How smart is /b/?
The stories and information posted here are artistic works of fiction and falsehood.
Only a fool would take anything posted here as fact.
Only a fool would take anything posted here as fact.
How smart is /b/?
>>704031833
one in two. Also, sage.
>>704031833
50%
Ok so they use the other coin to fool you. Just pretend it's one coin so 50/50
23.5% every 50%
>>704032202
>>704032223
Wrong, faggots.
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:
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
>>704031833
Every time the coin is flipped its 50/50. There is no diminishing returns on a determined probability
>>704032478
TH and HT are the same and can be treated as one, considering the fact that oder doesn't matter. Pretentious fuck.
>>704032596
You forgot this guy >>704032596
>>704032798
>TH and HT are the same
You're fucking retarded.
That coin has a better chance than op at getting some pussy
>>704032798
>TH and HT are the same
HAHAHAHAHAHA This is what the 50% tards actually believe.
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
You guys are wrong.
remember PEMDAS
It's 1/3. End of discussion
>>704033184
Show your work son
>>704033232
1/3
>>704033084
Your first example are penny and quarter. OP's pic is 1 dollar. They will yield different answers, so you cannot use a penny and a quarter to counter the argument.
TH and HT are the same in terms of probability, because they're interchangable.
>>704033529
>1 dollar
Troll harder.
1/3
>>704032478
>Acting as if TH and HT aren't identical.
>Shut the fuck up nigger
>>704033759
TH and HT are interchangable so they are treated as one.
1/2
Since one is guaranteed heads.
>>704033796
>>704033830
>TH and HT are interchangable so they are treated as one.
lol retards
1/3
>>704033862
Coin 1 isn't already heads, either Coin 1 or Coin 2 are already heads. The situations you could have are HT, HH, TH.
>>704033862
Coin1 could be tails, dumbass.
1/3
>>704031833
keep this in mind 1/3 faggots
>>704031833
HH
HT
never TT
TH
1/3
>>704034215
At least one. Could be either.
HH, HT, TH
1/3
>>704034152
>>704034149
It doesn't matter which one is con one, you impudent swines, there is a guaranteed heads, it doesn't matter which one is coin 1, whichever land heads is automatically coin one.
>>704034440
Did one of them landed heads or not?
Yes, or no?
>>704033830
You can treat them as the same-you are right. But if you do, you have to consider one head and one tail to be twice as likely as two heads. Therefore it's 1/3
>>704034501
>>704034529
At least one landed heads.
For a 2-coin flip, there are 3 equally likely ways to get at least 1 heads coin.
heads, heads
heads, tails
tails, heads
Those are the 3 options. They are all equally likely.
1/3
You all just got BTFO by logic and math, faggots.
If the question would've said 'coin 1 lands heads', it would indeed have been 1/2, because then only the following three combinations are possible:
HH
HT
But here, the question only gives a piece of information that eliminates the combination TT
Only the following three combinations are possible:
HH
TH
HT
Thus making it 1/3
50. IF ONE was Heads the other one is 50/50
If the other one isn't heads. it doenst matter so that doens't count
>>704034718
two* in first sentence
Guys, guys, it's really very simple. If you flip 2 coins and at least 1 landed heads, you could have:
coin1=heads, coin2=tails
or
coin1=tails, coin2=heads
or
both coins heads
1/3
Simple.
>>704034697
Did one of those coins landed heads or not?
It's a simple question.
Retards see pic related.
1/3
>>704034906
At least one.
1/3.
>>704034960
So, one of them landed heads, correct?
If you know one of the two coins landed heads, what are the odds that BOTH landed heads?
>>704034501
The possible outcomes are:
TT - 1/4
HH - 1/4
HT - 1/4
TH - 1/4
> B-But HT and TH are the same!
If you treat HT and TH as the same (i.e: disregard the coins' order), then you also have to recognise that HT/TH has double the chance of either HH or TT. You can test this yourself by flipping two coins, or one coin twice. This makes the possible outcomes:
TT - 1/4
HH - 1/4
HT/TH - 2/4
Then, as at least one of them landed heads, TT can't be an outcome, so we remove it from our possible outcomes:
HH - 1/3
HT/TH - 2/3
And there we have our answer, the chance of HH is 1/3.
If you don't agree, reread this post until you do, because it's correct.
This thread again... 1/3, everyone who says otherwise please revisit Bayes' Theorem and conditional probabilities
If after that you're still convinced it's 1/2, don't ever play chance games, you'll be broke in no time..
