How smart is /b/?

doesn't matter what anyone says. As soon as someone comes along with the right answer OP and others are going to sperg out and claim that they're wrong.

>>724809531
...%50? No idea

50%

>>724809855
>>724809877

Nice dubs, but both wrong.

>>724809741
I don't sperg out. i give the right answer and then call the other anon retarded for not understanding it.

50%

1/3

>>724809994
you just claimed that both of those anons were wrong and proved my point

1/4

>>724809531
Out of the 4 possible states, one is removed, leaving 3 possible states, one of which is the condition for the answer.
1/3

>>724810089

That's because they're wrong. No sperging out necessary. Your point is invalid.

>>724810175
oow sorry thought how big is the chance the both got head

75%

the question is what is the probability of both coins landing heads, if it were a single coin it would be 50%

>>724810485

Answer the OP question

>>724809531
1/3

4 possibilities
TH
HT
HH
TT


Given that one landed H, the TT is eliminated

Would go for 1/3

Outcomes for coins:
heads heads
tails heads
tails tails

33%

>>724810623
TH and HT are the same

>>724810658
>TH and HT are the same

No, anon. They are not.

>>724810623
This is not how reality works. The question is basically "what's the probability of getting heads on one coin" since the other has already happened and >>cannot affect the other coin<<

>>724810658
It's taking into account each coins as a separate entity. As either one of the two is guaranteed to land on heads you have to take that into account.

It's 1/3

>>724809531
this was a problem on my last stats test
lel
this nigga thinks learning a simple formula makes someone smart

25% perhaps? If both coins have a probability of 50% each then after two flips they would both have landed heads I guess.

>>724810658
TH and HT are not the same. IF you want to combine those two results into one, you have to combine their probabilities as well.

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

>>724811041

At least 1 landed heads.

TT
TH
HT
HH

If the first coin is heads, the full outcome is either HH or HT, so 50%
If the first coin is tails, HH can't be achieved so 0%

Daft question that requires fiddling with probability in a way that makes an actual answer impossible

It doesnt matter because they are euro's and they are worthless.

>>724810983
this fucking reeks of verysmart

>>724810983
You're missing the point, faggot.
It's not that being able to give the correct answer means you're smart.
It's that being unable to give the correct answer means you're stupid.

If at least 1 landed heads then we only care about the other coin. And that coin has a ~50% chance.

So about 50%

>>724811214
So a two coins flipped independently will affect each other?

>>724811135
what is conditional probability?

>>724811135

It's a basic conditional probability question.

When you flip 2 coins and at least 1 coin lands heads, you could have

heads, tails
or
tails, heads
or
both heads

All 3 are equally probable.

1/3

>>724811349
Doesn't matter, the entire thing depends on the first coin and leads to two different answers, so there realistically and usefully is no answer

>>724809531
A & B happening: 1/4
A happening: 1/2

B happening given A: 1/2(A) X 1/2(B) = 1/4 , ans.
It is a simple branch

File: 1488797756587.gif (912KB, 291x316px) Image search: [Google]

912KB, 291x316px

(heads/tails)*(heads/tails)=

1/2*1/2=1/4

>>724811397
you forgot both are tails xD

>>724810865
That's how reality work.
Should read about monty hall problem
https://en.m.wikipedia.org/wiki/Monty_Hall_problem

The question is not
"if I already launched one coin which landed head and then launch a second coin"
But "if I already launched 2 coins, and at least one landed head"

>>724809531
75%

>>724811397
A man flips a coin and its heads and bets me a dollar the next flip will be heads, what the chances this flip will be heads?

>>724811667
Yes, and since you don't know which coin will be heads there are two separate answers

>>724811658
>at least 1 coin lands heads

Try again.

>>724811743
50%, but that's a different question to the OP question.

Read the OP question again.

1/3

If at least one HAS to be heads then they're counterfeit coins and the whole puzzle is pointless

>>724811771
You didn't read about monty hall problem right ?
Or Just trolling me

>>724811743
50% for one coin flipping.
25% for 2 coin flip bet.
In probabilities it doesn't matter if the object are similar.
They will be always called A & B even for same values.
(A & !B) != (!A & B)

>>724810865
>The question is basically "what's the probability of getting heads on one coin" since the other has already happened

No, it isn't, retard.

the question is
>What is the probability that both coins landed heads given at least 1 coin landed heads?

4 possible outcomes from a 2 coin flip

HH
HT
TH
TT

3 of them contain at least 1 heads

1 of those 3 is both heads

1 of 3

1/3

Stay in school, kids.

