How smart is /b/?

>>564356804
50%
>op is a faggot

some

50%

>>564356804
they wont land because i will steal them

>>564356804
if one of the coins "at least" lands heads, then the image is implying that one will always land heads. so, it's a trick question.

it's 50%

>>564356804
100% (chance that OP is a faggot)

File: coinsvisualexplanation.jpg (740KB, 2442x1998px) Image search: [Google]

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>>564356981
>>564357031

Retards detected.

Answer = 1/3

Flip 2 coins. 4 equally probable outcomes
HH
HT
TH
TT

At least one landed heads, so TT is eliminated from the probability space, leaving three:
HH
HT
TH

HH is 1 of those 3.

1/3

Mathematically, we solve using Bayes' theorem:

Let A = "both coins are heads"
Let B = "at least one coin is heads"

Probability of A = P(A) = 1/4
Probability of B = P(B) = 3/4

Probability of A GIVEN B =
P(A|B) = P(A?B)/(P(B)) = (1/4)/(3/4) = 1/3

Pic Related: 1/3

75%

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>>564356804
New riddle.
OP sees two dicks in front of him.
What is the probability that both dicks land in his mouth given that he is a raging faggot?

>>564356804
75%

33%
/thread

>>564357159
exactly

all those retards that spew 33% do not include the implication that one of them is already given to us. they just follow normal permutations if both were flipped randomly

>>564357159
>the image is implying that one will always land heads. so, it's a trick question.

It's not implying that at all, and it's not a trick question. It's a basic conditional probability question.

The answer = 1/3

>>564356804
33%

>>564357293
nigga its 0% i stole them shits pointdexter.

File: coinsprobfags.png (16KB, 590x491px) Image search: [Google]

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>>564357440

You're a moron. That is all.

1/3

9% dipfucks

>>564357326
8/8

>>564357067
Lol

>>564356804
Mine always lands on its side... 0%

In space, they never land...

Do Euro's have heads?

>>564356804
>COME ON OP
1st: 1/2
2nd: 1/2

0.50 x 0.50 = 0.25

>>564357706

>At least one landed heads

1/3

>>564357578
exactly my point retard. you followed normal permutations.

it is implied that we already have one landed heads. that strikes out 2 combinations from the normal permutations

This is mere bullshit. It depends on the weight of the coin, the consistency of air, or the lack of air thereof.

It also depends on the force which was applied by the very mechanism that made the coin flip.

Once all the variables are comprehended, you can determine the exact result.
Probability is just the shit.

>>564358127
the true answer here. engineers know more shit than the typical statistician

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>>564356804
The odds are 1 in 3.

Logic:
1/4: both heads
1/4: first heads, second tails
1/4: first tails, second heads
1/4: both tails [option removed: failure to meet conditions]

Therefore, 1 of the 3 equally probably situations above lead to two heads.

File: Uni_Wash_Cond_Prob_slide_4.png (400KB, 921x631px) Image search: [Google]

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>>564358035
>it is implied that we already have one landed heads. that strikes out 2 combinations

No it doesn't retard. It excludes one; the only one that does not contain at least one heads. Do you even conditional probability?

Bayes' theorem:

Let A = "both coins are heads"
Let B = "at least one coin is heads"

Probability of A = P(A) = 1/4
Probability of B = P(B) = 3/4

Probability of A GIVEN B =
P(A|B) = P(A?B)/(P(B)) = (1/4)/(3/4) = 1/3


1/3

Source: Washington University Math Department
http://courses.cs.washington.edu/courses/cse312/11wi/slides/04cprob.pdf

Pic Related: 1/3

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>>564358323
The probability of being given tits, for providing adequate support, happens to be 100%, however.

At least, personally/

lol @ all the 50% retards getting BTFO

>>564358598
do a process tree on this and you will see this

1st coin: lands on heads.... ok continue on to determine if both coins will land on heads... at this point you have a 50/50 shot. since it is implied at least on lands on heads this is valid.

2nd option: 1st coin lands on tails. at this point, you have a 0% chance of them landing on heads, yet the 2nd one may come out as heads, implying the initial condition.

the 2nd option is a reversal of the 1st with the outcome that one of them is tails.

so by realistic process, it is a 50% chance.

statistics does not necessarily work in the real life like how your little statistic theorems tend to imply.

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>>564357293
I bet you're shit at gambling

>>564357293
Your equation takes order into account, though. Order doesn't matter. Only two possibilities matter: if the coins are the same state or not.

So, either HH or HT. TH is the same as HT. 50%

>>564358598
and what you forget to account for in your little permutation process is that the outcome of the 1st coin determines the end result of probability.

before flipping the 1st coin, you have 25% chance. after your 1st flip, your chances then go from either 50% to 0. and since it is implied that at least one lands on heads, you cannot reach the 0%.

>>564359963
this guy at least gets it

File: probability_2coins_at_least_one_heads.png (30KB, 908x451px) Image search: [Google]

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>>564359537
>so by realistic process, it is a 50% chance.

No. Do the fucking experiment yourself, faggot. Get 2 coins, a pen and paper. FLip 2 coins as many times as you can. I recommend at least 100 times.

Write down the number of times you got at least one heads.

Write down the number of times you got two heads.

You will notice the 2-heads number will be approximately 1/3 of the 'at least 1 heads' number.

Do it. The more times you do it. The closer you get to 1/3

Or, you know, you could just write a program and simulate it.

Like this.

Pic Related: 1/3

>>564359963
Yes, but two different orders give the same result, so considering the orders as distinct saves the trouble of giving the heads+tails possibility a x2 weight.

File: tumblr_li68rkRi7w1qcbgjmo1_500.jpg (27KB, 500x363px) Image search: [Google]

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>>564356804
>if we have two 50% chances and remove one, what are we left with?

funny how /b/ can't do 2nd grade math ever

>>564359552

I'm not. But if you think the answer is 50%, then I would like to have a little bet with you.

Answer this question first.

2 regular coins were flipped. Tails-Tails was not the result. WHat is the probability that both coins landed heads?

>>564360112
You are so fucking stupid. You can literally code the thing and figure it out for yourself when you're older.

The two coin flips are already given. It doesn't say: flip one coin, record result. Move on only if it's heads. Fucking idiot.

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>>564359963
>Your equation takes order into account, though. Order doesn't matter.

All that matters are the probabilities. Because there are 2 equally probable ways to get one heads and one tails, and there is only one way to get both heads, getting both heads has a probability of 1/3,

HH - 1/3
HT/TH - 2/3

Answer = 1/3

ITT: People shit at math and logic

Pic Related: Punnet Square

>>564356804
Xeno's paradox says the chance is 0%.

OP is right fags. You are only embarrassing yourselves.

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>>564360112

You are so retarded I don't even know where to begin.