>>704035049
At least one landed heads.
>what are the odds that BOTH landed heads?
The probability that both coins landed heads given that at least 1 coin landed heads is 1/3.
If you're not trolling, this is actually funny how retarded you are.
>>704035190
Did one of them landed heads or not?
Just answer my question.
>>704035057
it can land on the side which makes your pretty table incimplete
>>704035252
At least one landed heads.
1/3
>>704035289
>it can land on the side
Probability of that happening is so minute that it's negligible.
1/3
>>704034501
Let's just start rolling and see if your theory works out. I'll roll every possible combination!
First I roll Heads
Then I roll Tails
HT - value of 1
First I roll Tails
Then I roll Tails
TT - value of 0 (not a possibility)
First I roll Tails
Then I roll Heads
TH - value of 1
First I roll Heads
Then I roll Heads
HH - value of 1
Okay. So I've been playing this game and I've had all possibilities an equal amount of times.
Now let's look at the data
HT 1
TT 0
HH 1
TH 1
Okay. So there are 2 combinations where ONE of them is heads and the other is tails. The last, third combination is the heads
So out of the THREE possibilities, ONE of them is HH
1
----
3
>>704031833
Step up you fucking faggots
Argue with a damn statistics program
>>704031833
Here's the thing brothers. You cannot apply the problem at the start, 2 coins, unflipped, to the whole problem. Let's say that at the start there are two coins with possible outcomes of...
HH, HT, TH, TT
And after the coin is flipped the possible outcomes now become.....
HH or HT
TH and TT are no longer possible.
It's a trick question. While there are 4 possible outcomes at the beginning of the problem, halfway through the problem the possibilities become 50/50.
>>704035252
one of them handed head yes, but you only get this information after both coins were already flipped, you just did not get to see them yet.. this chances the probabilities
it would be 50/50 if they said coin 1 was heads, if i now throw coin 2 what are the chances for double heads? but that was not the question
>>704035574
You forgot the "given that at least one of them landed heads" part. Garbage in, garbage out.
>>704035712
No I actually didn't though.
>>704035314
Did one of the coins landed heads or not?
Why can't you answer to the question directly?
I know why, it's because the answer will make you sound like a fucking idiot, right? lol
>>704035660
read >>704034215
It DOES say 1 of them landed heads.
>>704035397
Still possible and it affects the result
>>704035632
> And after the coin is flipped the possible outcomes now become.....
> HH or HT
> TH and TT are no longer possible.
Only if the first coin you flip is H, which it may not be.
>>704032478
The coin doesn't care about your maths.
>>704035791
Is your answer the 0.25, or am I reading from the wrong place?
>>704035574
Fuck sake, you retard. You didn't account for the CONDITION that at least 1 coin landed heads.
This is a conditional probability question.
1/3
>>704035632
TH is still a valid outcome which satisfies the condition of having at least 1 heads coin, sop you're wrong.
You can have
HH or HT or TH
1/3
>It's a trick question.
No, it's a basic conditional probability question and you're a FUCKING MORON. HEY MORON, look, Washington University Math Dept. says you're a FUCKING MORON.
Source: (Slide 4)
http://courses.cs.washington.edu/courses/cse312/11wi/slides/04cprob.pdf
1/3
>>704035866
He said it was. He said the first coin flipped is a heads.
>>704035289
OP's coins are 2D, so the chance is 0. Checkmate.
>>704035949
But it may not be.
>>704035866
You are assuming the coins weren't flipped at the same time, and that's not stated anywhere in the problem. The only guarantee it gives you is that one of the coins landed heads.
It only says they were flipped, so if your answer only applies to a scenario where each one of them is flipped separately, then your answer is incorrect.
>>704036055
>>704036055
Then it's always heads...
>>704035946
From your slides
What is the probability that both flips land on heads if...
• The first flip lands on heads?
Let B = {HH} and F = {HH, HT}
P(B|F) = P(BF)/P(F) = P({HH})/P({HH, HT})
= (1/4)/(2/4) = 1/2
>>704035934
>>704035946
Answer is still .25
If you get a heads once with one coin and then flip that same coin again the chance of getting heads two times in a row is .25
You are both wrong and your logic is flawed.
Is you span this system out over a large number of tries you will find that you will succedd 25% of the time or close to it. Go ahead and try it yourself.
