.

If any 1 of the 2 coins is definitely heads, but you dont know which, then it is 1/3
if you do know which, then there is only probabity to deduce on the 2nd coin, so 1/2

[Anonymous No.2313378]

>>2313352


ok

[Anonymous No.2313380]

hahahaha this thread is worse than the one on /g/

goodjob shitspawns

[Anonymous No.2313405]

>>2313347
>question would change "at least 1 is tails"

In this case 1/2

If he would have said: Ever since I met this new girl Sally I all I think about is getting head. I decided to flip two coins and if at least one of them would be heads I would ask you to guess what is the probability of both being heads. If both were to be tails I would have not asked you anything because getting tail is shitty.

In this case it would be 1/3

[Anonymous No.2313411]

HT
TH
TT
HH

One goes away, three remains. the question is how probable one of the three is. All of them have equal probability. 1/3

[Anonymous No.2313417]

>>2313342
It isn't ambiguous, at least one heads (out of two) means one or two heads.

So if we were to draw up a sample of 5 HH, 10 HT, and 5 TT, only the HH and HT would fit the definition. If someone were referring to a random situation of paired coin flipping in which at least one is heads, 1/3 chance it's HH.

Take a damn genetics course, people. If you mix two heterozygous organisms for one allele, Tt and Tt, and the offspring shows a dominant trait, there is a 2/3 chance of it being heterozygous and 1/3 homozygous. This fact was used in the fundamental testing in genetics of Mendel's principles of segregation and independent assortment, and if it's wrong, then its foundations and continuing work on Mendelian traits is all wrong.

[Anonymous No.2313418]

>>2313405
err messed up numbers but didn't mess up the point that there is ambiguity

[Anonymous No.2313419]

YOU GUYS ARE PISSING ME OFFFF!
HERE YOU GO:

Two ways of reading the problem:

1) first interpretation:
TT is not supposed to happen, so you flip coins until you take one of the following possible flips: HH,HT or TH.
Then you take away the one H which was postulated which leaves you at: H, T or T.
--> The probablility for HH is 1/3

2) second interpretation:
You flip coins and always peek at the first one until it's H and then you take that flip. The chances that the first coin, the one you look at, is H is 1/2 because the overall possibilities are TT,HH,HT or TH. --> In any case, here the chance that the second one is H is also 1/2.

The difference is that the "I disregard this flip" decission is different in both cases. In the second one you only look at one. The question ask by op is vague, thats all.
cheers

[Anonymous No.2313422]

>>2313417
>If you mix two heterozygous organisms for one allele
for one locus*

[Anonymous No.2313442]

>>2313419
According to the question neither of these happened.
Two coins were flipped. At least one is heads. They both could have been tails, but that's no longer possible because one of them landed heads.

[Anonymous No.2313449]

>>2313419
>2) second interpretation:
>You flip coins and always peek at the first one until it's H and then you take that flip. The chances that the first coin, the one you look at, is H is 1/2 because the overall possibilities are TT,HH,HT or TH. --> In any case, here the chance that the second one is H is also 1/2.

No you are not told that one of them is heads and the other hasn't been looked at. You are not told that A is heads and the other isn't being talked about. You can't uncover A and say ok what's the probability of B? because A could be heads just as well as B. You can't start from the assumption that A is heads or you are adding information that OP did not give.

[Anonymous No.2313451]

sure is Monty hall paradox in here

[Anonymous No.2313479]

>>2313449
But one of those situations is necessary for a model of probability. Without knowing how the person in question determined that there was one coin turned heads, we can't know the probability.

If both tails is impossible due to some outside circumstance, like automatic re-flipping on TT, then it's 1/3. If it's determined by the exclusion of all TT in a group of flips, then it's 1/3. If the information that at least one coin is heads was obtained by looking at one coin, then it's 1/2.

The ambiguity of the question doesn't imply some purer answer, because there is not purer answer. The probability is dependent on the specifics.

[Anonymous No.2313477]

If you are saying x HAS to by y, then it isn't a probably problem, is it you fucking morons?

[Anonymous No.2313488]

>>2313442
>>2313449

I just presented the interpretations people are working here and I'm not arguing for one.
If you come to the conclusion 1/3 you work with 1), if you come to the conclusion 1/2 you worked with 2).

I'm not an experimental physicist and I don't bother much with questions not stated in clear mathematical terms which are already defined.