>>724811903
I know about Monty Hall and it's another retardedly phrased question whereby math autists don't take into account the obvious human interaction in the events. For there to be 100% probability that at least one coin lands heads (as per OPs question) one of the coins has to be double headed, in which case it's just a 50% that rides on the other coin. Doesn't matter what the numbers in your little textbook say, when you put something like this into a physical example there are things that change how it's got to be worked out

The confusion comes from the way the problem was stated and typically visualized. Most people are imagining looking at one coin, seeing that it's heads and then being aware that the second coin is independent assigning a probability of 50% for that coin. The question is actually asking you to flip both coins, and then have a second person tell you, at least one of them is heads, after looking at both coins, which gives the probability of 1/3. This is only confusing because in normal interactions, we naturally try to conceive of how we got each piece of information, and the most natural way of getting the information that one coin was heads is to look at a coin.

tl;dr problem is counter-intuitive because most people imagine needing to look at a coin to know the given information.

>>724812047
>No, it isn't, retard
Yes it is, double retard. For there to be a "given" in a situation, that has to be 100%. If one HAS to be heads, that coin doesn't affect anything else in the sequence

>>724812215
If you're not trying to troll here, I'm hope you don't vote.

If you're trolling....well good job, you got me

>>724812215
>For there to be 100% probability that at least one coin lands heads

What the fuck are you talking about, you idiot.

The OP question never says that 1 coin is 100% guaranteed to land heads.

2 coins were flipped and at least 1 landed heads. This is a perfectly realistic scenario and a basic conditional probability question.

>Doesn't matter what the numbers in your little textbook say

So you're saying that math is incorrect and you're right, then?

kek retard

1/3

File: 1487657522601.png (379KB, 500x284px) Image search: [Google]

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yall fucking retarded except for these two anons >>724811675
>>724810337

You can get the feel for coins and get the right height and flip speed to land 80% of shots called. And when u do land on the other 20 u learned what height or flip speed is to little or much and can adjust. Only solid thing to a coin toss is it landing and bouncing oba a hard surface so now it is influenced by the floors probability of pure randomness. Unless ur some calculating robot and take the bounce, stop time of the bounce, new flip speed distance from there to possible landing spot and even then you would have to do it twice to get a range on the bounce flip speed just to tune it in..... In theory

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>>724812433

The "given" is that AT LEAST 1 coin landed heads.

That ius not the same as saying "1 coin is 100% guaranteed to be heads."

This is why you are retarded, because not only are you mathematically illiterate, you also lack basic reading comprehension.

I hope English isn't your first language.

1/3

Pic Related

File: 1485315619207.jpg (11KB, 273x296px) Image search: [Google]

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>>724812484

>The OP question never says that 1 coin is 100% guaranteed to land heads. 2 coins were flipped and at least 1 landed heads.

...

>>724812481
You not being able to translate problems into real life isn't me trolling dear. When things in the real world are affected by outside forces (ie: the CERTAINTY of one coin being heads) it changes how the question works. 1+1=2 but two halves of an orange don't necessarily make a whole one. The physical world matters

>>724812516
So....explain it to me cause I still believe it's 1/3

>>724812751

You still don't understand how those are 2 different things?

Ok, let me explain it to you like you're a 5 year old child.

I flip a coin and it landed heads
IS NOT THE SAME THING AS
This coin is 100% GUARANTEED to land heads.

Do you understand now?

>>724812824
Nigger

>>724812484
>The OP question never says that 1 coin is 100% guaranteed to land heads.
Yes it does. GIVEN THAT AT LEAST ONE IS HEADS means that one HAS TO BE HEADS. You not being able to read doesn't make you right. Be angrier about your autism

>>724812971
>I flip a coin and it landed heads
That's not what the question says fucknuts

File: 1384551078849.jpg (15KB, 222x228px) Image search: [Google]

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>>724813005

Read this >>724812971

Realize you're retarded.

1/3

>>724813005
No, 100% chance that one of two isn't the same thing that 100% of one

>>724813157
Realise that you have no grasp on how the physical and theoretical are different

>>724813097

No shit, retard. Why do you think I was quoting the OP question?

>>724813216
If they're identical then it amounts to the same thing. You're still looking for theoretical answers to physical questions

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

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>>724813245
>the physical and theoretical are different

Bayesian probability isn't theory, it's theorem.

A mathematical proof:

This is a conditional probability question, so use Bayes' theorem to solve.
P(A|B) = P(A∩B)/(P(B))

Explanation for faggots:

COnditional probability questions take the form:
>What is the probability of Event A given Event B?

OPs question is
>What is the probability that BOTH coins landed heads, given that AT LEAST ONE coin landed heads?

