How smart is /b/?

50%. so fucking easy.

test

%50.

The outcome of the second coin flip has nothing to do with the outcome of the first.

16% ??

>>744381730
It's 50 fuck off

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1/3

900% probability that the one flipped first will be different than the second one flipped.

If they're flipped at the same time, that probability goes down to 842%

Math harder, plebs.

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>>744381788
>>744381857
>>744381862
>>744381951

Retards detected. It's not 50%. Try again. I'll give you 1 more try before I explain why you're retarded.

God, not this bullshit again.

Answer is 1/3. Don't argue.

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There's a difference between
>given that at least one of them landed heads
and "the first of the coins was heads"

Since there's no guarantee that the first one has landed heads, the answer is 33.333333333333333%

>>744381730
2 coins
25% chance both are heads
25% chance both are tails
50% chance of one head and one tail.

Therefore, the answer is 25%.

>>744382193
>"at least" one is heads
meaning 2/3 dumbass

Depends on who flips the coin.

>>744382353

Retard. At least 1 landed heads. They can't both be tails. 1/3

>>744381788
>>744381857
>>744381862
>>744381951
>>744382353
lol you fucking retards i'll explain it

4 outcomes:
HH
HT
TT
TH

>given at least one was heads
that eliminates TT. only 3 possibilities now. out of those, only 1 is both heads (HH), the other 2 are only one heads (HT, TH)

therefore 1/3

>>744382452
It was 25% before any coin was flipped. The fact that you flipped a coin does not affect the chances you had before you flipped it.

>>744381730
Would be 1/4 with two coins since there is a 1/2 chance of landing on heads for each coin.
If one coin is guaranteed to land on heads, then it would simply be a 1/2 chance of the other lands on heads.

>>744381788
>>744381857
Fucking brainlets I cant believe this
It's OBVIOUSLY 75%
OP's asking for the probability of both coins being heads, since we already have one we increase that probability by half. Fucking thirteen year old summerfags

>>744381730
>bout three fiddy

Seriously though, this question has no real life meaning as one cannot "guarantee" one will be heads. Therefore OP still a faggot

>>744381730
Not enough info. Are the coins fair? Are the outcomes independent of each other?

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>>744382640

Yes it does, retard. It's called conditional probability.

1/3.

>>744382560

Nope.

OP states that two coins are flipped, one lands on heads.

Therefore, there are only two possible outcomes; HH, HT.

Which happens depends on the flip of one coin, which is a 50/50 odds of landing one way or the other.

>>744382778
>OP states that two coins are flipped, one lands on heads.
>Therefore, there are only two possible outcomes; HH, HT.

TH is also possible. OP never says teh FIRST coin landed heads, just AT LEAST ONE landed heads. there are 3 equally probable ways to get at least 1 heads coin for a 2 coin flip.

HH
HT
TH

1/3

>>744382778
OP states
>AT LEAST one of them landed heads

Threfore three possible outcomes; HH, HT, TH

Learn to read, brainlet

>>744382715
Theyre fucking coins. Dont over complicate things you know the answer to.

Have we looked at the coins and collapsed the wave function?

>>744381730
lol obviously 50% chance either it happens or it doesnt

>>744382882
HT and TH are the same outcome. Either way, the probability of the desired outcome, HH, hinges on the outcome of a single coin flip because you know that the question assumes one coin did land on heads.

>>744381730
Given that 1 landed heads and seeing as each coin flip is an independent event (the probability of landing heads is not affected by previous coin flip) your probability of landing heads is 50%. Why 50%? Well if the coin is equally balanced on both sides then you only have 2 possible outcomes, heads or tails. In each independent coin flip you have 50% chance of heads or 50% of tails. The law of averages says that given a large enough sample size you can expect the 50/50 results.

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>>744383064
>HT and TH are the same outcome.

Now we know you're REALLY retarded.

Allow me to explain: Imagine using a penny and a quarter. You flip both. At least 1 landed heads. So you could have
>penny=heads, quarter=heads
or
>penny=heads, quarter=tails
or
>penny=tails, quarter=heads

Can you see how those are all different outcomes?
Can you see that they all contain at least 1 heads coin?
Can you count how many there are?