Did you even look at the link to the University of Washington Math Department?

There are lecture slides for simpletons like yourself who can't do a basic conditional probability question.

The answer = 1/3

Source: (See slide 4)
http://courses.cs.washington.edu/courses/cse312/11wi/slides/04cprob.pdf


Pic Related: 1/3

>>564360932
well realistically, if the end result was to get both heads, if someone was to flip tails on the first one, they would try again until the first one hit heads. because once they got tails on the first coin, they know that now they have no chance to obtain 2 heads

think realistically on this instead of some theoretical bullshit that would never actually apply to real-life scenarios. The reality of this is that they are trying to obtain 2 heads on the implication that at least one is heads. if they dont get heads on the 1st flip, then they know they wont reach it

>>564360860

I can't tell if you're genuinely retarded or trolling.

>>564357293
retard.. you forgot 2 no heads.

it would be 1/4 not 1/3 using your math.

which is consistent with 1/2 * 1/2 since the chance of two coins coming up heads if flipped once is 1/4.

since one is already flipped to heads, the answer to the op is 1/2 or 50%.

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Here's some simple R code for all the fucking retards who think "statistics does not necessarily work"

list=c()
for(i in 1:100000){
result=sum(sample(c(-1,1),2,replace=T))
list[i]=result
}
sum(list==-2)/sum(list>=0)

Simulates 100,000 coin flips. Tails are -1, heads are 1. Therefore -2 represents two tails, 0 represents some combination of 1 heads 1 tails, 2 represents 2 heads.

>>564361595
take your theory elsewhere where all chinks and ragheads sit behind a desk to solve problems that have no implication to real-life scenarios.

on the other hand, i will just go back to using my engineering skills to fix shit and design state of the art technology... something that permutations and probability will ever be able to do

they may give some insight to scenarios, but they will never tell you what will really happen in that one result

You're all dumb as fuck

>>564361830
The question is theoretical. You aren't answering the question. You are answering: given a heads ON THE FIRST FLIP, not just given at least 1 heads. You are ignoring the possibility that the heads could have been on the second flip, because remember, ORDER DOESN'T MATTER.

Christ, go back to high school.

File: coinsprob (2).jpg (15KB, 461x366px) Image search: [Google]

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>>564361830
>well realistically, if the end result was to get both heads, if someone was to flip tails on the first one, they would try again until the first one hit heads.

Dumbfuck, the flip has already happened and we are told that at least one coin landed heads. It could be EITHER coin.

3 equally probable outcomes containing at least one heads coin:

HH
HT
TH

HH is 1 of those 3

1/3

>think realistically on this instead of some theoretical bullshit that would never actually apply to real-life scenarios.

You are either retarded or just lack imagination. Here's how this scenario can happen in real-life.

You and a friend are in a room. You place a blindfold over your head. Your friend flips 2 coins. He tells you that at least one landed heads. Now you have to work out the probability that both landed heads. The answer, if you're not retarded and can do basic math, is 1/3.

What this essentially means is; if you and your friend continue to do this over and over and over again, the number of times you get both heads will be approximately 1/3 of the number of times you get at least one heads.

>if they dont get heads on the 1st flip, then they know they wont reach it

That's why you are NOT TOLD that one of the coins is tails, retard. Stick to the OP question.

Answer = 1/3

>>564362354

What the fuck are you talking about moron?

TT is excluded as we know we got at least one heads.

Answer = 1/3

Stay in school, kid.

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>>564362448

Oops, messed up greater than / less than. Fixed.

>>564362832
kid. the question is "what is the odds that a single coin flip lands on heads"

and your answer is 1/3... drop out of whatever school you are in right now

>>564362448
nigger you realize your code is implying tails tails is a possible result in your permutations (i.e. list==-2)

your R code is saying that for your 100000 flips, you have a 33% chance for tails tails to be the result for ALL possible combinations.

you forget to imply that you eliminate the possible combination of TT and the fact that at least one of them lands on heads

>>564357293
The fact you flipped a fucking coin before you flipped the second coin couldn't make any less difference to anything. If im sitting here and i flip a coin and you flip a coin and my lands heads does that change the out come of yours no you fuckwit op is such a faggot

>>564362693
this guy knows

lrn2stats /b/

It's 1/4

>>564363053
No, the question is "What is the probability of 2 heads given at least 1 heads"

>>564362492
>take your theory elsewhere
>theory

Nigger, are you actually this retarded? Are you telling me you don't know what a fucking mathematical theorem is?

Are there really people this fucking stupid on /b/?

>>564363082

No it doesn't. The denominator is only situations in which there was at least one heads. Check again, keep trying to wrap your head around this basic math problem.

1/3

>>564363053
>the question is "what is the odds that a single coin flip lands on heads"

No it isn't you fucking retard. Reading comprehension fail.

The question is;
WHat is the probability that both coins landed heads when at least one coin landed heads.

3 equally probable ways to get at least one heads

1 way to get both heads

1/3

>>564363505
> >=0

do you know what greater than or equal to 0 means?

the head-tail combinations are 0. your HH combination is 2, which would be included in your summation.

are you seriously this retarded?

You guys are all faggots..... It's 50%.
Look at it like this...

HH
HT
TH
TT

TT is out since neither is heads.
HT &TH are the same fucking thing so they equal one.
That leaves only two possible outcomes.
Therefore its 50% faggots
*drops the mics*

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>>564363765

See
>>564363045

Not that it changes the answer.
Here's a histogram for you. Taking into account only the -2 and 0 bars, what do the relative probabilities look like there? 1/3 are -2 (two heads) 2/3 are 0 (one of each).

>>564363097
>If im sitting here and i flip a coin and you flip a coin and my lands heads does that change the out come of yours

I never said it did. What the fuck are you talking about, retard?

I never said the result of one coin affects the result of the other. That would be retarded.

The answer is 1/3.

>>564363857
yes and no.

what these statistical niggers dont seem to realize is that once you 1st coin is flipped and it comes up as tails, there is a 0% chance of getting both heads, even given that the 2nd coin is flipped as heads

Does anyone remember the name of this fallacy? Just put a link to wikipedia so all the retards can understand.

>>564364068
again, your analysis takes into account that TT is a possible combination, which by OP's original problem statement, the TT combination is excluded

>>564363857
>HT &TH are the same fucking thing so they equal one.

Kill yourself if you are really this fucking stupid.

File: Proof.png (98KB, 1600x1200px) Image search: [Google]

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1/3. Here's proof

>>564364356

No, that's why we only use the two bars in which TT is NOT an option.

Good lord it's depressing that someone could have the answer someone presented to them correctly in so many different ways and still not understand.

>>564364081
piece wise probability begs to differ

keep on looking at this problem as a general probability question.

0%

Euros do not have heads.

