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/?
33% easy
Anyone who is about to answer 50%; STOP.
Turn off your computer. Walk outside.
Keep walking until you reach some fast moving traffic. Step out in front of an oncoming vehicle.
The answer is 1/3.
>>708004055
50-50
75%
>>708004367
>>708004886
Trolling or retarded?
>>708004281
edgelord?
5/7
>>708004937
I found the 50% 'tard, everyone.
71.43%
Anyone got the mathematical evidence behind this shit? I'm intrigued.
>>708004055
50% son
25%
100%
>>708004055
One coin landing heads. Done. And no more maths about that one. It is heads already, no matter what. So you have one heads. And now on to coin number two.
It can land either head or not. If not, we do not have two heads. If head, however, we have two heads. Everything is determinated by coin number two. And it can land in one of two possible ways. That is all that matters. So 50/50 chance, = 50 % chance of two heads.
>>708005468
Every time you flip a coin there is a 50% it will be heads the second time it is still a 50% chance
63%
>>708004055
Its binary.
From 00 to 11 there is
00
01
10
11
>>708004055
if both were flipped and in the air, the chances of both landing on heads is 50%.
one had landed on heads, so out of the both of them and seeing one is heads already, the chances of the second landing of heads is 33%.
1/2-1=33%.
>>708005468
there are 3 possible outcomes
both land on heads
both land on tails
or they land on different sides
so it's 1/3 or 33.1/3%
>>708004055
33% nigga
>>708005846
^retarded
Consider the outcomes of 2 coins, HH, HT, TH, TT, notice there are 3 with at least 1 heads, and of those 3, 1 is HH. Thus the probability of two heads given at least one heads is 1/3 or 33.33%.
t. Mathfag who wrote a probability midterm yesterday
>>708005959
yes but lets say the 1 represents heads."given that at lease one of them landed heads" so that leaves us with
10
11
so 50% yeah?
51/49
>>708006158
What about 01?
>>708006158
00 too which represents both on tails
>>708006320
but the lesson left us without double tails.
>>708006296
This would be the same as 10 as one is guarenteed heads.
>>708006436
You're incredibly wrong, you should look in to quantum
>>708006383
oh shit im stupid it is 50% i misread the lesson
>>708006436
They're not the same, you retarded fuck.
1/3
>>708006548
never mind it is still 33%
>>708006599
What is the coin landed on its edge?
>>708005846
You obviously can't read the part is, "Given that the first landed heads". which precludes calculating the probability of instances where the first flip lands tails.
>>708006072
>there are 3 possible outcomes
>both land on tails
That's not a possible outcome. Go kill yourself.
>>708006711
true true then it is 25%
>>708006722
>first landed heads
Consider reading the picture, it says at least one landed heads
>>708006722
>first
No.
1/3
>>708007016
what about the sides? what if mid flip someone stole your coin?
>>708007129
1/5
>>708006133
HT and TH is redundant. 50%
>>708007166
What about possible world ending scenarios.
>>708007199
>HT and TH is redundant
You're retarded.
>>708007129
Assume a fair coin with only heads or tails as outcomes
>>708007199
it is actualy 33 1/3% because 33.33% x 3 =99.99% not 100% you fuck
>>708007312
Who decides what a fair coin is?
>>708007357
if 1/3 = 33.33333333 ect. how is 3/3 100%?
>>708007447
1/3 actually = 3.3xinfinite so technically there is no such thing as a third
>>708007385
It's literally a definition where the chances are exactly 50/50
>>708007609
Why must we be literal?
The first one counts to the percentage so it 50% chance then the next coin flipped is another 50% chance. To find the chance of getting both you times them so it is 1/2*1/2 which is = 1/4 or 25% it's gcse
>>708007609
50/50 means 2 possible outcoms there are 3
1=heads 0=tails 1 has to land on tails do
10 heads tails
01 tails heads
11 heads heads
>>708005959
That's a good way of putting it, thanks for clearing it up for me mang
>>708007777
yeah but TT was eliminated. So its HT TH or HH
>>708007447
>>708007543
Base 10 math causes some glitches. If you used some multiple of 3 (6, 9, 333, etc) as a base, then 1/3 would no be a repeating number.
Of course, for whichever number you pick as a base, you get some problems anyway.
>>708007777
checked boi
>>708007967
I'm a fan of base 12.
P(H and H) = probability of getting 2 heads = 1/4
P(H) = probability of getting 1 head = 1/2
P(H|H) = P(H and H)/P(H) = (1/4)/(1/2) = 2/4 = 1/2, by definition of conditional probability.
>>708008043
>>708008158
>>708008196
>>708008234
>>708008269
>>708008304
>>708006750
This. One definitely lands on heads. Therefore it's 50/50 whether they both land on heads or not.