They are all equally probable.

3 possible and equally probable outcomes.
1 of those 3 is both heads
1 of 3
1/3

Stay in school, kid.

>>744382868

>What is the probability that both landed heads given that at least one of them landed heads.

Read the question again.

If one of them landed heads up then the question is really what is the probability that the other lands heads up. Which is %50 regardless of what order you flip them in. One of the two will always lands heads up and you can ignore it for all intents and purposes.

It's a stupidly worded question meant to start an argument.

>>744381730
The same amount of probability of jews running this country, and use shekel math schemes to distract us.

>>744383064
HT and TH are different, not the same at all.

The question asks
>"Out of the outcomes where at least one coin (i.e. one or two coins) lands heads, what is the probability both landed heads?"

There are 3 outcomes where at least one lands head.
(first coin H, second coin H)
(first coin H, second coin T)
(first coin T, second coin H)
Out of those, 1 outcome is where they both land heads. 1/3.

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>>744383242
>Given that 1 landed heads and seeing as each coin flip is an independent event (the probability of landing heads is not affected by previous coin flip) your probability of landing heads is 50%.
>previous coin flip

you're assuming the "FIRST" coin flipped is the heads coin. this is a false assumption. First coin could be tails and second heads

3 equally probable outcomes.
Heads - Heads
Heads - Tails
Tails - Heads

1/3

See Bayes Theorem

>>744383381
thank you, at least one other person has the reading comprehension merit badge

People not understanding that HT = TH


kek.

>>744383381
Out of the outcomes where at least one of them landed heads. Not the 'first one landed heads'. You can flip T first, then H. That counts as at least one of them landing heads.

3 outcomes.
Out of those, 1 is double heads. The other 2 are only single heads. 1/3.

>>744383381
>If one of them landed heads up then the question is really what is the probability that the other lands heads up.

EEERRRRR incorrect, buddy. You lack both reading comprehension and math literacy.

Read this >>744383363

>>744381857
This is called mutual exclusivity

>>744383363
Read the question.

>What is the probability that both landed heads given that at least one of them landed heads.

Of the three outcomes you've listed, two are functionally identical because you know that one of the two coins will always be heads up. Whether it's the first or second doesn't matter. Flip them at exactly the same time and it wouldn't matter. The order is irrelevant.

Flip one and it lands tails, you know the second is going to be heads. Flip heads and the second one might be tails or it might be heads.

The only thing that can vary is whether one lands heads or tails, and that's a 50/50 shot.

>>744383532

gr8 b8 m8

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>>744383363
> getting this triggered

>>744382778
This.

%100

Proof: just tried it, it worked.

Checkmate, Christians.

>>744382776
This is the solution...

There is absolutely nothing which has a 100% probability.

Apart from OP being a faggot.

>>744382776
Future events cannot affect the past.
Prove me wrong.

>Do we count the answer after one of them has been determined it is heads?
50%
>If not.
1/3

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>>744383631
>Of the three outcomes you've listed, two are functionally identical

No, they are not. they are separate and distinct outcomes and are both equally likely to occur.

How the FUCK can
penny=heads, quarter=tails
be functionally identical to
penny=tails, quarter=heads ???

ITT: Mathematically illiterate plebs

Here, I drew you retards a Venn diagram too.

1/3

>>744383631
Youre a special kind of stupid aren't You? Just smart enough to be dangerous

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>>744383701

>explaining probability makes you triggered

1/3

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>>744383846
you need to get laid

>>744383482

The question only asks what is the probability that both are heads up, not which order or which coin has what result. Just what is the probability of a specific outcome.

HT or TH doesn't satisfy the outcome, only HH does. The chance of getting either HT/TH or HH is 50/50.

>>744383839
>Do we count the answer after one of them has been determined it is heads?

Of course we do. It's stipulated in the prompt.

>>744383839
this is correct reasoning

>>744383832
>Future events cannot affect the past.
>Prove me wrong.