>>564364356
It's not excluded. You just have to flip it again because you're not allowed to have TT
See>>564364556

>>564357293
>TH
>HT
not sure if retard or troll

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>>564364113

Do you not realize how retarded you are?

This is what you said:
>once you 1st coin is flipped and it comes up as tails, there is a 0% chance of getting both heads

Well isn't that fucking AMAZING. You can state the fucking obvious. Now tell me why you didn't state the following aswell;

>once you 2nd coin is flipped and it comes up as tails, there is a 0% chance of getting both heads

Oh wow, HOLY SHIT, can you fucking believe this?

If you flip 2 coins, and at least one of them is tails, that means you have a 0 probability that both are heads.

AMAZING. WHo would have thought.

I guess that's why the question mentions NOTHING ABOUT TAILS COINS, and simply states that AT LEAST ONE coin landed heads, moron.

3 equally probable permutations all satisfying the condition of having at least one heads coin:

HH
HT
TH

1/3

Stick to the question, idiots.

>>564359963
you're the one taking order into the equation.
the original question clearly stated that "given that at least ONE of the coins landed heads".

the only correct answer to the question is 1/3 probability.

>>564365335

Thank you for being able to use logic like you are above 13

>>564360395
>making a java program for this problem
>making a JAVA program for this problem
>making a java PROGRAMM FOR THIS PROBLEM
wtf dude

>>564364632
but annnnonn... this is a general probability question...

>>564364632

It's a conditional probability question, simpleton.

Go and try it yourself. Let us know how you get on.

>>564364867
well from what i see, you are dividing the amount of -2 (TT) by any amount that resulted in anything less than (or greater than from your first one) or equal to zero

what you are doing is you are dividing the total combinations of TT by TH, HT, and TT (or HH from your first)

tell me how that is not excluding the TT combination if you are having that in the numerator?

>>564365634
lol you can see who went to a shitty school for their discrete maths

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>>564364974
>>TH
>>HT
>not sure if retard or troll

For anyone who thinks that HT and TH are the same, read on;

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 = heads
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

or written another way

HH (1/4)
HT or TH (1/2)

Have we all got that now? The answer is and always will be = 1/3

Pic Related: 1/3

File: 1345885142795.jpg (71KB, 397x500px) Image search: [Google]

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Its 50% and 33%
Boy grill paradox

>>564365717

Again, see >>564363045

Just change it so -2 represents HH and 0 represents 1 of each and 2 represents TT. It is only HH divided by HH and 1 of each, as the question specifies.

The difference between tails being negative and heads being negative should not be causing you to scratch your head so much.

File: simulation.png (8KB, 613x465px) Image search: [Google]

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>>564356804
Here's another good one to troll with OP. Always causes a shitstorm,.
(the answer is B)

it's 1/3 if we presume the coins aren't biased towards one of the two possible outcomes, which in reality, they are.

File: coinsprobMatlab.jpg (66KB, 664x406px) Image search: [Google]

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>>564365634

Would you prefer C++, or Pythin, or MatLab, or fucking Excel?

The result is still 1/3

>>564356804
But a coin has three sides. It is possible for one or both to land in between heads or tails.
Now figure it smarty pants

>>564366386
should be A as the bottom path is a longer path right?

>>564366386

Explain the answer, son. I'm not a physicist.

File: balls slow mo2.webm (852KB, 288x288px)

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>>564366815
But the bottom path is faster.

File: image.jpg (139KB, 653x816px) Image search: [Google]

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>>564357293
HT and TH is the same thing you faggot

>>564366397
>it's 1/3 if we presume the coins aren't biased towards one of the two possible outcomes, which in reality, they are

Not sure wtf you are trying to say here. Elaborate so I can tell you how retarded you are and correct you.

>>564366572
give me some true c

>>564367365
>HT and TH is the same thing you faggot

Read simpleton >>564365915

>>564367054
Since there's no friction there is absolutely nothing to slow down ball B at all in the horizontal direction, so it speeds up going down hill. When it reaches the bottom, all of it's speed is converted into horizontal speed, and it pulls ahead. As it slows back down to it's original speed, it never loses its advantage.

>>564367172

How can friction on the top ball be ruled out as a factor?

>>564367389
He's being pedantic. Yeah, in reality, coins aren't totally perfect. Questions like this assume that they are.

Some people don't think statistics are applicable in real life. You'll find many of them in Vegas.

File: image.jpg (461KB, 920x1092px) Image search: [Google]

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>>564367562
What website did you find this on OP?

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>>564367395

Have some porn instead.

Porn shows the answer is 1/3

File: image.jpg (81KB, 398x455px) Image search: [Google]

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>>564368230
Blowjob Asslick
And
Asslick Blowjob
Is the same thing

File: coins_events.png (10KB, 501x348px) Image search: [Google]

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>>564368008

Ah yes. 51% chance for heads depending on certain factors etc.


Yeah, we're assuming a 1/2 probability of landing heads for the OP question, otherwise shit gets very pedantic.

1/3 guys. I proved it with Math

File: coining.png (263KB, 1400x1050px) Image search: [Google]

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>>564368230
>>564366572
>>564365892
>>564365335
i made a litte image for you

>>564368598
I can't imagine being as stupid as you

>>564368656
you ARE OP YOU SHITHEAD
>troll 4/10, made me make an image

>>564368067

I made it myself. It's a fairly common basic conditional probability question, anon.

>>564368907
Oh shit nigga, punnit squares i remember that shit

>>564368598
>Blowjob Asslick
>And
>Asslick Blowjob
>Is the same thing

Nope. One could give you a nasty infection.

>>564368857

I clearly said
>THE OP question

As in the question in the opening post, you stupid fucking nigger.

51% ;)

>>564365493
if we already have one on heads we are just flipping a single two sided coin so it's 50/50

there is no probability added if stating with 1 on heads is certain

>>564368675
That's not the question.

>>564356804
Intetionally ambigious troll question.
It asks you to work out the chance of something and also tells you the result, but with false tense.

Eg, the question "should" read 'What WAS the probability'.

'What IS the probability' of something that already happened is a nonsense.

It's just a troll. Both answers are right, or, wrong, depending on your POV....there is no definitely right answer because the question is flawed.

>>564369524
it is
and >>564369370
awaiting your reply

>>564368230
I think you tried everything OP, you should rest. They'll never understand. Not that I agree with you or anything...

>>564368675

Jesus Christ, you are retarded.

I'll try to make this as easy as possible for you to understand.

If you flip 2 regular coins, there are 3 EQUALLY PROBABLE WAYS to get AT LEAST ONE heads coin. These are as follows: (Pay attention)

coin1=Heads & coin2=Heads
coin1=Heads & coin2=Tails
coin1=Tails & coin2=Heads

1 of those 3 is both heads (HH)

1/3

Do you know what Bayes' theorem is?