So here

A = "both coins are heads" = {(HH)} = 1/4
B = "at least one coin is heads" = {(HH), (HT), (TH)} = 3/4

P(A|B) = P(A∩B)/(P(B)) = (1/4)/(3/4) = 1/3

Kys that's 2 questions at once

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

>>724813509
I don't deny that the probability of (on paper) getting HH out of a choice of HH, HT, and TH is 1/3 but what you seem to not understand is that the world isn't a piece of paper, and tampering with the real world causes it to have different results

>>724809531
conditional probability: P(A|B) = P(A&B)/P(B) (apologies for incorrect notation). reads as probability that A occurs given B occurring is the probability of both divided by the probability of b occurring independent.

Changing this to our situation, A=B=H (not same coin though). The joint probability of getting both heads is 0.25, the probability of getting heads on one coin is 0.50. So 0.25/0.5 = 0.5.

The above is operating on the fact that the coins are distinguishable. Let us assume we cannot distinguish the coins, this changes the situation so that we can no longer determine which of the coins flipped landed on heads, we just know that one did. In this instance we know there are three possible outcomes: HH, HT, TH. In this instance we arive at the 1/3 answer.

File: CoinsSimulation.png (111KB, 641x650px) Image search: [Google]

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>>724813717
>I don't deny that the probability of (on paper) getting HH out of a choice of HH, HT, and TH is 1/3 but what you seem to not understand is that the world isn't a piece of paper,

You fucking retard.

Do you beleve that math does not apply to real life?

Take 2 coins and flip them 100 times. Count how many times you get at least 1 heads coin (~75 flips)
Count how many times you get 2 heads (~25 flips)

25(both heads) out of 75(at least 1 heads)

=

1/3

Try it, faggot.

Or if you're not retarded, write a simulation.

Pic Related: 1/3

>>724813964
the 1/2 comes from the assumption that a specific coin was heads, the 1/3 comes from the assumption that any coin landed heads.

>>724810752
I actually have degree in math. The problem here is that people are failing to distinguish between two separate problems.

Combinations represent equivalence classes of permutations. In this problem no additional information is specified regarding any criteria by which we could differentiate the coins, so it's safe to say that we're looking at combinations of possible outcomes rather than permutations. Thus we have: {{H, T}, {H, H}, {T, T}}
(Yielding a 50%)

However, if we were looking at permutations, we'd have: {(H, T), (H, H), (T, H), (T, T)}, in which case the probability is 33.3%.

Im more disappointed than usual for a thread like this. This is not rocket science.

>>724813987
>Do you beleve that math does not apply to real life?
Of course that's not what I think, but there are extra factors to take into consideration. If I have 3 oranges and cut them in half then glue them together after shuffling them around, I don't have the same three oranges even though 0.5x6=3 every time

>>724813964

holy fuck, anon, how can you make such rudimentary mistakes?

>The joint probability of getting both heads is 0.25
Correct

>the probability of getting heads on one coin is 0.50.
Correct. The probability of getting AT LEAST 1 heads in a 2 coin flip is 0.75 or 3/4

>The above is operating on the fact that the coins are distinguishable. Let us assume we cannot distinguish the coins

That makes ABSOLUTELY no difference to the probability.

>>724814300
It does make a difference, see >>724814142

>>724809531
P(heads|heads) = (1/2)(1/2) = 1/4 or .25

>>724814142
>Combinations represent equivalence classes of permutations. In this problem no additional information is specified regarding any criteria by which we could differentiate the coins, so it's safe to say that we're looking at combinations of possible outcomes rather than permutations. Thus we have: {{H, T}, {H, H}, {T, T}}
>(Yielding a 50%)

If you have a math degree, your university and/or professors are shit.

Do you honestly believe that the probability of getting 2 heads coins where at least 1 coin landed heads CHANGES depending on whether you choose to view them as permutaions or combinations?

Do you understand how retarded that is?

I really hope you're trolling about having a math degree.

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>>724814237
THIS HAS TO BE BAIT, PLEEEEEAASE. PLEEASE I'M DYYYING

>>724811847
how is it different

>>724814389

It makes NO difference to the probability whether you can distinguish between the coins or not.

You are retarded if you think it does. Genuinely. Retarded.

Just think about it.

>>724814650
Nope. The physical world matters and if you don't take everything into account when you try to solve problems then you're forcing yourself to be stupid. Try to refute the orange thing, you can't

I'm starting to think everyone is trolling here, the answer is 50%.

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

You fucking morons

>>724814721

Because his question is asking
>what is the probability that the next coin flipped lands heads? Answer = 50%

OP question is
>What is the probability that both coins landed heads given at least 1 coin landed heads. Answer = 1/3

Why?