Look up delayed observation double slit experiment. Quantum mechanics says you're wrong.

Answer - 1/3

>>744383981
we're dealing with coins, not photons

>All of these kids forgetting that the coin can be balanced on its edge.
There are three terminal states, children.

flip both coins at the same time, we know one of them will be heads, what we are left with is 50/50 percent chance of getting another heads

it is 50%

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>>744383927
>you need to get laid

I'm laying the smackdown on mathematically illterate retards, son.

Pic Related: 1/3

>>744383482
Given that at least 1 landed heads, then TT is not an outcome. Given that you weren't given a coin flip order HT = TH and your only possible outcomes are HT and HH. Bayes Theorem applies to things like cancer where your probability or having cancer is affected by family members having/had cancer. The coin flips are independent events.

>>744383938

HT = 1/3
TH = 1/3
HH = 1/3

Stay in school.

>>744384127
(everyone be nice to the autist, he can't do much so give him a moment)

>>744383890
>>744381730

>Two regular coins were flipped. What is the probability that both landed heads given that at least one of them landed heads?

That's what the image says. Don't trust me? Scroll up and check.

Two coins got flipped. One of them is heads, full stop. %100 guarantee that one of the coins is heads. There is no ambiguity there. You've got a heads coin, every single time.

Got it?

Sure?

Ok.

So then. If one of those coins is heads, what is the probability that the other coin is heads or tails?

>>744384200
1/3 obviously

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>>744384063

The result of the coin isn't affecting the past probability. It affects the FUTURE probability.

This is basic conditional probability.

If we flip 2 coins, we get HH 25% of the time.

If we flip 2 coins and are told that AT LEAST ONE landed heads, we get HH ~33% of the time.

Why? Because the outcome of TT is no longer possible given AT LEAST ONE coin landed heads. So from thi spoint forward, the probability of HH has changed from 1/4 to 1/3

Answer to OP is 1/3?

>>744384195

>knowing basic conditional probability and gettin lulz from explaining it to retards means you have autism

What's it like being retarded, lad?

>>744384378
there are only two results
(HT = TH) and (HH)

you always have 50% chance of getting HH, because HT and TH are the same thing

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>>744384176
>Given that at least 1 landed heads, then TT is not an outcome.
Correct.

>Given that you weren't given a coin flip order HT = TH
Incorrect. These are 2 separate and distinct outcomes, just as HH is distinct from TT.

>your only possible outcomes are HT and HH.
and TH

>Bayes Theorem applies to things like cancer where your probability or having cancer is affected by family members having/had cancer.
HAHAHHAHAHAHA Bayes' Theorem applies to conditional probability, lad, which is what the OP question is about.

>The coin flips are independent events.
Correct.

1/3

If you still don't understand why, answer pic related.

>>744384494
is correct.

P(heads = 2 | heads >= 1) = P(heads = 2) / P(heads >= 1)
= (1/4)/(1-1/4) = 1/3

>>744384180
There is no difference between TH and HT because one is always heads in this scenario. TT cannot happen because there is a head already present, and because we already have a head then HT = TH
We take H as a given. Therefore the remaining chance is H/T. 1/2 chance.
The easy way to do this is to flip two coins and remove any times that you don't get at least one head. You will only have scenarios wherein HH happens and HT happens, roughly 50% of the time each.
I just tried it myself and I had 11 HH and 9 HT
Which we can agree us closer to 50% than 33.3r%
Anybody who considers TH == HT needs to understand that because the only counted occurrences are ones in which one heads is present, if you distinguish the two coins it becomes
TH 1/4
HT 1/4
HH 1/2

>>744384428
it would be funnier if you were right

>>744384200
>So then. If one of those coins is heads, what is the probability that the other coin is heads or tails?
50%, but that's a different question to the OP question.

>>744384635
No its not.

>>744384494
>there are only two results
>(HT = TH) and (HH)

If you want to pretend that TH and HT are the same outcome, then you must add their probabilities together, in which case
HT/TH = 2/3
HH = 1/3

Answer is still 1/3

Exactly
Even if oyu want to take HT and TH as the same outcome, fine. But you must also realise that it is TWICE AS LIKELY as HH. This question is about probability. Therefore one H and one T, no matter what order it's in, is twice as likely as HH.