>>704035803
yes, and it also says "both coins WERE flipped" before that
to sum it up:
2 coins WERE flipped by someone, you don't know the result
that someone tells you ATLEAST 1 is heads
this info gives you some information about the outcome, but nothing about a supposed second coin flip, they both already landed, so 1/3 is the only correct answer
>>704034828
>HT/TH - 2/4
You're not treating them as one because the 2/4 is still saying that they are seperate.
TT - 1/4
HH - 1/4
TH - 1/4
HT - 1/4
and since TH and HT are treated as one, we get
TT - 1/3
HH - 1/3
TH/HT - 1/3
and since TT is out of the picture, you get
HH - 1/2
TH/HT - 1/2
HH = 1/2
>>704035803
>Did one of the coins landed heads or not?
At least 1 landed heads.
>Why can't you answer to the question directly?
I did. You can't answer "yes" or "no" to that question because that question specifies 1 coin landed heads, which doesn't allow for the possibility that 2 coins landed heads, so the question as phrased is not relevant to the OP question.
>It DOES say 1 of them landed heads.
No, it says "At least 1 coin landed heads." There is a difference between those two statements.
If I tell you that your parents were standing on the edge of a cliff and ONE OF THEM JUMPED OFF, you'd be upset.
If I tell you that AT LEAST ONE of them jumped off, there's a chance that you're now a fucking orphan.
Do you understand the difference? YOu fucking simpleton?
1/3
>>704033084
good thing they aren't different coins in this situation, cunt
>>704036148
What time they were flipped doesn't matter. They're independent; the probability doesn't change if one was flipped before the other, if they were flipped at the same time, if they were flipped after midnight, etc..
I could also call them the left coin and the right coin, doesn't matter.
>>704031833
75%
>>704036191
Yes. Now read the next part, which is the same as OP question.
1/3
>>704036191
"The first flip", not "at least one flip".
Whether you're saying one pre-defined coin lands on heads, or just either of them, does matter.
>>704036257
That someone tells you that at least one of those coins LANDED heads.
Why are you focusing so much on the "at least" part? I already stated it doesn't matter which one landed heads, IT DOES matter that one of them did land heads, but that part you are completely skewing over, for some retarded reason.
Answer me the following questions:
How many coins were flipped?
Did one of them landed heads?
What are the odds that both landed heads, IF YOU ALREADY KNOW that one of them landed heads?
>>704036246
>If you get a heads once with one coin and then flip that same coin again the chance of getting heads two times in a row is .25
You're retarded. Holy fuck.
>>704035803
It does say that both coins were flipped, assuming simultaneously. I read it the first time and thought it said "you have two coins, and flip the first one and it is heads... If both coins are flipped simultaneously the chances of the second coin are 1/3. But if the first coin is flipped and comes up heads, the second coin has a 50% chance of coming up heads, or tails. If the first coin is flipped and the outcome is known, then for the second coin the chances are 50/50.
>>704036350
You're retarded.
1/3
>>704031833
answer is 50/50 you faggots either they both land on heads or they don't
>>704031833
This is why you gotta love /b
>>704036373
>HurR the coins are the s-same that means it changes the probabilities HurR Duru
Retard
1/3
>>704036564
2
yes
1/3
XD, seriously, do the experiment yourself a couple of times (you need someone to flip 2 coins and only include the flips were atleast 1 lands heads), guess double heads each times, you'll be wrong more often then you'll be right
>>704036246
So the chance of getting two heads, given you've already gotten one heads, is exactly the same as the chance of getting two heads not given that?
Is your chance of rolling twenty 6's the same as your chance of rolling twenty 6's given you've already gotten nineteen 6's?
>>704033529
this triggered me
>>704036599
Is my $1000 statistical program retarded?
Or are you?
>>704036564
>How many coins were flipped?
2
>Did one of them landed heads?
We don't know. All we know is that at least one landed heads, so it could be 1 or it could be 2.
>What are the odds that both landed heads, IF YOU ALREADY KNOW that one of them landed heads?
We already now that AT LEAST 1 landed heads, so then the answer is 1/3.
>>704036673
Your explanation treats TH and HT as if they're unique. You're the fucking pretentious retard here. Not to mention counter-productive due to the fact that you barely explain why I'm wrong and just made up your own answer on why you're "right".
>>704036965
the program is not, nor is the other anon, the culprit is the user and specifically the use of the $1000 program
>>704036350
> You're not treating them as one because the 2/4 is still saying that they are seperate.