Because when you flip 2 coins, there are 3 equally probable ways to get AT LEAST 1 heads:

coin1=heads, coin2=heads
or
coin1=heads, coin2=tails
or
coin1=tails, coin2=heads

All 3 are equally likely. HH is 1 of them.

1/3

>>724814675

Meant this reply >>724814979
for you, anon

>>724814795

The answer is 1/3, you fucking mongoloid. read your article.

>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

File: Uni_Wash_Cond_Prob.jpg (137KB, 921x631px) Image search: [Google]

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If FIRST coin landed heads, answer = 1/2

If AT LEAST 1 coin landed heads = 1/3

So 1/3 for OP question.

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

>>724814795
>claim the answer is 50% and that you are trolling if you answer 1/3
>post wiki that explain why the question is ambiguous and both 1/3 and 1/2 are correct with different assumption

Penis. Penis is always the answer.

>>724815427

Except OP question is not ambiguous. It's a clear basic conditional probability question that is easily solved.

The answer is 1/3 btw.

>>724815248>>724814477
>>724814627
>>724814300
>>724814237
>>724814179
>>724814142
>>724814107
>>724813987
>>724813717
>>724813581
>>724813509
>>724813157
>>724812971
>>724812854
>>724812824
>>724812751

this question is purposefully ambiguous which leads to the two answers 1/2 or 1/3 probability. both are correct, depending on your interpretation of the question

ITT OP trolls everyone with this shit question posted at least once every week on /b/

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

and read it IN FULL. not once does it say that there is a definitive answer to problems that are presented in the manner that OPs is

>>724815664
if you actually read the wiki you could understand why it is ambiguous.
i know the answer can be 1/3.
but you need assumptions to make that the correct answer. i know, they are basic and standard assumption we are use to make in probability problem, but they are NOT in the question.
our usual attitute in making these assumptions doesn't make the 1/2 answer wrong.

claiming 1/3 is the only correct answer is just as stupid as claiming 1/2 is

>>724816290
>but you need assumptions to make that the correct answer

no, you don't. All information in the OP question yields an answer of 1/3.

If you want an answer of 1/2, THEN you need additional information/assumptions.

It's a basic conditional probability question with one correct answer and the answer can be demonstrated with Bayes' theorem.

1/3

>>724815664
sorry, but you seem to lack reading comprehension skills. it isn't a "clear basic conditional probability question" because the answer is rooted in assumptions made by the reader

>>724815687
>this question is purposefully ambiguous

It's not ambiguous. You're just unfamiliar with conditional probability. Actually read the article, lad.

The only way that the answer could be 1/2 is if we ASSUME that we know which SPECIFIC coin is heads. This assumption cannot be applied to the OP question.

1/3

>>724809531
http://math.stackexchange.com/questions/991060/flip-two-coins-if-at-least-one-is-heads-what-is-the-probability-of-both-being

why do you faggots argue about things when the answer is freely available?

>>724816549
it isn't explained how you know one is head (boy).

you ASSUME that the way you know it is:
>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.
instead of:
>From all families with two children, one child is selected at random, and the sex of that child is specified to be a boy. This would yield an answer of 1/2.

if you can't understand why this is an assumption you are making there is nothing i can do to help you solve this

>>724816567

>because the answer is rooted in assumptions

no, anon. An answer of 1/2 is rooted in assumptions which are NOT present in the OP question.

this is why 1/2 is not correct and 1/3 is the correct answer to the OP question.

See pic and source here >>724815405

prove me wrong

Protip: You can't.

>>724817275
>prove me wrong
https://en.wikipedia.org/wiki/Boy_or_Girl_paradox
done, read it.
what have i won?

>>724816290
Fuckin' nerd.

>>724817143
>it isn't explained how you know one is head (boy).

Exactly. You are simply told that AT LEAST 1 is, which gives an answer of 1/3.

>you ASSUME that the way you know it is:
>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.

This is essentially the same as OP question

>instead of:
>From all families with two children, one child is selected at random, and the sex of that child is specified to be a boy. This would yield an answer of 1/2.

This is NOT the same as OP question as the heads coin is NOT specified.

>if you can't understand why this is an assumption you are making there is nothing i can do to help you solve this

You stupid cunt. The 1/3 people aren't making any assumptions. they are using ONLY the information provided in the question to answer the question.

The 1/2 people are the ones MAKING ADDITIONAL ASSUMPTIONS, like how we KNOW 1 is a boy/heads.

Do you understand now, you clown?