[Anonymous No.2313492]

If you are saying x HAS to by y, then it isn't a probability problem, is it you fucking morons?

[Anonymous No.2313518]

>>2313479
This is an abstract question devoid of any question-giver, you can't add information like "he was only looking at one." The statement is to be taken as absolute truth: "at least one is heads," which can refer to any of 75% of the situations, not 50%. You don't get to narrow it down because you want to simplify and make A definitely heads. TH has "at least one heads" just as much as HT does.

[Anonymous No.2313527]

>>2313451
Different problem and not a paradox. In that exercise we choose one of 3 doors to find a car. Monty opens a door and it's a goat. Should you switch from your door to the other? Yes. What is the probability that the other door is a car? 2/3.

[Anonymous No.2313541]

>>2313488
It is defined. All possibilities that satisfy the conditions of at least one head are included. Intuition that you can simplify can just make A heads is not warranted. Look at a punnet square: 3 possibilities exist.

[Anonymous No.2313551]

Because one coin has already been defined as being heads, the first toss is a 100% probability(e.g: not really a probability). The second is a 50% probability. Average of the two is 75%.

[Anonymous No.2313552]

>>2313518
It's up to interpretation because you can shift the words slightly without changing the meaning to get different impressions from mathematicians.

"You flip two coins. One is heads. What is the probability that the other is heads as well?" carries the same meaning as the question, but through one or two synonyms and change of sentence structure, it implies a different situation.

Making a decision based on an implication is a definite cry for more information.

[Anonymous No.2313569]

>>2313518
>The statement is to be taken as absolute truth: "at least one is heads,"
and you can arrive at that truth through different means. If the coin flips were random, then the "truth" peeked at either one or two coins to give you that information.

[Anonymous No.2313571]

Ya, to be honest I lean more to the 1/3-interpretation myself, can see the problem why one would like to point out the 1/2-interpretation as well.

I call it "1/3-interpretation" even though you probably don't like that, I apologise.
But to me it's at least obvious that if you ask a question about possibilities, you rather not aximaticize one of the possible outcomes away - in the end this IS a possible outcome of the coin-flip experiment. So this is not an elegant question.

To me at least. Now let me go back to differential geometry or something :)

[Anonymous No.2313582]

/sci/ is just as retarded as /g/

Successful troll is very fucking successful.

[Anonymous No.2313585]

>>2313551
The coin wasn't defined as heads. The two coins were flipped simultaneously and at least one of them landed heads.

[Anonymous No.2313591]

>>2313585
What I meant to say was one of them is heads, I simply used first out of convenience.

[Anonymous No.2313607]

>>2313552
>you can shift the words slightly without changing the meaning

No you can't, this is why it's ALWAYS worded EXACTLY the same way whenever this thread is made or whenever geneticists talk about homozygous/heterozygous dominant traits: "At least one is heads." This is qualitatively different from saying "One is heads" without referring to the other. Because in this case you KNOW A is heads (or B it doesn't matter) and you don't know B. In the first case you don't know either, so you have to consider the possibility that A isn't heads.

"At least one is H":

HH
HT
TH

"One is heads the other is unknown":

HH
HT

TH is illegal as defined by the new wording only.

[Anonymous No.2313651]

>>2313607
For the record mathematicians have come to the consensus that it's up to interpretation.
http://en.wikipedia.org/wiki/Boy_or_Girl_paradox

You can't see the ambiguity of the question? Two coins are flipped. Then, you are given information on the two coins.

Either:
The statement was dependent on the coin configuration
or
The coins were flipped and reflipped until they fit the statement.

If the statement was dependent on the coin configuration, such as a 50% chance either way of saying tails or heads if it's HT, saying tails if it's TT and saying heads if it's HH, then yes. 1/3 chance.

If the situation arose from flipping and reflipping the coins to fit the statement, and the criteria for the statement is that both coins are checked, then yes. 1/3 chance.

But if the criteria for the rejection of the coins was based on checking one coin, then it's 1/2.

The question itself is evident of how information affects the probability of things. Specifying the method for gaining the information is important for calculating probability correctly.

[Anonymous No.2313672]

>>2313607
>This is qualitatively different from saying "One is heads" without referring to the other
the statement "one is heads" doesn't SPECIFICALLY refer to one and not the other, and "at least one is heads" doesn't specify whether it's referring to a specific one being heads or either being heads.