What the hell does that mean?
> TT - 1/3
> HH - 1/3
> TH/HT - 1/3
Literally get a coin right now. Throw it twice. Write if you got TT, HH, or TH/HT. Repeat.
You will get TH/HT twice as often as you get HH.
>>704036882
Yes. That is exactly what I am saying. You are looking at short term probability but that is not how a statitical pricedure is measured. You would have to look at the process over a long interval of inputs.
If you ever even managed to roll 19 6's in a row you would only be able to roll another 6 1/6 of the times that you ever even succeded in rolling 19 6s
>>704036356
>If I tell you that AT LEAST ONE of them jumped off, there's a chance that you're now a fucking orphan.
This is a pretty retarded false equivalency, since it assumes only two possible outcomes of an extremely complex situation "them jumping" or "them not jumping" and compares it to a coin flip.
Keep the subject on topic, and avoid using retarded examples are only comparable in your mind.
This isn't a hard question to answer, just say yes, or no:
Did one o the coins landed heads or not?
>>704037092
Bro. You don't have to be mad just because you are wrong. It happens man it's okay
>>704036965
Your program is fine. You're just retarded and using it incorrectly to answer a different question. Your program is answering teh question
>What is the probability of flipping 2 coins and they both land heads?
When you SHOULD be asking a conditional probability question:
>What is the probability that BOTH coins landed heads GIVEN THE CONDITION that at least 1 coin landed heads?
Let's play a game, faggot.
If you flip a coin and it is heads, what is the probability that the next flip is also heads?
>>704037031
I'm the guy that explained it to you, not the one who called you retarded (but you are).
>>704036395
Ok, so, you are going to tell me if one of them landed heads, or are you going to refuse to answer and bring up another bullshit to explain your twisted line of thinking?
>>704037092
I'm not mad, actually I'm laughing my ass of and enjoying the retardness of the people claiming anything other than 1/3
>>704031833
Not this bait again... here's the answer, though.
This question is purposely unclear and is meant to mislead. There are three possible answers depending on the mechanics involved:
>One specific flip is a guaranteed heads, the other is a 50% chance. So effectively, you flip only one coin.
>Possible outcome sets: (HH, HT) or (HH, TH), depending on which coin is guaranteed to be heads
50% chance of two heads
>Flip twice, if neither coins are heads, re-flip both coins.
>Possible outcomes: HH, TH, HT
33.33...% chance for two heads
>Flip one coin. If it is not heads, the second is automatically heads. If not, flip the second coin
>Possible outcomes for flip 1: T,H (50% probability for each)
>Possible outcomes for flip 2 if flip 1 is H: T,H (splits the 50% probability for flip 1: 25% each)
>Possible outcomes for flip 2 if flip 1 is T: automatic H (maintains the probability of flip one: 50%)
25% chance for two heads
Someone please /thread this so we can move on.
>>704037278
.25
>>704037332
What? Yes; one of them landed heads.
>>704036880
>2
>yes
Ok, so if one of the coins landed heads, and YOU KNOW IT because it says right here >>704034215, then what are the odds that BOTH landed heads?
Remember, you admitted that you KNOW one of them is BOUND to be heads already
>>704033084
Whew lad
>>704033084
>>704032478
It upsets me that people don't understand this
>>704037031
>Your explanation treats TH and HT as if they're unique.
They are unique, you fucking retard.
Do you think that
penny = heads & quarter = tails
is the same as
penny = tails & quarter = heads?
If you do, then you are beyond retarded and they're is nothing we can do to help you understand how the answer is 1/3.
>you barely explain why I'm wrong and just made up your own answer
I posted solutions
>>704032478
>>704033084
>>704033384
>>704034697
>>704034930
>>704035314
>>704035946
Here's a simulation.
Also confirms 1/3
>>704031833
There are four possible outcomes when you flip a coin:
Heads/Heads
Tails/Tails
Heads/Tails
Tails/Heads
Tails/Tails is eliminated by the "at least one of them landed heads" statement of the problem. That leaves:
Heads/Heads
Heads/Tails
Tails/Heads
The odds it will be the first one is 1 in 3.
>>704036797
one of the coins is already heads
the other one is either heads or tails
>>704037650
Wrong
>>704037482
Good. If one of them landed heads, and remember what you said here:
> Yes; one of them landed heads.
Those were your own words.
What are the odds that BOTH coins landed heads?