>>564369869
But it's not. You said that, after flipping one coin, if it doesn't land heads, you abandon ship. That's not the question.

Here: I have two coins that add up to thirty cents. One of them is not a quarter.

What are they?

>>564369951
You've wasted way to much time trying to convince them by simply arguing. I would bet my hand many people agree with you, but are just trolling.

This is just another take on the monthy hall problem. Sources usually shut people up more than "what that other anon said" http://en.wikipedia.org/wiki/Monty_Hall_problem

>>564369448

Read the thread before posting next time.

>>564369916
>Not that I agree with you or anything...

You should, because I've given you the math. Agree with the math.

>>564369951
holy shit, bayes has nothing to do with this
I SAID THERE IS NO THING LIKE COIN 1 AND 2 YOU RETARD

>>564370428
>>564370428

You're probably right, but I'm drinking the last of my beer before having a fap so I have a few minutes to waste anyway.

>>564370623
I was just being a tsundere.

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>>564370680
>conditional probability question
>Bayes' theorem has nothing to do with this

Oh my...

>>564371115
this time, I'm not sure if you're being trolled or if he's really a moron. probably both

>>564369951
That's the answer to the question: "You flip two coins, in the cases where at least one lands heads, what's the chance of two landing heads?"

The problem with OPs question is part of it is essentially asking: "You flip a coin and get heads, what are the chances that you got heads?"

Is that 50% or 100%? I don't know, and neither do you...it's nonsense.

I really hope anyone not answering 1/3 is trolling

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>>564356804

>>564371337
>part of it is essentially asking: "You flip a coin and get heads, what are the chances that you got heads?"

WHAT?!?!?

How could you interpret...

What?

I

I don't even...

>>564371337
No it's not.

Obviously you're too retarded to handle coins, so I'LL flip the coins, out of your view.

I flip one coin.
I flip the second coin.
Now I tell you that, this time, at least one of the coins came up heads.

This is all you know about the coins. I don't tell you if the first one came up heads, or the second one came up heads. All I told you is that, of the coins I flipped, this time I have at least one coin that came up heads. Was it the first? The second? I don't give you that information.

Here's a similar problem:

Let's say I flipped two coins (without cheating) and hid them from you. What would be the probability of having two heads?
50% * 50% = 25%
Let's say I lift one of my hands, showing you a head. Now what's the probability that the second coin is head?
If you say 50%, you're wrong. Telling you that there's at least a head doesn't increase chances of getting two heads. The coins are still the same. Telling you something shouldn't have any impact on luck. So it would still be 25%.

>>564371953
haha, same thought process here

>>564372140
Monty fucking Hall.

I've seen threads like this before but never seen people not understand it this fucking hard.

>>564371723
It's a troll question dude (have you not been here before?)

It says two fair coins were flipped but also that one of them landed heads. Not IF it landed heads, or WHEN it lands heads....or anything like that. It guarantees the outcome of something it also says is a 50/50 chance. Self-contradictory nonsense.

The people disagreeing with you don't not understand probability (though, mebe they do), they just interpret the question differently.

No-one is arguing with the maths, they're arguing about whether or not bayes theorem applies....because the question is intentionally ambigious as to whether or not "coin 1" is definite heads, or just one of two coins at least one of which happened to land heads.

>>564372140
>Let's say I flipped two coins (without cheating) and hid them from you. What would be the probability of having two heads?
>50% * 50% = 25%
This is correct.

>Let's say I lift one of my hands, showing you a head. Now what's the probability that the second coin is head?
>If you say 50%, you're wrong.

This is incorrect. The answer to that actually is 50%.

The answer to the OP question is 1/3

>>564372565
It's not ambiguous. It's just saying that, when these two coins were flipped, both did not come up tails. It is in no way ambiguous.

>>564371953
>this time

And there's the difference.

No-one is arguing the maths, it's just different interpretations of a question POSTED ON B intentionally designed to illicit different interpretations, and have people argue for ages about maths when they're not even disagreeing about maths.

>>564372690
Yeah. I just realized I fucked my own logic. You could have provided an argument for saying I'm wrong though.

Let's say I "told you" one of them was a head instead of lifting my hand. Then it would be true, 25% chance.

>>564357578
Wrong. it should look like.

Two Random Flips. Order is insignificant
H H - 1 possible outcome
H T - 2 possible outcomes
T T - 1 possible outcome

Where 1 is explicitly known in this case H; we take a derivative.
H H
H T
H T
T T

One must be heads; that entirely eliminates T T;

Since we know one is heads, we must pay careful attention to order. Each individual outcome had 25% before heads was known but that's different now because one is known to be heads; it can be reorganized to prioritize the fact that one is heads therefore the other has X% chance to be tails.

H H - 50%
H T - 50%
T H - Eliminated; First outcome not heads.
T T - Eliminated; First outcome not heads.

You cannot make the argument that both are flipped at the same time because it is known that one must be heads. It's not predetermined. it is known after the flip. 1 is heads; therefore what is the chance that the remaining coin is also heads. It is 50%

>>564372946
It is. It obviously is...have you not noticed the whole thread of people arguing about it?

You don't think it is because you've interpreted it the more common way (at least for maths students), and have spent ages arguing & cementing it in your mind.


Consider the following two questions (assume gender genetic is 50/50 and totally random).

Q1:
I am male.
What was the chance that I was born/conceived/developed/whatever male?
Q2:
I am male.
What is the chance that I am male?

>>564373092
The question says

>given that at least one of the coins landed heads

not

>given that at least one landed heads

Again, it says
>at least one OF THE COINS

Not Coin 1.

>>564373585
You are arguing a grammar error when the statistics are correct.
>die in a fire plebian.

>>564373483
I interpreted it the right way because I studied writing, not math.

There is nothing in the question that suggests the "first" coin is heads.

>>564356804
I'm going to write a simple program. Paste the logic I used here for the calculations, and the post the results after a large number of iterations.

>>564373808
I am arguing that, grammatically, the question is not ambiguous, and the answer is absolutely 1/3.

>itt: gambler's fallacy

>>564373024
>Then it would be true, 25% chance.

Nope, it would be 1/3

50%

>>564373483
i agree with most what you say, but i dont think there is any way how the bayem theroem could apply. i tried to get to the other point of view and everything was pretty clear, until the point a table came in. the table named coin 1 and coin 2. i dont think you can do that because they are identical. ONE lands on head. which is not important. it cant be, because that would mean the coins wouldnt be tossed at the exact same time and so can be differed. it also depends on the way you do it. do you throw away one coin because it doesnt matter? do you eliminate the tail tails and add up the others? or do you throw coin 1 and.. wait, that isnt even possible. it cant be 1/3 in reality, no way how you do it

>>564373092
>H H - 50%
>H T - 50%
>T H - Eliminated; First outcome not heads.