1/3

>>724817616
>he can't even realize he is making assumptions
ok, you are retarded, waste of time.
just read the wiki a few times or ask someone else to explain it to you.

The odds of a coin landing on heads is 1/2
Since the landing of both coins are independent events, that is, one does not affect the odds of the other one landing on something, the calculations become simpler.

One coin will always fall on heads. In this scenario, this coin can be removed from the question completely.
The one other has 1/2 chance to land on heads.
If this is the situation, the odds of both coins landing on heads is 1/2.

If, however, you analyse it from the perspective of the system getting to this point altogether, you have to assume the chances of both coins landing on heads.
In this case, the odds are calculated by multiplying the odds of each individual coin landing on heads.
1/2 * 1/2 = 1/4
So the odds of both coins landing on heads is 1/4.

tldr: OP cannot formulate questions clearly.

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

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>>724817819

What assumption have I made?

Make reference to the OP question and exactly what additional information I have applied to the question.

If you can do that, I'll concede the argument.

But you can't, because I am not making additional assumptions. The 1/2 people are.

Pic Related: Actual Math yields 1/3

>>724817941

>gets question wrong
>blames question

kek

>>724809531
Does order matter?

>Y
1/3

>N
1/2

>>724818252

Moron.

>>724818424
How?

>>724818628

the probability does not change depending on whether you think order matters or not.

Prove it to yourself by flipping 2 coins 100 times.
Count how many times you get both heads.
Count how many times you get at least 1 heads.

Probability you get both heads when you have at least 1 heads will be 1/3.

>>724818083
i don't give a fuck about your math, i know how to get the 1/3 answer. it the same way you can get the 1/2 answer actually, just with a different assumption.

again:
we know "at least one is head"
we don't know HOW we know it. it is ambiguous.

to solve the ambiguity:
you are assuming
>someone else looked at the coins and told me at least one is head ( hh ht th possible scenarios, 1/3)
where it could easly mean
>one coin is on the table and i can see head, the other one fall off and i haven't seen it yet (so ht hh scenarios, 1/2)

and both are legit assumptions. get over it.

>>724818848
Well, if order doesn't matter, then one coin can be eliminated as a possibility, therefore leaving the chances as 1/2

You, however, believe that order does matter, and I can respect that

>>724818230
Shit
Oh well, I didn't see the 1/3 perspective, that's the correct one.
Still, OP is a dick

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>>724819076
>i don't give a fuck about your math
>your math

It's not my math. it's just math and the fact you dismiss it shows that you are mathematically illiterate when it comes to conditional probability. Where is "your" math, anon?

>you are assuming
>someone else looked at the coins and told me at least one is head ( hh ht th possible scenarios, 1/3)

That's not an assumption, you stupid cunt. I read the question. the question states at least 1 out of the 2 landed heads. The question does not specify which coin. No assumptions made no matter how hard you pretend that I have.

>where it could easly mean
>one coin is on the table and i can see head, the other one fall off and i haven't seen it yet

Those are assumptions, dumbfuck, not included as information in the OP question.

1/3.

>>724819112

Moron.

>>724819567
Name calling won't get you anywhere unless that name is "late for dinner", you know ;)

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you guys are real morons.
half of you dont know how it works (it;s supposed to be 50%)
the other half swallows bait like a hungry hungry whore

>>724809531
OP is a great mathematician.

>>724819529
>Where is "your" math, anon?
https://en.wikipedia.org/wiki/Boy_or_Girl_paradox
here, i've linked it to you like 5 times, just read it.
in "bayesian analysis" you can learn how to get both 1/3 and 1/2 with the same math. just with a different assumption.


the question is ambiguous.
solving an ambiguity require assumptions.
if you solve the problem you are making assumptions, even if you are to stupid to realize it.

>>724820481

Read it. The 1/2 answer is the one with the added assumption, as you've shown in your last post.

The 1/3 answer does not make any additional assumptions on the OP question.

The 1/3 answer is, therefore, the correct answer to the OP question based on the information in the OP question and when no additional assumptions are made.

I hope you learned something today, because I don't think you're retarded; you're just stubborn.

Remember: There is no ambiguity in the OP question. The OP question (as it is, with no assumptions) gives a 1/3 answer.

Stay in school, lad.

>>724821052
it really looks like you don't even know what assumption and ambiguous mean.
you make assumptions solving every question. (just read the "common assumptions")

when you have a question that can be solved in 2 ways, it is called ambiguous.

solving it one or the other way imply assuming one situation over the other(s).

also, i don't really think i've something to learn from someone who can't even read and understand a wiki page.

the wiki proves you're are wrong, if you refuse to understand it i can't do nothing about it. ty for the waste of time.