Keep in mind that you already said that you KNOW ONE of them DID land heads.
>>704037437
So you've already flipped the first coin. The second coin is spinning mid-air. You're saying that the chance of that coin coming down heads is 25%? Not 50%?
If you were to flip 10 coins in a row and they all happened to come out heads, are you saying that the next coin has a 0.0009765625% chance of coming out heads?
https://en.wikipedia.org/wiki/Gambler%27s_fallacy
>>704037437
>.25
Fucking lol I hope you are trolling.
You are all wrong
S=side/circumference
Hh
Ht
Th
Sh
Hs
Ts
St
Tt
1/7 is answer. Time paradox
>>704037761
The possible scenarios are:
HT - 1/3
TH - 1/3
HH - 1/3
So 1/3.
If you disregard order, you could also group them like:
One head one tail - 2/3
Two heads - 1/3
Which still comes up with 1/3.
>>704037650
REKT.
ITT: idiots that think intuition can match education.
Your intuition is fucking WRONG, morons.
>>704037002
>We don't know.
Ok, I'll just assume you're a slow reader, and a little retarded so you can't understand what words mean so quickly.
Look at this image very patiently, here: >>704034215
Take your time, don't need to rush it, please. Now, try to tell me if you can understand what it says.
>>704037510
Yes, I admitted that, there are now 3 situations left
Coin 1 was heads and Coin 2 was tails
Coin 2 was heads and Coin 1 was tails
Both coins were heads
With this view the probabilities are equally distributed, 1/3 for each situation.
Now if you're going to say "but but but, the first 2 scenarios are the same!!!". Sure you can view them as the same, however if you do the probabilties are not equally distributed
One coin heads, one coin tails
Both coins were heads
The first scenario is twice as likely as the second. The answer for this question for both views is thus 1/3.
>>704037208
>Did one o the coins landed heads or not?
We don't know, you fucking retarded. All we know is that at least one did. So we can't say "Yes, one coin landed heads" because that eliminates the possibility that both coins landed heads. DO you understand English, you fucking pleb.
This question is more relevant:
>Did at least one coin land heads?
YES.
>>704037999
Ok, did one of the coins landed heads, or not?
Just answer me this question.
>>704037426
/thread
>>704038096
That image cuts out the "at least". We don't know if one in particular landed heads, but we know at least one of them did. (I'm not the guy you're replying to)
>>704037773
Yep
>>704031833
50/50 since one of them is already landed on heads.
HH or HT
HH or TH
>>704038178
Yes; one of them landed heads. We don't know which one, but one of them landed heads.
https://jsfiddle.net/GustvandeWal/fjb49mw2/
Run this simulation multiple times by pressing Run in the upper left corner. You'll see it always turns out around 33.3%
>>704037773
The thing is however the question clearly states that both coins WERE flipped. Meaning they already landed, since it's pretty impossible to ask a question in between the two coin landings....
>>704037753
Programmer here... He's not wrong. That is, indeed, a program designed to simulate this exact problem. He ran it with 100 million tests, and it came up 33.3% (one in three.)
>>704037747
Which 1?
Lets use computer logic here.
You have a chance of rolling 00 01 10 or 11
For those who don't know here are what they are in number
00 = 0
01 = 1
10 = 2
11 = 3
So, we have a 1/4 chance to get any of those combinations. But we know one thing, we for sure roll a 1 in either spot.
That in mind we now only have these choices, 01 10 and 11. For those who say "But 10 and 01 are the same!" I say no..
10 ~= 01 in the same way
2 ~= 1
Which means there is a 1/3 chance to get 11 for you have 3 possible rolls. 01,10, and 11
>>704038380
So
HH or HT or TH
1/3
>>704038583
I wasn't asking about the original problem in that post.
>>704038629
Anon, they can't even understand the difference between HT and TH and you expect them to understand binary?
OK FUCKHEADS
What if I told you the answer depends on how to interpret the question
>>704038629
Forgot to mention, the reason this is, is because we aren't told which digit gets put as 1, the same as we aren't told which coin is flipped as heads. If we were told that specifically the left coin(or in the binary case, the left digit) is flipped heads (or 1 in the binary case) then yes, we could say there is a 1/2 chance because we would have the option of HT or HH (10 or 11 in the binary case)
>>704038952
>What if I told you the answer depends on how to interpret the question
Then we'd call your reading comprehension into question.
The question is clear and concise. It is a conditional probability question and it has a correct answer of 1/3.