[Anonymous No.2313709]

It's like this, think in binary. You have the following possibilities:

00
01
10
11

According to OP's question, at least one of them is 1. That is, we discard "00". What is the probability of obtaining "11"? 1/3 (there's "01", "10" and "11).

The other question gives us a 1/2 chance. Then it'd be something like: the first (or last, as you want) number is 1. What are the chances that both numbers are 1?
Of course that leaves us with 10 and 11, thus being the chance 50%.

[pascal !n5Z3VuZapw No.2313720]

>>2313709
11
01
10
11

[Anonymous No.2313758]

>>2313720
a(h) b(h)
a(h) b(t)
a(t) b(h)
a(t) b(t)

[pascal !n5Z3VuZapw No.2313770]

>>2313758
a(h)b(h)
a(h)b(t)
b(h)a(t)
b(h)a(h)

[Anonymous No.2313783]

>>2313651
>But if the criteria for the rejection of the coins was based on checking one coin, then it's 1/2.

That's true. That's exactly the problem with that interpretation: "at least one is heads" doesn't describe one coin. The "two coins" are treated as one set, not independently, so you can't legally say coin A is heads. It's as if people think they can mentally mark the two coins and say one is heads and the other can be either, but you can't, because the first could be tails.

>The question itself is evident of how information affects the probability of things. Specifying the method for gaining the information is important for calculating probability correctly.

Precise wording does matter, and that's the point I've been trying to make. Such a statement like OP's, however, could only be interpreted differently if, like we always do, we reconstruct what others mean, filling in the blanks and making corrections; sort of like for the sentence "I could care less," which we would never take literally. This is changing the meaning. The statement should to be taken at face value, or else we're not allowing precise meanings in mathematics.

[Anonymous No.2313790]

>>2313770
You already have two heads and you are still missing two tails.

[Anonymous No.2313793]

>110 posts and 18 image replies omitted. Click Reply to view.

Sometimes I feel like I don't even know you /sci/

;_;

[pascal !n5Z3VuZapw No.2313801]

>>2313790
it is 2 different sets containing 2 heads.

And why would I have 2 tails? it is not a possibility in this problem.

[Anonymous No.2313808]

>That's exactly the problem with that interpretation: "at least one is heads" doesn't describe one coin.
Sure, at least one is heads doesn't say a specific one is heads. We're talking about PROBABILITY here though, so any statement that is made assesses the coin flips in some way.

Even a non-human informant would have a method for evaluating the coins. I could check a coin, see that it's heads, and ask you the question. I'd be perfectly within the parameters of this ambiguous wording, and the answer would be 1/2.

[Anonymous No.2313818]

>>2313672
Well, to include the whole context...

The original question is "You flip two coins. At least one is heads." This can't mean anything different from two coins, unless you want to argue the speaker is starting an anti-grician language, but then you might as well argue it's not English and the words mean whatever you want them to.

The question "You flip two coins. One is heads. What is the probability that the other is heads as well?" The "other" word denies that both coins could be referred to when saying "one is heads." This is also unambiguous and has a different meaning.

[Anonymous No.2313830]

>>2313818
The second one is unambiguous, the first one isn't. The first one orginally arose as a rewording of the second. Again, the wikipedia article.
http://en.wikipedia.org/wiki/Boy_or_Girl_paradox
The question in the OP can fit the second question and the implied meaning, and is therefore not specific enough to be a proper question in a field of mathematics.

[Anonymous No.2313846]

>>2313808
There isn't an informant at all.

>I could check a coin, see that it's heads, and ask you the question

You could, but saying the same sentence provides the same information. I would still be justified, assuming I hadn't seen you check just one coin (in which the rest of the information would present itself to me) that the first coin could be tails. You could also tell me that the first coin is heads, which would provide more information, because TH would be ruled out.

OK guys I have to go, but I"m glad this didn't turn into a name-calling extravaganza.

[Anonymous No.2313852]

HH
TT
HT
TH

1/4

[Anonymous No.2313854]

>>2313323
>>2313338

not stipulated in the original question.
you cannot add such things down the road simply because your delicate sensibilities have been disturbed


me and the general public at large will not envision a coin lacking mass.
we can not flip a non existing object nor would gravity affect such a thing. It couldn't land anywhere.
Coins in all fact, have a shape.
Coins are three dimensional as well...

a coin has three states of being while at rest...
heads, tails, and edge.
we all know that.

now scurry off and do the calculations correctly.