TH is valid. It satisfies the condition of having at least one heads coin.

HH
HT
TH

1/3

>>564357326

100 %.

>>564356804
50% because you have reduced it to 1 coin dumb fucks

>>564374704
that is the problem i just told about. what reason do you have to differ TH and HT?

>>564374518
Again, you're right. Damn my logic is failing me tonight. See, it's a confusing subject anyways ^^

Case 1: HT
Case 2: TH
Case 3: HH
Case 4: TT

I stated that 4 didn't happen, so I eliminated a possibility. So it's indeed 1/3. I am ashamed

>>564374660
Why are we throwing single coins away? There is no single coin, on its own.

Just imagine both coins are flipped simultaneously.

>>564373926
>>564374156
Yeah well, unfortunately for you English does not have exact right & wrong answers like maths. The question is obviously ambiguous as so many people interpret it differently. That's how English works. That's why the usage of words like 'meme' & 'beta' on 4chan isn't "wrong".

>>564374660
The other people are interpreting the question as something along the lines of. "calculate these odds ignoring cases of double-tails."

>>564374942
Then if they're the same, why eliminate TH?

>>564361830
>realistically
This is a theoretical probability problem. Realistically, you can't interpret a word problem written at a fourth grade level, let alone comprehend the FIFTH grade math behind the problem itself. I understand if you're a little confused, maybe dizzy, have a headache. These are normal symptoms of being too stupid to comprehend your own consciousness. It's a very serious condition, and you should seek treatment immediately in the form of remediation beginning with the third grade to be safe, and continuing through high school. You'll need to earn your GED from a public or private institution for the clinically retarded. This should fix most of your daily life problems as well.

>>564375106
You don't have to be exactly wrong to still be wrong.

Just because some people misinterpreted the question doesn't mean the question is flawed, it means that some people are bad at reading comprehension.

>>564375082
>Just imagine both coins are flipped simultaneously.
For him, this is difficult, because one coin is guaranteed heads....so imagining a fair flip with a guaranteed outcome is....a contradiction?

>>564375082
okay, then i throw them both now:
let me give you some examples:
one is head, one is tail 1:0 for not both head
both are head 1:1

both are tails 1:1 i eliminate the result

and >>564375231, thats why

>>564375843
as you see, you cant have it given that you throw them simultaneously

>>564373092
>>Order is insignificant
Sure. Time doesn't matter.

>>HH - 50%
>>HT - 50%
>>TH - Eliminated
Wait, didn't you just differentiate HT and TH? Contradiction much?

Order doesn't matter indeed. But there are two coins, not one. What if a coin was red and one blue?

blueH, redH
blueT, redH
blueH, redT
blueT, redT

The probabilities should be the same even if the coins are different colors. But suddenly you can't ignore the fact that blueT,redH isn't the same as blueH,redT.

>>564375490
>Just because some people misinterpreted the question

Who is to say you are not in the group that misinterpreted the question?

Of course YOU think you're right, that's...tautological. But no way in hell can you prove it.

The fact that the question is often interpreted two conflicting ways is, by definition, evidence of it's ambiguity.

>>564375560
It's not guaranteed. The event occurred, and now, I am telling you that, in this particular event, there is at least one head.

Think of it this way. I'm going to flip two coins at the same time, and then I'm going to give you some information.

I flipped them. Both are tails, so never mind.
I flipped them. Both tails again.
I flipped them. Ah! This time, I can tell you that at least one of the coins came up heads. What are the odds that they BOTH came up heads?
>You answer
Now, let's do it again. I flipped the coins. Oh, this time, they both came up tails again. Let's try again...

and so on.

>>564361263
HT=TH

So lets take an example you flip the coins one at a time. Before you flip the odds are 1 in 4 that they will both be heads. You flip the first coin which comes up heads. So you have H_. When you flip the second coin the odds of it coming up heads is 50/50 so there is a 50% chance of HT and a 50% chance of HH.

I don't get how people could be this dumb.

Correct Answer: 1/3
If you flip 2 coins and T-T is an eliminated result, there are 3 possible results, thus a 33% chance for H-H.

Correct Answer: 1/2
If one of the coins must always be heads. This eliminates T-T as a result, and implies 1 coin is fixed to land on heads, thus the result for H-H is determined on the flip of only ONE of the coins (50%), as the other must absolutely land on heads.

>>564376261
Why does the first one have to come up heads?

>>564374942
>what reason do you have to differ TH and HT?

They are two separate and distinct results, each with their own probability.

Read this >>564365915

>>564376087
Yeah, you're just writing down your interpretation of what OP is asking, and those that disagree with you are thinking "That's not what OP says".

Surely it isn't difficult to see why some people think the phrase "at least one of the coins landed heads" guarantees that at least one of the coins is heads?

>>564376261
>HT=TH

No, they are not the same. You can't be this retarded.

Read this post >>564365915

>>564376295
best answer here, but thats also the greates problem

>Correct Answer: 1/3
>f you flip 2 coins and T-T is an eliminated result, there are 3 possible results, thus a 33% chance for H-H.

T-T is in reality still a probality, even if its elimated. so it can still occur and there is still a total probality of 25%. because of that, it makes the difference between HT and TH wayne and elimates it too

>>564376261
HT means that the coin A had heads and coin B had tails. TH means that the coin A had tails and coin B had heads. Two different events, both with their own probability.

There are 4 possibilities (HH, HT, TH, TT) all equally probable (so they each have 1/4 probability). Let's flip them. Oh, well I can tell you that TT didn't happen. So there's only 3 possibilities left (HH, HT, TH) so they each have 1/3 probability. What is the probability of HH? 1/3

>>564376496
Because "given that" means "in this instance".

>>564376027

Exactly. The answer is 1/3.

People thinking that HT=TH are not thinking logically.

They both give a one heads - one tails result, but are two distinct permutations, each with their own probability.

File: sheeeit.jpg (215KB, 1268x773px) Image search: [Google]

215KB, 1268x773px

Guys guys.

I made a program and did the calculation after 1 million simulations.

It's 1/3

This is the code for replication; I did mine in C# with a button and a label.

I admit I was wrong.

>>564377074

Good explanation.

>>564377646
>coin1
>coin2

>>564377874
I'm not understanding your problem.

Is _1 and _2 too mentally wrecking for you?

>>564377085
That's how you're interpreting it in this instance (ha). It isn't a given (ha).

And arguably still doesn't solve the problem.

>>564377646
Yeah, put it into code, that'll help.


OPs question implies that two fair coins are flipped but the outcome is partially guaranteed, which is a contradiction. No amount of maths or code'll help that.