Anyone who says otherwise is either illiterate or mathematically illiterate.
>>704038357
You don't understand what it means for something to be given, or for probabilities to be independent. Alternatively you're just trolling.
Say you were in a casino after those 10 coin flips, would you bet a lot of money on the next coin flip coming out tails?
>>704038952
It's not down to interpretation. The fact the question does not tell us which place the coin that lands head will be in, which is to say it doesn't tell us exactly which coin will land heads, then we have 3 possibilities instead of 2. If we were told which coin would land heads, then we would have 2 possibilities because then there would only be 1 coin to toss because the other is already determined.
>>704038952
There is nothing unclear in the question. Anyone saying 1/2 or 1/4 is incorrect.
You flip two coin, you know one is is going to be heads. So you're waiting on 1 coin to land h or t. 50℅
>>704039859
You know that at least one of them is going to be heads, not that the first one is going to be heads.
>>704039859
Yes, but which coin will be heads? TH HT or HH 1/3 chance
>>704039950
He didn't ask what the chances of the order they might drop.
>>704032478
stfu u dumbfag. this ridiculous answer to every moronic how smart is b hurr durr question is finally getting on my nerves. either you faggots are actually that stupid or you have a lot of free time when you're not sucking dicks for comfort because you can't get a girlfriend. kys. also saged
>>704040415
> He didn't ask what the chances of the order they might drop.
What does that even mean?
The possible outcomes are:
TT - 1/4
HH - 1/4
HT - 1/4
TH - 1/4
If you treat HT and TH as the same (i.e: disregard the coins' order), then you also have to recognise that HT/TH has double the chance of either HH or TT. You can test this yourself by flipping two coins, or one coin twice. This makes the possible outcomes:
TT - 1/4
HH - 1/4
HT/TH - 2/4
Then, as at least one of them landed heads, TT can't be an outcome, so we remove it from our possible outcomes:
HH - 1/3
HT/TH - 2/3
And there we have our answer, the chance of HH is 1/3.
1/4
>>704040746
>answering hs question in paragraphs
>underage b&
>>704040924
I just copy pasted what was written earlier.
>>704040686
>I'm retarded and don't understand the correct solution and it makes me mad waaaaaah
kek
1/3
>>704040746
You take a coin out, because it has no chance, its 100% going to be heads. Your left with h or t.
>>704041555
No coin is "100% going to be heads", either coin (or both) could be heads.
>>704042940
"At least one of them" means either coin could be heads, not one in particular is heads.
>>704042314
The odds of getting ht/hh/th in one of those orders is 1/3 but the chances of it being hh is 50% due to the fact one is going to be heads. So the other can only be heads or tails.
(HH, TH, HT, TT)
One coin will land on heads out of the two coin tosses. It could be the first OR the second coin that is tossed. Therefore, we have to account for ALL the possible outcomes instead of simply eliminating the probability of the coin that is "given to land on heads".
Therefore, we assume that the outcome will be either (H X) or (X H). This is the given.
X = T or H
Now, let's flip our two coins.
(H,T) (T,H) (H,H)
1/3 of these outcomes is the proper outcome.
Therefore, the probability is 1/3
>>704043337
> The odds of getting ht/hh/th in one of those orders is 1/3
So HH is in the list that you're saying has a 1/3 chance to get?
> but the chances of it being hh is 50%
You just said it was 1/3? Or are you saying that HH is different to HH?
> due to the fact one is going to be heads. So the other can only be heads or tails.
You can't do this, as you don't know which one is going to be heads.
Read:
>>704040746
>>704043337
>it's 1/3 but it's 50%
You're retarded.
>>704031833
50% for one head and 25% for two heads.
Because https://en.m.wikipedia.org/wiki/Independence_(probability_theory)
/thread
>>704044356
The thread's pretty much over anyway. What you're saying doesn't apply when it's given that you get at least one head.
>>704044356
You fucking retard.
https://en.wikipedia.org/wiki/Conditional_probability
1/3
>>704043680
If you put one coin down as heads (because you know one is heads) the only difference between ht and th is if you flip on the left or the right side of it. So it can be hh or ht/th
>>704044601
Yes it does, you retard.
Without this magical scenario that at least one will come up heads out of the two coins, you have 1/4 chance of getting two heads.
Since one of these coins out of two will land on heads, you now know that the possibility of getting two tails is eliminated.