>>724809531
nobody cares about the odds of monopoly money (euros) falling down . keep ya change ya cuck

>>724821144
>>724814142
Answer this, nigger

>>724822199

OP question:
>2 coins flipped. At least 1 landed heads.
>heads coin not specified
>answer = 1/3

Your interpretation of OP question
>2 coins flipped. At least 1 landed heads
>heads coin is face up on table
>other coin fell on floor I can't see it yet
>answer is 1/2

Which one of us is making the assumptions, faggot?

>>724822203

>worth more than dollar
>monopoly money

kek

>>724822199
>the wiki proves you're are wrong

Actually, it shows he's correct and you're wrong.

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>>724816910
>2 coins
>1 coin will ALWAYS be heads

It's 50%.
Two conditions:
1 coin must be heads.
1 coin can be heads or tails.

It doesn't matter which coin will be heads because one of them will ALWAYS be heads. So the other coin has a 50/50 chance.

It's not "throw two up and guess which one is the 100% heads" game.

Imagine two coins, but one is a double headed coin. It doesn't matter what that coin is because it will always be heads and thus can be discounted from the toss.

Saying you have no idea which coin is the 100% heads coin is just pedantic. We already know one is.

>>724822642
op:
>2 coins flipped. At least 1 landed heads.
>somehow i know one is head
>it is not clear how i know it
>the problem can't be solved if we don't decide how we know the source of this knowledge

your assumption:
>someone who knows both coins told me: 1/3
another reasonable assumption:
>i saw only one, and not the other : 1/2

>>724823214
>>1 coin will ALWAYS be heads

Incorrect. D- for effort.

>>724823387
>at least one coin will always be heads
Are you in need of assistance?

25%

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

400KB, 921x631px

>>724823299
>>somehow i know one is head
>somehow
the question told you

>>it is not clear how i know it
the question told you

>>the problem can't be solved if we don't decide how we know the source of this knowledge
the question told you and it's a basic conditional probability question which is easily solved.

P(A|B) = P(A∩B)/(P(B)) = (1/4)/(3/4) = 1/3

>your assumption:
>someone who knows both coins told me: 1/3

Incorrect. Question provided all information to yield 1/3 answer.

Try to keep up.

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

1/3

>>724823161
t. i can't read

wiki clearly explain that the question is ambiguous and the solution depends on assumptions.
the question requires assumptions to be solved.
and since nobody is telling us which assumptions are wrong both 1/3 and 1/2 can be correct, given different assumption.

he is arguing that solving for 1/3 doesn't require assumptions, because he is too stupid to realize he is making assumptions.

>>724823539
>always be heads

Incorrect. Either coin could be tails, just not both at the same time.

>>724823773
source:
https://en.wikipedia.org/wiki/Boy_or_Girl_paradox

learn to read.

>>724823878
>wiki clearly explain that the question is ambiguous

No, the Wiki is about the Boy/Girl paradox, not the OP question. The Op answer is 1/3.

1/3 answer requires no assumptions.

1/2 answer does.

You keep proving yourself wrong. Well done.

>>724824144

I read it. So should you.

>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

>>724824274
sorry am new to this thread

how did you get to 1/3?

wouldn't it be 1/4 (1/2 * 1/2 = 1/4)

>>724824025
No. Stop assuming.
The picture said one coin will always be heads.

You're over thinking it.

File: 1488596396281s.jpg (3KB, 125x120px) Image search: [Google]

3KB, 125x120px

>>724824274
he can't even understand that boy = head and girl = tail

ffs, under "common ASSUMPTIONS" it is even written :
>The mathematical outcome would be the same if it were phrased in terms of a coin toss.

i'm done here, you can't even understand a wiki page

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

10KB, 501x348px

>>724824734
>how did you get to 1/3?
>wouldn't it be 1/4 (1/2 * 1/2 = 1/4)

it would be 1/4 if there was no condition.

But the condition that at least 1 coin landed heads, means that tails - tails is no longer a possible outcome, leaving 3 equally probable outcomes:

heads - heads
heads - tails
tails - heads

which all contain at least 1 heads.

heads - heads is 1 of those 3.

1/3

Math solution has already been posted.

>>724824807
>The picture said one coin will always be heads.

No, anon. It did not.

>>724824904

You can't understand that OP question is equivalent to
>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

It's not our fault that you're mathematically illiterate, anon.

>>724809531
66,6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666 that it won't

>>724824610
oh, so you are "assuming" we are in that situation.
good to know.

>>724824982
ah shit thanks

>>724809531
The only correct answer: Insufficient information to answer the question.