So, excluding TT:
Probability of HH: x
Probability of only one H: 2x

Answer is stil 1/3, dumbos.

ITT: negros struggling with basic probability

>>744384635
No it isn't, because OP question does not ask for the probability of TH or HT, only HH
If one H is always a given, then the probability of HH exclusively depends on the second coin toss. TH = HT not because they aren't different outcomes, but because they're both simply not HH. TH happens 1/4 of the time, HT happens 1/4 of the time, TT happens 1/4 of the time and HH happens 1/4 of the time.
This means the chance for two of the same faces is 2/4 and two different ones is 2/4
Since TT is not an option, it cannot occur, however it two of the same face still occurs 2/4. TT's quarter is not shared equally between the other three possibility's but rather given exclusively to HH
This mean its a 2/4 chance for two different faces (1/4 each) and a 2/4 for HH
50% chance

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>>744384597
>There is no difference between TH and HT

You're dumb, son.

Flip a penny and a quarter. If they do not both land tails, then you are left with 3 equally likely outcomes
>penny=heads, quarter=heads
or
>penny=heads, quarter=tails
or
>penny=tails, quarter=heads

1/3 to get both heads

>The easy way to do this is to flip two coins and remove any times that you don't get at least one head.
Correct. I suggest you do this at least 100 times with a pen and paper and write down how many times you get both heads, You will soon notice that you get both heads about 1 out of every 3 cases where you get at least 1 heads. Because I'm not retarded, I wrote a program that simulates this exact coin flipping. Oh wow, look at that result. Pic related.

TH 1/3
HT 1/3
HH 1/3

Fixed that for you, anon.

>>744384567
dear sir you can't have conditional probability alongside independent events. You yourself have admitted that the coin flips are independendent events. Stay in school lad and don't go gambling.

>The coin flips are independent events.
Correct.

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>>744384682
>>744385061

It is different, because you're asking for the probability of a SINGLE coin.

OP is asking for the probabillity that BOTH coins landed heads given AT LEAST ONE landed heads.

the heads coin could be either coin, meaning you can't just ignore a coin and pretend its the heads coin because it could very well be tails.

In the OP question, the only possibilty that can no longer occur is tails, tails.

the other 3 outcomes are all possible and equally likely. i know this is a difficult concept for you lads to understand because probability is often counter-intuitive, but the answer to OP question is 1/3

If the OP stated that the FIRST coin landed heads, then th eprobability would be 50% or 1/2.

But since we don't know WHICH coin landed heads, either coin could be tails, just not both at the same time, and the probability of getting both heads is 1/3

Pic related

Source: Washington University Math Department (See slide 4)

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

>>744385070
>he thinks he is not retarded because he can program

you sir have autism

>>744384597
I understand your point of view cause its the most immediate one. This riddle is just a joke made by a certain wording.

You believe basically only one coin is being tossed, because you already know one landed, and it lande heads. In this case the question about two coin tossed is a non question beucase only one coin is tossed at the end of the day, so 50% is correct.

But by the original question both coin are flipped together and only after they both have landed you are given to know that at least one of them is heads up. In this case the anon answering up is right with his reasoning. You get to exclude tt. In you assumption instead you exclude tt and th. Yours is an entire different scenario. Basically there's no first coin. Only -t and -x

>>744382413
2/3 are NOT both heads, moron

50%
one is already flipped on heads. the chances that the other flips head too is 50%.
basically the question is "how are the chances one coin flips head" since the other will flip head anyways.