>>564377831
i finally think you are not a troll and so im ready to discuss with you. so please read >>564376295 and >>564377056
and tell me your meaning about it. please no differating between coin 1 and coin 2, they are the same..

>>564376658
If HT=/=TH, this implies the coins are not identical. If the coins are not identical and one must be heads, this further implies one coin is incapable of being tails and the result of H-H is dictated by one coin alone. Thus a 50% chance.

>>564378169
Are you retarded?

Code definitely helps that.
One coin is heads; code checks to see if one coin is heads if not, reflip because we need at least one heads.

Now that we a coin that is heads are both heads, if so +1, else loop again, increment total rolls.

>>564378092
please read >>564377056
>>564376295
and >>564375843
too. this code wont help because it gets the random independantly and thats the cause for this result

If one lands heads then it can be safely nullified from the equation.

P(0.50) * P(0.50) for both heads,

But if one hands heads always then...

P(1.0) * P(0.5) = P(0.5)

So 50%...

But we really shouldn't need to explain that, retard.

>>564378092
Try labelling them
"the at least one coin that is heads"
and
"the other coin"

>>564378468
HT=/=TH doesn't imply they aren't identical. It implies they aren't the same coin.

Everytime someone calls us retards on the thread, it boosts my self-esteem. It was great thinking and debating with you guys, but those of you who don't agree with a computer's result will never agree with anything, and I believe this conversation is dying. Good night!

>>564378545
Wrong again, this code is perfectly fine.

T T is not a result because one of the coins is heads therefore T T is undefined.

The code checks to make sure one coin is heads; if both coins are tails, the entire flip is ignored because they aren't allowed and the flip happens again with 2 random coin results.

As soon as it determines that one of the coins are heads, it tries to determine if both coins are heads.

33.3% yolo

>>564378545
oh fuck, sorry. we both are retards.
you stupid fuck didnt count anything on head head. of course this shit gets on 33% because you made three ifs with one count up. it isnt differed between head head and tail tail

>>564357293
Actually, I retract my 50% statement, I forgot to impletement the other possiblity or 1H1T.

This guy wins, everone else go home.

Bayes Theorem, retards.

No, Gamblers' Fallacy, retards.

I'll write code to simulate Bayes Theorem.

Yeah? Well I'll write code to simulate Gamblers' Fallacy.

My code says ~1/3, suck it moran.

My code says ~1/2, eat shit.

You're a retard!

No, you're a retard!

Retard! retard! retard! retard! retard! retard! retard! retard! retard! retard! retard! retard! retard! retard! retard! retard! retard! retard! retard! retard! retard! retard! retard! retard!

>>564379185
>>564378960
btw, C rules, i like you

Don't believe me? Try this shit yourself
>>564378960

Take two coins and flip them around 40 or so times. Each time you get both tails, ignore it and flip it again more times. After 40 or so non TT Flips, how many times were both heads; the answer is 33%

>>564356804
Possible outcomes are
TT
TH
HT
HH

Given that at least one of them is heads, possible outcomes are
TH
HT
HH

Therefore, the probability that both of them landed heads is 1/3.

>>564379380
Flip a fair coin and a double-headed coin 40 or so times.

>>564378960
int total_headhead;
in total_headtail;

if (_1==1 || _2 == 1){
if(_1==_2) total_headtail++;
else total_headhead++;

>>564379809
that's backwards bro.

if (a == 1 || b == 1) {
>>if (a == b) totalHH++;
>>else totalHT++;
}

>>564380076
give code and tell if i was right

>>564378169
>OPs question implies that two fair coins are flipped but the outcome is partially guaranteed, which is a contradiction.

It was never guaranteed, it's simply partial information about the result.

What are you having trouble with. There is no contradiction

>>564379746
But that's the same as saying: If coin1 is always heads, what's the probability of coin2 being head. That's not the question OP asked.

>>564379451
This guy is still at this? Its been like 2 hours

File: 1370658503613.gif (2MB, 360x256px) Image search: [Google]

2MB, 360x256px

LOL so many retards with their 33%...

The real answer is 50%, trust me.

At least one coin lands on head so we already have H

The second coin can either land on H or T.

So the only 2 possibility is HH or HT, that makes 50%.

HT = TH, SAME DAMN THING.

File: sheeit2.0.jpg (186KB, 1271x771px) Image search: [Google]

186KB, 1271x771px

>>564379809
Also, same result dude.

>>564357293
u sir, r r-tarded. its 50%

>>564380616
This guy knows whats up

>>564378254

2 regular coins were flipped.
At least one landed heads.

Only TT is no longer possible. 3 valid and equally probable outcomes remain, each satisfying the condition of having at least one heads.

Both heads is 1 of those 3.

1/3.

Why would you think I was trolling?

I even provided the Math and a Washington University link.
http://courses.cs.washington.edu/courses/cse312/11wi/slides/04cprob.pdf


Answer = 1/3

>>564380843
>Given the one is heads, that one is out of the question, it has happend. Then the only question comes with the second coin. said coin has 50/50 chance therefore 50%

>>564380616
They are the same thing, however, it's still 33%. Look at my code.

>>564380427
Partial information about the result is a partial guarantee of the result. At least one coin will come up heads....so it can't be a fair flip of two coins, if it was, there would be a chance for no heads.

>>564365634
>Thinking writing 25 lines of code is a lot of work
wtf dude

>>564378468

Oh Jesus. Read this anon's post >>564378643

>>564380897
TH can't happen because the first coin is already H given the problem statement

>>564356804
74%
Coins always land on tails more then heads.
Given one coin always lands on heads 50% given the other one has a 50/50 that's an extra 25% add in the variable that heads is always lower then heads you get 74

>>564357159
wtf is a trick questoin about that.
Is the trick about reading a question to its end?
This is not a trick question it is an adhd pitfall
A trick question needs at least one step in mind that can go wrong.
If you just wipe otu half of the equation at the end of the sentence its not a trick.
>Op confirmed faggot and idiot the same time.
>Well done

>>564378551
>If one lands heads then it can be safely nullified from the equation.

Which one?

Both coins are variables as either of them could be tails, just not both.

3 equally probable permutations:

HH
HT
TH

1/3

File: tombstone-4.jpg (32KB, 500x318px) Image search: [Google]

32KB, 500x318px

Bomp

>>564367365
Go read up about the binomial theorem, then come back and feel stupid.

>>564379451
33% should be the correct answer. However, eliminating/ignoring T-T results is basically the same as confirming coin A will always be heads (this way T-T is an impossible result). With coin A as heads, there is a 50% chance coin B (and both coins together) will also be heads.

Probability of H-H?
1/4 correct
1/3 correct neglecting 1/4 of the results (T-T)
1/2 correct with the absolute of one coin being heads

>>564380778
give me how you got the percent etc.just the complete fucking code...