You all lose.
You all are losers.
You all are dumb.

>>724825216
>is equivalent
if you assume it, yes.

>>724825257

It's not an assumption.

The alternative is that one child is selected at random and its sex is given.

this does not happen in the OP question.

Let me explain so that even simpletons can understand.

You have childA and childB.
We select childA.
Its a boy.
The probability that both childA and childB are boys is 1/2.

To get the 1/2 answer, we must know which specific child is male.

To get a 1/2 answer for OP question, we must know which specific coin is heads, and to do that requires an assumption, and is therefore incorrect.

OP question does NOT specify which coin is heads. It tells us that at least 1 coin landed heads. It could be either coin, meaning either coin could be tails, just not both at the same time.

3 equally probable ways to get at least 1 heads coin for a 2 coin flip

HH or HT or TH

1/3

REKT

>>724809531
Flip two coins. You get 3 outcomes as the coins are not distinguished from one another, the two coins are essentially one entity with three possible states.

HH
HT
TT

Eliminate TT which leaves two outcomes, each with 50% chance.

>>724826034

In that case HT is twice as likely as HH which gives the answer 1/3.

>>724826034

Flip 2 coins as many times as you can.

See how many times you get HH
See how many times you get HT

Realize you're retarded.

1/3

>>724810208
wrong. there are two states:
heads, tails or heads, heads.

>>724810485
"given that at least one landed heads".

>>724826164
No it's not. Because the coins are not distinguished.

One coin lands heads, one lands tails, that's one state with the same probability as the others.

>>724811523
Not True
The Bayes Rule defines it. And esspacially for such an easy problem.

>>724809531
its 33%

>>724826253
No you're the retard because we're given the context that one coin is heads. so you eliminate one of the outcomes from your 1/3, leaving 1/2.

>>724826164
What because TH isn't an option if HH is he result
P(HH|HT) = .5

>>724826312

or tails, heads

3 outcomes

1/3

File: bayes.png (19KB, 618x225px) Image search: [Google]

19KB, 618x225px

>>724809531
Applying Bayes' theorem
P(A): chance that at least one of the coins is heads = 3/4.
P(B): chance that both coins are heads = 1/4.
P(B|A): chance that at least one of the coins is head given that both coins are heads = 1.
P(A|B) = 1* (1/4) / (3/4) = 1/3.
It's like the first lesson of probability theory.

>>724826428

There are 2 equally probable ways to get one heads and one tails, you fucking retard.

heads, heads
heads, tails
tails, heads

1/3

>>724826591
Wrong because TH isn't an option if HH is the result.***

>>724825938
i know it is not easy to understand, just try harder and maybe you'll get it.
make a new bookmark with https://en.wikipedia.org/wiki/Boy_or_Girl_paradox
try again tomorrow, read it alone, ask someone else to explain it.
maybe someday you'll get it

>>724811049
>2/3
all these posts and only one right answer so far.

>>724826554

>win the lottery
>don't win the lottery
>2 outcomes, therefore 50%

^THIS is how retarded you are.

The probability of gettting 2 heads when at least 1 coin landed heads is 1/3.

prepare to get mathzmerized.

> take 2 fried chickens
> throw both in micro waves for random times.
> there is a 50/50 watermelon that one, both, or neither fried chickens get burnt.
2 fried chickens microwaved, 3 possible kfc results, at a 50/50 watermelon.
2x3x0.5=3
now take the result of yo watermelon and divide into yo mofugn chickin mufugah pop a cap in you ass nigguh what.
2x3/3=2
yo ass has a watermelon of 2 thachoo burn yo fried chicken.

>>724826593
Wow... how to be a retard 101

>>724826591

What?

>>724814775
The answer should be easy to obtain then. Do the coin experiment.

>>724809531
Sample space:
HH >At least 1 head
HT > At least 1 head
TH > At least 1 head
TT > no heads

3/4

>>724826980
I fucked it up
P(HH|H) = .5

>>724826679

the problem is that the 1/2 people are mathematically illiterate, so posting Bayes' solutions means nothing to them.

We have to treat them like children, anon. Explain it in a way that even a child can understand.

>>724826714

Neither is HT, dumbass.

1/3

>>724826760

Anon, where's "your math?"

>>724827101
God damn it, this is why I only managed a B- in probability. I didn't finish.

So we have a sample space of {HH, HT, TH}

We want BOTH heads.
1/3.

>>724827101

now finish the question.

Protip: It's 1/3

>>724827247
Yeah it is after the first flip
The what the conditional bar is for
Lrn2notation

It's 50/50, twice over.... It's just less likely to happen the second time

>>724827296
>https://en.wikipedia.org/wiki/Boy_or_Girl_paradox
in the link.