>>744385070
I actually have now reached 50
22 HH, 28 TH/HT
I welcome other people to try this too. Maths attempts to solve probability, probability is not dictated by maths. No matter how you look at it, if these tests keep coming out at in and around 50% then the answer is 50%
I'm not disputing that 3 outcomes exist, they just simply aren't all equally weighted, at least in practice. One is always H, meaning the only factor is the second coin. It doesnt matter if its the first or second coin you flip, because one of them always has to be heads, meaning the only variation is in the second coin.
Look at it this way;
In the scenarios remaining, we have:
TH HT HH
Or
HHHH TT as possible individual coin results.
4 heads and two tails
If we take the three given heads out we get
H TT
T and T are not two distinct entities, they are the same result as we still only have one coin.
H will appear 50% of the time. And the two possible occurances of T will appear 25% of the time each.
The flaw in your logic is that you think HT and TH are seperate, and yet you don't see the difrerence in HH and HH, when the given H is on either side.
HH in which the first H was the given H will appear 25% of the time
HH in which the second H was the given H will appear 25% of the time
TH will appear 25% of the time
HT will appear 25% of the time

>>744382868
it doesn't matter

>first coin go heads
>50% chance the other will flip heads too
>first coin go not heads
>the other will go heads

only one coin matters since the other goes heads anyways. it doesn't matter if the first or second is the magic heads coin, only the other one is important.

One of the coins HAS to be heads.
Therefore, only one coin can be tails or heads. 50/50.

>>744385126

>can't have independent events in conditional probability

Damn, you're a moron.

Buy a lotter ticket. you either win or you dont. One event

Buy another lottery ticket. you either win or you don't. One event.

What is the probability that you win twice?

What is the probability that you win twice when you win at least one time?

OMG CONDITIONAL PROBABILITY 2 SEPARATE EVENTS HOW IS RTHIS POSSIBLE????!!!?!?!?!?

Answer to OP is 1/3.

they are independent events, so the probability of one event happening doesn't effect the probability of the other. the answer is 50%. statistic major here

>>744385410

>can't program
>can't do basic probability
>you, sir

Go back to reddlt you fucking faggot.

1/3

>>744386236
*tips fedora*

>>744386101
HHAHAHHA this is rich a fucken mong calling me stupid when he doesn't know the meaning of independent event. Here is a hint retard "Idendent"

>>744385754

Incorrect. Read the explanations in this thread.

1/3

>>744382560

2 outcomes:

HH
HT

since the first coin has to be heads. hence 50%

>>744382201

jesus they are independent events, the conditional probability makes no difference

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>>744381730
Justin Trudeau says, "100%"

>>744386324
No, the first coin does not have to be heads. The second coin can be heads if the first isn't.

3 outcomes:
HH
HT
TH

Out of those, 1/3 probability of both heads.

>>744386324
Read the OP it doesnt state one coin always lands heads. It says at least one of the coins will be heads.
That means either can be heads and either can be tails, but at least one of the 2 will land heads. So 3 possible outcomes.

File: coins2_1.jpg (60KB, 1066x398px) Image search: [Google]

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>>744385786
Keep going, anon. Approach infinity. realize 1/3 is correct. Bayes' theorem doesn't lie. It's a mathematical proof.

>>744385786
>I'm not disputing that 3 outcomes exist, they just simply aren't all equally weighted,
Yes, they are. You can't reason why they're not.

>One is always H
Incorrect. 2 coins were flipped and at least one landed heads, One isn't ALWAYS heads. This is the error in your logic. You assume that 1 coin is ALWAYS heads as if it is left on the table in a heads up position and not counted. ytou are, therefore, denying the coin the ability to land as tails, where the OP question DOES NOT deny either coin the ability to land tails. The only possibility that the OP question disallows is that both coins land tails. the other 3 outcomes are possible, and EQUALLY LIKELY to occur.

>It doesnt matter if its the first or second coin you flip, because one of them always has to be heads, meaning the only variation is in the second coin.
It's amazing how you just contradicted yourself and yet fail to see it. Again, you say it does not matter if the heads coin is first or second, then you immediately say that only the result of the "second" coin matters, thereby falsely assuming that the "first" coin landed tails. Do you understand that there are 3 possible outcomes and they are all equally likely?

So far, the 50% people have used flawed logic and zero mathematical solutions.

The 1/3 people have used
>Bayes' Theorem
>links to University Math department explanations
>Venn Diagram
>Probability trees
>Computer simulations

1/3 is correct. Deal with it.