Therefore your 1/4 chance of getting two heads becomes 1/3 because you eliminate the possibility of flipping two tails.
1 being the probability and 3 being the amount of flips necessary for outcome of two heads.
4/4 - 3/4 =
>>704045071
You can't put one down as heads. You have to flip both of them, like it says in the question. You don't know beforehand that the left or right one will be heads, just that at least one of them will be (it does make a difference).
>>704045071
>If you put one coin down as heads
Nah, you're fixing a coin. Answer to your scenario is 1/2
OP question doesn't fix a coin. 2 coins were flipped, and at least 1 landed heads by chance. It could be either coin, which means either coin could be tails, just not both at the same time. 3 equally probable ways to achieve at least 1 heads coin for a 2-coin flip:
HH
or
HT
or
TH
1/3
>>704045193
> Yes it does, you retard.
I'm right though. Read >>704040746
> Without this magical scenario that at least one will come up heads out of the two coins, you have 1/4 chance of getting two heads.
Correct.
> Since one of these coins out of two will land on heads, you now know that the possibility of getting two tails is eliminated.
Right so far. The possible outcomes, each equally likely, are HT, TH, HH.
> Therefore your 1/4 chance of getting two heads becomes 1/3 because you eliminate the possibility of flipping two tails.
Yep. You have reached the correct answer. Your chance of getting two heads becomes 1/3.
> 1 being the probability and 3 being the amount of flips necessary for outcome of two heads.
What, where does this come from? 1 is the probability of what? Why are you flipping something 3 times?
> 4/4 - 3/4
Explain.
>mfw i will never ever see two tails
>>704031833
There are 4 possible outcomes.
(T,H) (H,T) (H,H) (T,T)
1/4 of these possible outcomes in (H,H)
>Assume atleast one coin will land on heads
Ok, with this information we can eliminate the possibility of getting two tails. That means there are now 3 possible outcomes.
(H,T) (T,H) (H,H)
1/3
>>704045236
I am just saying ht/th are the same, if you were on one side of the table it might be th but if you walk around to the other side of the table, it will be the ht. They are the same.
Fucking mind boggling how people need to write 500lines trying to explain how it's this or that.
It's 1/3, if you need a wall of text to understand you're dense.
>>704045818
>I am just saying ht/th are the same
HAHAHAHAHAHHAHAHAHAHAHHAHAHAHAHAHAHAHAHAHHAHAHAHAHAHHAHAHAHAHAHAHHAHA
Ha
Ah
Kill yourself.
Chances are that you don't even have two of those. Get a job niggers.
>>704045744
>(T,H) (H,T)
Flay yourself
>>704045818
It's fine to say that they are the same. What you need to understand then is that, if you treat them as the same, then TH/HT is twice as likely as HH.
Go here and repeatedly press the button: https://www.random.org/coins/?num=2&cur=60-gbp.1pound
You will get TH/HT half the time, HH a quarter of the time, and TT a quarter of the time.
>>704045818
And if you look from underneath a glass table then HH=TT? You need to stay consistent.
>>704046102
Flipping each coin is a separate event, you fucking imbecile.
Each coin has two sides. You have two coins.
2*2 = 4
4 possible outcomes.
Fuck yourself with a bread knife
>>704046143
I guess I am not thinking they are flipped at the same time.
>>704046921
It literally doesn't matter if they are flipped at the same time.
>>704046921
Does rolling multiple dice at the same time alter the probability?
>>704037936
Even if it could land on the side you're and idiot and didn't account for the whole sample space. I know you're trolling though and you didn't even do the final part right where you eliminate most of the sample space that doesn't have any heads at all.
3 choices for 1st coin and 3 choices for the 2nd coin means 3×3=9 outcomes total. You are missing the SS outcome.
>>704047025
Yeah you're right. Just had to put my stubbornness away and actually digest what you are saying.
>>704047463
I think you might be the first person who's ever managed to change their mind in one of these threads.
The coins are both dead AND alive.
And tell Mr. Barker you'll take the other door.
>>704047463
A convert.
Welcome to the 1/3 master race, anon.
lol. Fuking retards here.
If you dont understand the math, TAKE TWO COINS AND TRY IT.
Throw both coins 20 times Record the results. Its not going to be 50%.
You are fucking welcome
>>704047520
Nah man, there's always at least 1.
Get it?
>>704047520
Thats because everyone that doesn't agree with 1/3 is fucking retarded, anon
>>704043024
>"At least one of them" means either coin could be heads, not one in particular is heads.