>>724809531
Well it says that at least one of them landed heads, so 50%. That is one coin guaranteed to be heads and one coin with two sides.

If that isn't the answer, then whoever worded it like that should be killed.

so i have gone as far as
> only 3 results can occur, 1 of which we seek
> result 1: 1 heads, 1 tails
> result 2: 2 heads
> result 3: 2 tails
> 1/3 is 0.33
> 33% chance of getting desired results on first try
and thats where i stop. because yes, thats all i know to do

>>724809531
Three possible ways at least one lands heads
One possible way they both land heads
Probability is 1/3

(If you don't believe me about the 3 possible ways, write in red on the heads side of one and in blue on the heads side of the other. It's now undeniable that the event of one coming up heads is distinct from the event of the other coming up heads, so indeed 1/3 and not 1/2)

>>724827839
We don't know which at-least-one though. 1/2 treats both "only one" possibilities as the same coin coming up heads. 1/3 accounts for the fact that there are two of them, so if only one comes up heads, it could be either of them, which makes the event of "only one" twice as likely as otherwise.

>>724828002
so if we assume that 1 is guaranteed heads, then we also assume only 1 coin is being flipped.

answer is 50/50

>>724827180
Allright. The most basic way to calculate the probability of something: you divide the number of the favourable outcomes by the number of all possible outcomes.
All outcomes:
1) First coin heads, second coin heads
2) First coin heads, second coin tails
3) First coin tails, second coin heads
NOTE: First coin tails, second coin tails can't be an outcome, since OP told us, that we know at least one of the coins is heads.
Favourable outcome:
1) First coin heads, second coin tails.

Favourable / All = 1/3.

To those of you who are arguing the coins aren't numbered, and first coin heads, second tails and vice versa are the same instance:
Try throwing two coins like 20 times, and note the results. You'll see that about half the times, one is heads, other is tails.

Dunno why I keep posting this, lost of ppl explained it in this thread. BTW this is low quality b8, if OP rly wants to troll, he should start a monty hall problem thread.

>>724828589
it doesn't work like that

>>724826714
>TH isn't an option if HH is the result
>HH is the result
>HT is still possible even though HH is the result

Learn to formulate sentences, you fucking retard.

There are 3 equally likely outcomes that satisfy the condition of having at least 1 heads coin.
HH
HT
TH

1/3

>>724828546
we don't need to know which one will land on heads. The coins are identical.

One of the identical two sided coins will 100% land on heads.

If Coin 1 was the guaranteed heads, Coin 2 could either land on heads or tails.

If Coin 2 was the guaranteed heads, Coin 1 could either land on heads or tails.

50% each so 33%overall for both to be heads (2 tails, 1 tails, 0 tails) but bc theres a certainty of one heads you may as well only flip one so its 50 %
It limits possibilities to HH or HT
This is ignoring a vertical superstate

>>724828915
Fuck you cunt
Enjoy your lack of basic education

>>724816910
lmao you stupid fuck if YOU read the article then you would see that the CREATOR OF THE DAMN QUESTION ACKNOWLEDGED IT AS AMBIGUOUS HIMSELF

Surely it's 3/4?

>>724829277
Yeah, but there are two "ifs" there. You can't just pick an "if" and say "this is the one," even though they're the same. You have to account for both of them.

The three possibilities:
>One coin lands heads and the other tails.
>One coin lands heads and the other tails. (Yes, there are in fact two of these.)
>They both land heads.
Hence 1/3

>>724809531
Stop the government from monitoring your online activity http://traineddog.club

>>724830360
Dodgy link you have there pal

>>724830360
Don't do this, it's illegal. The government's prime responsibility is to keep its people safe, that responsibility is more important than your personal privacy and interfering is a federal crime. If they can't find out what you're looking at online, how do they know it's not a blueprint for a homemade nuke.

Fucking hell shit like this is why we're all fucked.

One coin is guaranteed to land on heads.

The other coin has two options, either heads or tails.

Its 50%

33% duh

If you don't believe it, let's write a simple python script that does the work:
-----------------------------------------
from random import randint

bothHeads = 0
notBothHeads = 0

for i in range(0,100):
x = randint(0,1)
y = randint(0,1)

#0 is heads, 1 is tails
if(x == 0 and y == 0):
bothHeads = bothHeads+1
else:
notBothHeads = notBothHeads +1

print(bothHeads)
print(notBothHeads)

------------------------------------------------
Output:
29
71

Result: Yep, it's 33%

>>724834240

>thinking retards can understand code

Good job anyway.