>>744386324
The chance of HH is 50% smaller than the chance of getting HT (since you can also get that with TH)

>>744385985

So you agree that there are 3 equally likely outcomes

first coin=heads, second coin=heads
or
first coin=heads, second coin=tails
or
first coin=tails, second coin=heads

1/3

>>744386178
>statistic major here

What retard college did you go to?

>>744386870
There's 100% probability that there is a heads coin. That leaves one coin left, with a probability of 50% of being heads also.

>>744386944
there's no "first coin / second coin", your first 2 options are literally the same, mathematically

you only have 2 options. heads/tails or heads/heads
heads / tails and tails / heads are the same

{(heads, tails)} = {(tails, heads)}

disagreeing is like saying

{1,2,3,4} is not the same as {4,3,2,1} which it clearly is. the order doesnt matter, they're the same set

one is already heads. it doesn't matter which one. It could be the first or last, it's already accounted for and that removes it from the equation.

That only leaves two possible outcomes for the one that ISNT heads yet.

50%

You can even test it in action. Get a double sided heads coin, and a regular coin. Flip them both at the same time; flip them in any order; shit them out of your ass on the floor and see how they land. It's going to be 50% every time.

jesus christ you faggots that think its not 50% really cant comprehend things.

>>744387271
>heads / tails and tails / heads are the same

No, they're not. Read this >>744383363

They are 2 distinct outcomes, each with an initial probability of 1/4.

Flip 2 coins 1000 times. you will get
HH - 250 times
HT - 250 times
TH - 250 times
TT - 250 times

Out of all cases where you get at least 1 heads (HT, TH, HH = 750 times), you get both heads 250 times

250/750 = 1/3

>>744387672
>It could be the first or last, it's already accounted for and that removes it from the equation.

there are 3 equally likely outcomes

first coin=heads, second coin=heads
or
first coin=heads, second coin=tails
or
first coin=tails, second coin=heads

All 3 outcomes are equally likely

1/3

You don't know which coin landed heads, therefore they are both still variable and NEITHER can be removed from the equation.

>>744387679
TT is not an option in this case, so this logic is invalid.

>>744387759
>You don't know which coin landed heads

you comprehend the question wrong. It's not asking you what the outcome probability of both coins flipped is, its asking what the probability of the unknown coin landing heads is. Since we know that one is already heads, and it doesn't matter which one, it doesn't factor in. Flip them at the same fucking time; one is always heads, and only the other is the variable, it doesn't matter which coin is always heads, because it's a constant.

File: coins3.jpg (18KB, 470x342px) Image search: [Google]

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>>744387271
>{1,2,3,4} is not the same as {4,3,2,1} which it clearly is. the order doesnt matter, they're the same set

You're confusing "set" with event outcome.

The sample set for a 2 coin flip is {HH, HT, TH, TT}
and each of those outcomes are equally likely (1/4)

When at least 1 coin landed heads the sample set is reduced to {HH, HT, TH}
and each of those are equally likely (1/3)

1/3

>jesus christ you faggots that think its not 50% really cant comprehend things.
We just understand basic conditional probability.

1/3

Pic Related: Punnet Square

>inb4 w-w-whats a punnet square??

>>744388111

Did you read the whole post?

Basic stats. Use binomial distribution. Two trials at .5 prob each. 0.5 x 0.5 = 0.25 or 25.percent chance of getting two heads in row.

>>744388245
using a punnet square to factor in an outcome that cannot exist in the confines of the question invalidates the square.

>>744388240
>It's not asking you what the outcome probability of both coins flipped is

What is the probability that both coins landed heads given at least one coin landed heads?