>>564380897
>Suppose you flip two coins & all outcomes are >equally likely.
>What is the probability that both flips land on heads if...
>At least one of the two flips lands on heads?

Yep, Bayes Theorem. No doubt.

OPs question however, is MUCH closer to

"You flip two coins and at least one is heads
What is the probability that both are heads?"

>>564379254

Gambler's fallacy doesn't come into the OP question.

The answer of 1/3 does NOT contradict the gambler's fallacy.

You should know this.

>>564381682
It does for some people, it's an ambiguous question.

>>564381043

Real code should be:

//One coin always lands on H
var coin1 = head;

//Second coin lands on either H(0) or T(1)
var coin2 = (Math.random()*9999)%2;

console.log(coin1,coin2);

Answer will always be HH or HT, thus 50%.

>>564381397
It's not basically the same. "at least one of the coins is heads" is a different statement than "coin A is heads."

File: andrew_frey.png (258KB, 609x548px) Image search: [Google]

258KB, 609x548px

The probability of at least one landing heads is 3/4. The probability of both landing heads is 1/4. Multiplying them together gives 3/16, which is the correct answer.

>>564381052
>At least one coin will come up heads
>will come up
>will
>in the future

Are you trolling or do you genuinely have difficulty with reading comprehension.

The coins were ALREADY FLIPPED and you are told that AT LEAST ONE coin LANDED heads.

Where is the contradiction?

Have you never heard of conditional probability?

>>564381493
This is the complete fucking code.

I randomized two coins.
I checked if either coin was heads with
>>if (_1 == 1 || _2 == 1) {

If neither were heads [both tails]
iTT++;

If both were heads; increment.
>>if (_1 == _2) iHH++;

otherwise it's a heads and tails.
>>else iHT++;

Loop 1 million times.

After the loop.
iHH / (Number of total valid results)

A valid result is anything NOT TT because one coin must be heads. Therefore the sum of iHH and iHT are valid results.

iHH / (iHH + iHT);

Result is ~0.333...

>>564381207
>TH can't happen because the first coin is already H given the problem statement
>the first coin is already H

Nowhere in the question does it say that the FIRST coin is heads. It says AT LEAST ONE. It could be EITHER coin.

HH
HT
TH

1/3

>>564381998

It IS the same. Learn 2 logic...

>>564382175
where did you read a pseudo? i dont know, make pics, use github, dropbox, i dont care

>>564382083
>The coins were ALREADY FLIPPED and you are told that AT LEAST ONE coin LANDED heads.

That's even more problematic.
See eg, Q1/Q2 in
>>564373483

>>564382175
Note; it takes into account both HT and TH outcomes; therefore iHT accounts for roughly 50% of all rolls, TT for 25% and HH for 25%.

>>564381645
>>What is the probability that both flips land on heads if...
>>At least one of the two flips lands on heads?

That's what happens in the OP question.

The answer is 1/3.

What's the issue?

>>564382383
where did I read a pseudo?
I don't understand the question, please repeat in moar english.

>>564382703
>pseudocode
i dont want that shit, i want the .c file

Lets try something simple.

OPs scenario: Bayesists; calculate the probability of TT.

File: +rubber_ripley.gif (1MB, 269x151px) Image search: [Google]

1MB, 269x151px

>what is the probability that both coins landed heads
1/4
>given that at least one of the coins landed heads
If both are heads, then this statement is always satisfied. It's just there to confound the problem. The answer is 1/4.

It's 1/4. You people are thinking too deeply about the question. The second statement is necessarily true if the first one is.

File: coinss.jpg (119KB, 1600x900px) Image search: [Google]

119KB, 1600x900px

>>564381909
>it's an ambiguous question.

It's a basic conditional probability question; a fairly common one, and it's written in a clear and concise manner. It has a correct answer.

The correct answer = 1/3

This answer can be proven and demonstrated using
>Bayes' theorem
>Punnet squares
>Probability trees
>computer simulation
>physical experimentation
>venn diagram

Pic Related: 1/3

>>564381998
At least one of the coins is heads = coins are not T-T

T-T: impossible
T-H: at least one coin is heads
H-T: at least one coin is heads
H-H: at least one coin is heads

T-H: one H one T
H-T: one H one T
H-H: two H

Two possible results:
1: one coin is H, one coin is T
2: two coins are H

>>564382863 I already gave it to you in that image. that's all the code. It's not that fucking hard.

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Windows.Forms;

namespace Two_Coins_One_Head
{
public partial class Form1 : Form
{
public Form1()
{
InitializeComponent();
}
private const int _iSIMS = 10000000;
private Random randVal = new Random();

private void butGo_Click(object sender, EventArgs e)
{
int iHH = 0;
int iHT = 0;
int iTT = 0;
double myPercent = 0.0;
for (int i = 0; i < _iSIMS; i++)
{
int _1 = getRandomInt(0, 1);
int _2 = getRandomInt(0, 1);
if (_1 == 1 || _2 == 1)
{
if (_1 == _2) iHH++;
else iHT++;
}
else iTT++;
}
//Display info in the label.
myPercent = (double)iHH / (double)(iHH + iHT);
lblResults.Text = "Results: " + myPercent.ToString("P2");
}

private int getRandomInt(int Min, int Max)
{
return (int)((Max - Min + 1) * randVal.NextDouble() + Min);
}
}
}

>>564382339
They aren't. Flipping one coin and flipping two but ignoring TT are not equivalent.

In the case of "Coin A is heads," the possible outcomes are
HT
HH

In the case of "at least one coin is heads," the possible outcomes are:
TH
HT
HH

In outcome set 1, HH is probability 1/2. In outcome set 2, HT is probability 1/3.

Try flipping coins sometime.

>>564382961
It's also a basic (and common) example of gamblers fallacy.

It is ambiguous, the frequent arguments ITT (which is reposted a lot) between gamblers & bayes is irrefutable proof of its' ambigiuty

File: not_podracing.jpg (53KB, 444x337px) Image search: [Google]

53KB, 444x337px

>>564383146
>lists three possible results
>Two possible results:

>>564382409

There are two coins. Your 'I am male' analogy doesn't work here.

There are two children. At least one of them is a boy. What is the probability that both are boys?

>>564383182
going to work, brb

This is where math fails. Math says 1/3 but it's 1/2 if you think about it logically.

>>564383146
Yes, and if you ignore TT, HT occurs with 2/3 probability.

Just to confirm: The people who don't think it's 1/3. They're just trolling right? They're not really that thick.

>>564383416
HA!

VICTORY!

That exact phrasing of the problem has been confirmed as ambiguous by far better people than you.

https://en.wikipedia.org/wiki/Boy_or_Girl_paradox

>>564383371
>It's also a basic (and common) example of gamblers fallacy.

No, it isn't.