[Anonymous No.2313855]

>>2313846
Ugh. The formation of words as a descriptor of two unknowns require an underlying process. Without knowing the process, we can't know the probability.

[Anonymous No.2313886]

Is it just in /sci/´s nature to make things more complex than they have to be?

You know before you flip the coins that one coin is a magical coin which only lands with heads up, so thats about it, there are 2 equal probabilities that the other coin will also be heads up so its 1/2, no need to prove your math skills here, its probably a troll question made specially for you faggots to debate on some meaningless shit when the answer is obvious, i know math hurp durp, im gonna make things more complicated and therefore show others how awesome my brain is hurp durp

[Anonymous No.2313915]

God told me it's 3, 7 or 12. I'm feeling like 7.

[Anonymous No.2313919]

>>2313886
Third posting of the wikipedia article:
http://en.wikipedia.org/wiki/Boy_or_Girl_paradox
Not exactly a troll question, it is pretty complicated.

[Anonymous No.2313922]

>>2313886
>You know before you flip the coins that one coin is a magical coin which only lands with heads up
Nope. That changes everything.
Two coins were flipped. One of the two coins landed heads. What is the probability that BOTH coins are heads? The answer being 1/3.
This is only being complicated by people who change the question or add information.

[Anonymous No.2313937]

This is.. so weird. /sxi/ is full of morons.

It's 1/3. The math has been done. What seems to baffle most people is the way the question is put.

It doesn't tell you which coin is heads. Just says at least one is. Therefore you can't assume it was the first one. And because you don't know which one it is, both

HT and TH are a possibility.

So the final combination is HT, TH or HH which makes it 1/3 (because only the last one has both as heads).

[Anonymous No.2313943]

>>2313937
and I can't spell /sci/

[Anonymous No.2313955]

Here are the possibilities : TH, HT and HH. TT has been ruled out by hypothesis. So that's one in three (P=1/3) chance of having both heads. It's not that hard.

[Anonymous No.2313981]

>My face when this is purposely ambiguous and not conditional probability.

[Anonymous No.2314036]

>>2313943

this jpg would be funnier if the 2 pictures would be reversed

[Anonymous No.2314043]

>>2313922

IRL? Sure.

But the question as I see it specifically excludes the possibility of getting TT, which allows for the assumption that one of the coins will magically land on heads. Always.

It doesn't matter whether it's 'Coin A' or 'Coin B' that's guaranteed, all that matters is that one of them can never be a tail. Following both scenarios you'll either get a guaranteed head with A followed by either a head of a tail with B, OR you get a head or a tail with A followed by a guaranteed head with B.

So your 4 outcomes are:

Head & Head
Head & Tail
>coming from A having a guaranteed head
Tail & Head
Head & Head
>coming from B having a guaranteed head

Which give us our 1/2

It's in no way applicable to an RL setting, but that's what I believe the question is asking.

[Anonymous No.2314061]

>>2314043
WHICH IS WHY IT'S UNIVERSALLY ACCEPTED BY MATHEMATICIANS TO BE AMBIGUOUS AND UP TO INTERPRETATION. BECAUSE THE SELECTION CONDITION OF THE COINS IS UNDEFINED.

IS THE STATEMENT TAILORED TO THE COINS? IF SO, IS THE HEADS/TAILS DISTINCTION RANDOM?

OR ARE THE COINS RE-FLIPPED WHEN BOTH AREN'T HEADS, OR WHEN THE FIRST ONE CHECKED ISN'T HEADS? OR IS THERE AN UNKNOWN CONDITION?

WITHOUT SPECIFICS EVERY ASSUMPTION IS WRONG AND NO SOLUTION IS THE ONLY ANSWER. ALL CAPS BECAUSE I'VE SAID IT TOO MANY TIMES. READ THE FUCKING WIKIPEDIA ARTICLE.

[Anonymous No.2314069]

>>2314036
Agreed. I used to wonder why it is like that. Then I just accepted it could be read from right to left.

[Anonymous No.2314070]

>>2312828

Tell me you're just pretending to be a moron. He's right in using Baye's theorem in solving the problem.

[Anonymous No.2314181]

>>2314061

y u mad?

[Anonymous No.2314205]

This shit is appearing on every fucking board..

It's a fucking paradox caused by vagueness.

[Anonymous No.2314223]

I can believe you are still debating about this one when >>2313743 as already been solved...