It means ONE OF THEM is heads, you are the only one trying to make a case that which one gets to be heads matters at all. The problem isn't asking which one will land heads or in which order, it's simply asking what are the odds that BOTH will be heads, considering that at least one of the two must be heads 100% of the time.
You are trying to answer a different question here.
>>704047520
There are people who troll both sides of the fence, you know.
>>704047621
If you throw both coins 20 times, and among those 20 times at least one of them lands heads, as the problem CLEARLY states MUST BE the case, then you'll have a 50% HH result.
WTF are you even smoking?
>>704047787
> It means ONE OF THEM is heads
At least one of them is heads, not a specific one.
> you are the only one trying to make a case that which one gets to be heads matters at all.
No I'm not. It's the main way of explaining why 1/3 is correct.
Read: >>704040746
50%
The two tosses are independent of each other.
>>704048219
But that's wrong; actually try it.
>>704048219
Autism. TRY IT. 30 throws. Remove the TT
Tell me how many are HH?
>>704048325
>At least one of them is heads, not a specific one.
Exactly, one of them is heads, not a specific one.
If one is heads, then you are only flipping to see the results for the other one. It doesn't matter which coin is heads, since either one of HAS to be heads 100% of the time.
You are counting as TT as a valid flip, then removing it in case one of the coins lands H, which is a mistake, since it's not fully assuming the conditions stated by the problem, that in 100% of the cases 1 coin MUST land heads.
>>704048219
It doesn't say "Assume one coin is already heads"
It says "given that AT LEAST one of them landed heads"
It's another way of saying that (t,t) is impossible making what was once a 1/4 probability a 1/3 probability.
>>704048604
When you are asking the probability of the outcome of two coins both with their own probabilities, they most certainly are dependent.
>>704048775
> You are counting as TT as a valid flip, then removing it in case one of the coins lands H
It's removed from the possibilities BECAUSE it's an invalid flip, I'm just showing you how to get to that point.
> If one is heads, then you are only flipping to see the results for the other one. It doesn't matter which coin is heads, since either one of HAS to be heads 100% of the time.
You can't do this in statistics. You don't know which coin lands on H in order to consider the flip of "the other one" - it relies on things that aren't determined.
>>704048775
>If one is heads, then you are only flipping to see the results for the other one.
No. BOTH coins are still variable as either of them could be tails. The only limitation is that they can't BOTH be tails at the SAME TIME.
So you could have
heads, tails
tails, heads
both heads
Pic Related
Answer is 1/3
>>704048685
You can't "remove" TT, idiot.
If you are going to count TT as a valid flip, but then remove it later to try to explain this problem, then you are not taking into account the magical "at least one of them lands heads everytime", that the problem clearly implies it must happen every single time.
In reality you can't even remove TT from the equation at all, so why are you trying to explain mathematically something that involves a probability that isn't applicable whatsoever in a real scenario?
If you are only talking about a hypothetical scenario where 100% of the time one of the coins must be heads, then you are basically just flipping one coin, but if you are trying to use this explanation in a practical situation, then there's simply no way to remove TT to begin with, unless you aren't using two "regular" coins, so the answer must be always 25%, and the problem can't be solved.
>>704048812
No, you are mistaken.
Saying that TT is impossible is one thing. Saying one of the coins isn't T is another.
If one of the coins isn't T, then the other one must be either T or H.
How is that so hard for you to understand?
>>704049862
>the problem can't be solved.
>basic conditional probability question
>can't be solved
Holy fuck, you're retarded.
See slide 4
http://courses.cs.washington.edu/courses/cse312/11wi/slides/04cprob.pdf
1/3
>>704049862
> If you are going to count TT as a valid flip, but then remove it later to try to explain this problem, then you are not taking into account the magical "at least one of them lands heads everytime", that the problem clearly implies it must happen every single time.
Removing TT, as it is not a possibility, is HOW you take that into account. Flips of TT are not valid, so they aren't considered in a question.
Given a die rolls over 3, what's the chance of it rolling 6?
You could work this out by rolling the die, and removing any rolls that are 3 or under, as they are not over 3.
>>704050132
Either coin could be tails, you fucking simpleton.
Just not both simulataneously.
For a 2-coin flip, there are 3 equally likely ways to get at least 1 heads.
coin1=heads, coin2=tails
or
coin1=tails, coin2=heads
or
both coins=heads
1/3