The gambler;s fallacy is thinking that the result of one coin affects the result of another or affects the next flip.

The OP question has NOTHING to do with the Gambler's fallacy. It does NOT contradict the gamber's fallacy. It is a basic conditional probability question.

2 regular coins were flipped. All possible outcomes are;

HH
HT
TH
TT

At least one landed heads. Only TT is now excluded;

HH
HT
TH

Both heads (HH) is 1 of the 3 remaining EQUALLY PROBABLE outcomes.

1/3

>>564383847
Everyone who responds to this vague question is trolling/trolled. There is no correct answer because the question is malformed.

>what is the difference between a duck

>>564383394
>2 possible results (1H+1T, 2H)
>that's 3 results!

wtfamireading.jpg

>>564383371
>the frequent arguments ITT (which is reposted a lot) between gamblers & bayes is irrefutable proof of its' ambigiuty

>nobody but you is arguing anything about the gambler's fallacy, this is because you don't understand the OP question and how it is unrelated to the gamber's fallacy.

The reason people disagree is because some people are idiots and some people can actually do proper math.

Bayes' theorem and the gambler's fallacy do not contradict each other. they BOTH support the correct answer of 1/3.

>>564384286
That's like saying a red grape and a green apple are the same as a green grape and a red apple.

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>>564360872
question ignored. Tails then heads is not a valid flip since the first was heads. Leaving with a 1/2 chance of the next being either heads or tails. we already know the outcome of the first, so the second is totally independent. making it 50/50. any other answer is incorrect

>>564383448
v0.5

#include <stdio.h>
#include <stdlib.h>

int main()
{
int iHH = 0;
int iHT = 0;
int iTT = 0;
double myPercent = 0.0;
for (int i = 0; i < 1000; i++){
int Coin_1 = rand()%2;
int Coin_2 = rand()%2;
if (Coin_1 == 1 || Coin_2 == 1)
{
if (Coin_1 == Coin_2) iHH++;
else iHT++;
}
else iTT++;
}
//Display info in the label.
myPercent = (double)iHH / (double)(iHH + iHT);
printf("Results: %lf" ,myPercent);

return 0;
}

>>564383560
If by HT you mean 'one coin heads and one tails', you are correct, sir. This also gives us the result that with 66% of the flips being one heads and one tails, 33% would be H-H. It also confirms that there are only two possible results, thus "50%", even though one result is twice as likely.

>>564383936

Read the article, son.

>"Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys?
This question is identical to question one, except that instead of specifying that the older child is a boy, it is specified that at least one of them is a boy. In response to reader criticism of the question posed in 1959, Gardner agreed that a precise formulation of the question is critical to getting different answers for question 1 and 2. Specifically, Gardner argued that a "failure to specify the randomizing procedure" could lead readers to interpret the question in two distinct ways:

From all families with two children, at least one of whom is a boy, a family is chosen at random. This would yield the answer of 1/3.
From all families with two children, one child is selected at random, and the sex of that child is specified. This would yield an answer of 1/2."

Protip: If one coin or child is SPECIFIED, that's when the answer becomes 1/2

For example:

2 regular coins were flipped. The first coin landed heads. What is the probability that both coins landed heads?
Answer = 1/2

Similarly
There are two children. The older child is a boy. what is the probability that both children are boys?
Answer = 1/2

When NO child or coin is SPECIFIED (this is the same as the OP question), the answer = 1/3

For example:

2 regular coins were flipped. At least one coin landed heads. What is the probability that both coins landed heads?
Answer = 1/3

Similarly
There are two children. At least one child is a boy. what is the probability that both children are boys?
Answer = 1/3

Read the entire article next time.

1/3

50%

>>564384476
1/10

>>564384519
>Tails then heads is not a valid flip since the first was heads

The question never says that the FIRST coin landed heads, you fucking retard.

1/3

Wait a minute, those aren't regular coins, they're Euros.

>>564383945

You've been here for 3 hours arguing about a math problem. What the fuck is wrong with you?

>>564385237
....

Yeah, and that phrasing, that EXACT phrasing you used, is ambiguous as to which it is.

There are quite a few really high quality refs for it.

You're.....doing the same thing again. Like there's something seriously wrong in your head. Many many many highly intelligent people & mathematicians & universal acceptance that phrase is ambiguous, and you're saying "no it's not because here's my interpretation".

Have you been prescribed some sort of medication?

>>564385641
1/10 doesn't even make sense for odds.

>>564385237
This guy gets it.

>>564385236
>This also gives us the result that with 66% of the flips being one heads and one tails, 33% would be H-H. It also confirms that there are only two possible results, thus "50%", even though one result is twice as likely.

So HT/TH is TWICE AS LIKELY as HH (66% vs 33%), but it's still 50% you'll get HH?

So 33% = 50%?

What the fuck am I reading?

ok, fuck this shit. i respect your code, but i dont think it is right. well, i admit i cant tell because its fucking 6 am here and my head hurts and stuf... i will do it tomorrow, now i will go to sleep. give me email or whatever shit and i will send you my code. also i will start a new thread with it and playing faggot op

>>564385868
>Yeah, and that phrasing, that EXACT phrasing you used, is ambiguous as to which it is.

It isn't. NO coin was SPECIFIED. At least one coin means EITHER coin.

It's not ambiguous, you stupid fuck. It's right there in the article. Read it. It tells you which phrasing and conditions results in an answer of 1/2 and which phrasing and conditions results in the answer of 1/3.

I quoted the fucking article and provided examples in my previous post.

It's not ambiguous. People are simply fucking retarded and lack reading comprehension and basic math literacy.

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Today I learned that /b/ will take on mathematical paradoxes like they raped its mother.

/b/ conquers

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>What is the probability that both coins landed heads
Ignore the rest. It's 1/4.

My code gives me 50% chance that both land on H.

justpaste DOT it / gsl0

AS I SAID: LEARN 2 LOGIC...

Post your code here and I'll tell you where you've gone wrong.

>>564386092
Nope. 50% = 1 of 2 results.

>>564387419
oh god, please tomorrow...
>>564387594
go to bed, your brain is tired too, he already did, look again

My code is on justpaste DOT it / gsl0.

i set the appoointment to exactly in 14 hours. i will be here and make the thread

>>564387710

2 results does not mean they are equally probable.

I buy a lottery ticket.

There are two possible results:

Result 1: I win the lottery
Result 2: I do not win the lottery

Do I have a 50% chance of winning the lottery?

>>564387852

Paste it here. I'm lazy.

No, the probability of HH is 1/2 that of HT. If you try it 100 times, 33 will be HH and 66 will be HT

>>564388215

I tried but it doesn't let me.

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>>564388497
>If you try it 100 times, 33 will be HH and 66 will be HT
>66 + 33 = 100

I jest.