Answer = 1/3

>>744388245
no, you're just bunching up subsets into variable names to make them appear the same

the sample space for 2 coins is {(H, H), (H, T), (T, H) and (T, T)}, two of which are the same subsets
because the order doesnt matter in sets

>>744386870
This entire post is all the evidence I need to show that you don't understand what you're talking about. When i say 'the second coin' I am not implying that one is face down heads, however I might as well. Because if one is not, then the other is. Regardless of order, i one of the two will always be heads, and hence i consider this to be the first coin, regardless of whether or not it is the first coin I flip. I specified this in the post, you were just unable to understand this and assumed it a contradiction. Regardless of order, there is a 0% chance that I wont have a head, and hence i can always assume that I have a head. As this is the only certainty in the equation, i consider this the first coin i work with.
You also said that the statement "one is always H" is incorrect, when it is in fact correct. I did not state that 'coin A is always H', I stated that one coin will always be H, i did not specify which of the two coins would have to be H.
I mathematically proved it and you chose of course to not address that bit. All you've proven with this response is that you don't understand basic english or the concept of logic.
One coin will always be H. If you call that incorrect, then you do not understand the question.

>>744388561
*make them appear different

what you did is saying (12, 34) is not the same as (43, 21), because of course those are different numbers

>>744383981
Actually anon, there is recent discussion that future events actually cannot affect the past.

>>744386944
no
only one coin matters. we don't know if the first or second but it's irrelevant anyways. only one coin matters.
50% chance

>>744381730
33% (1/3)

File: coinsss.jpg (53KB, 360x640px) Image search: [Google]

53KB, 360x640px

>>744388396

Stop talking and show me your math solution.

Here is the correct solution:
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

>>744388368

Now read the question, dingus.

>>744388561
>two of which are the same subsets

Which 2?

>>744388913
was trying to remember this formula, thank you anon

>>744381730
2 to the second is 4 so there's a 1 in 4 chance that both coins will land heads.

If you already flipped 1 and it landed heads, that leave son.y 2 possibilities left, so a 1 in 2 chance that both wind up heads after one already lands heads.

>>744388650
>When i say 'the second coin' I am not implying that one is face down heads, however I might as well.
So you claim you're not being retarded but you might as well be?

>Because if one is not, then the other is.
So we could have the following cases using your logic:
coinA is not heads, coinB is heads
or
coinA is heads, coinB is not heads
or
coinA is heads, coinB is heads

3 equally likely outcomes. 1/3

>One coin will always be H.
>will always be
>will
>in the future

Incorrect. 2 coins were flipped and at least one landed heads. Could be first coin. Could be second coin, meaning either coin could be tails, just not both at the same time.

HH, HT, TH all equally likely
TT no longer a possible outcome

3 outcomes.
1 of the 3 is HH
1 of 3

1/3

>Take 2 Coins
>Flip both at same time 100 times
>50 times 1 head 1 tail
>25 both head
>25 both tail
>fuck
>gotta count out the 25 which are both tail
>25/75 were now both heads
>1/3 (divided by 25, i dont know how deep the explanation has to go for undereducated board)

TL,DR: 1/3 or 33%
Cunts need to distract the failed tries

>>744388858
>we don't know if the first or second but it's irrelevant anyways.

So you agree that both coins are variable but this variabilty is irrelevant?

HAHAHAHAHHAHAHAHAHA

1/3

>>744388913
>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?

you're wrong. the question is "what is the possibility that the other coin flips head". the always heads coin doesn't matter since it always lands on head.

George Carlin was right.

>>744389598
This is the right answer.

50%

>>744389593
yes, one coin is irrelevant.

>>744388913
except the question isn't which subset of coins flipped is HH, it's the total outcome of both coins flipped where one coins outcome is already know, but its position in the flip is variable.

It doesn't matter which coin is heads. One is always going to be heads. What matters is the one that can produce a variable outcome. In the frame of the question H/T and T/H are the same outcome, simply because one of the flips was already going to he H without variable. An outcome of T on the first flip invalidates the next flip, we already know it's going to be H and that it's not H/H. Landing H first moves the variable onto the second coin since we can assume it was the H outcome all along.

Math about it all you want, but in practical application the outcome will always be 50/50, since the question is only asking for the total sum of the outcome, it's either a true (HH) or false (HT/TH).

>>744389674
>George Carlin was right.
did he made a "how to troll /b/ " guide?