>>708008331
>>708004055
The probabillitty would be 2 2ths because 1+1=2 and 2 is more than 1
>>708008147
Why must you make such basic errors?
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
>>708008374
>>708008366
Retard
>>708008387
Who says 2 is more than 1?
>>708008387
Wut
>>708008429
quad 7s boi
>>708008387
> 2 2ths
FYI all of you who answered 1/3 aren't smart
You just saw some youtube video or internet articles explaining the answer
stop with the "I am so smart" delusion.
>>708008578
>>708008445
That's not very nice.
The controversy is not in the math, but in the wording of the problem. It can plausibly be taken to mean two different things. The same is true for all meme question of this type. There is more than one correct answer, depending entirely on how you interpret the English.
>>708008669
Who goes on the internet to call someone a retard? we all have feelings here.
>>708008387
>>708008710
So its an english question and not a maths question?
>>708004055
Even if the coins, then why would they both have the chance?
>>708008387
The fuck did I just read?
>>708008632
I have bad news for you - smart people don't go to 4chan
>>708006113
^I have some bad news for you son
>>708007967
someone with a brain
>>708008710
>basic conditional probability question
>meme question
Kill yourself.
>>708008870
Wow. The first correct answer here!
>>708008387
?
>>708008632
>thinks math is magic and nobody understands it
>>708008710
^this
>2 coins were flipped
alright
>1 already landed on heads
ok, that's out the way then
>what's the probability of the second coin?
1/2
As with all 4chin match questions, they are always fucky with the wording causing a lot of different interpretations.
>>708008938
no u
01
10
11 <- both
1/3
>>708008710
This is the truth of all these nonsense clickbait problems, including that other "algebra" one with the horseshoes and boots and horses.
Basic math doesn't change. The wording of the problems do, and it's possible (and preferable for the people who make this shit up) to flatly state the problem in an ambiguous way so as to cause the most confusion and debate.
>>708004055
50/50.
If we flip two coins, there are four possible outcomes: Two heads, two tails, head/tail or tail/head.
Now, at least one of the coins landed heads according to the task. Which means the double tail outcome can no longer happen. This is as much information as we get. Our remaining outcomes are:
HT, TH and HH. Given that every side of the coin has a 50% chance to appear, the chances for each outcome to happen are the same. However, only one out of the three outcomes is the scenario we look for. The chance is 1/3.
>>708004055
Can't you put that in the form an equation or something? I doubt your brainlet self can, but it's worth a shot.
>>708008387
All outcomes are 50/50
They will or they wont.
>>708008416
> B = "at least one coin is heads" = {(HH), (HT), (TH)} = 3/4
If the first coin is heads (H), how is (TH) a possible outcome?
Surely it's either gonna be (HH) or (HT)?
what is the probability that some retarded kid will get trolled, get excited and make a retarded post?
100%
>>708004281
>>708008387
2 2ths?
There are only two posibilities left. HH or HT. 50%. There is no HT or TH. It's the same. Wherever you want to place the H the only two possibilities in the next slot is H or T. The first coin is a H. The second is H or T.
It's not 33% that it's H or T. If you had a hundred coins and 99 were H.
Does that make the final flip a 1% chance it is heads?
>>708004224
wrong.
>>708004055
Could you put that in something that is not some retarded orgy backwash of a language?
>>708009648
This
>>708004281
the awnser is 50% though, go kill yourself gooklord.
If the order of the coins matters, so Heads-Tails is different from Tails-Heads, the answer is 1/3.
But, if the order does not matter (as it seems), so H-T is practically the same as T-H, it's 1/2.
Not that hard to understand people.
>>708008387
2 2ths
>>708004055
the awnser is 50/50.
It would be 33% if they both had a chance of landing on tails, but given that one of them already landed on heads as seen in the picture. The second coin has a 50% chance of landing either on heads or tails.
So at the end, it's either a 50/50 chance of getting heads on both coins.
>>708009692
But no heads is not a possible outcome.
>>708005468
Use Bayes' Theorem.
Any explanation that doesn't use it is wrong (even if it gets the correct answer).
>>708005803
Nope.
>>708009975
just to add this, I am assuming its asking howmuch the % after the 1st coin landed. If they are asking what the % is including the first throw we already know is heads, it's still 33% then.
Both coins have landed since "at least one is head" so its 1/3. If only one had landed and was head its obvious 1/2
>>708009062
You're an idiot.
>2 coins were flipped
alright
>1 already landed on heads
>ok, that's out the way then
No, at least one landed heads. Could be either coin so you can't exclude any coin.
>>what's the probability of the second coin?
That's not the question. First coin could be tails.
Look, retards, this isn't very difficult.
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
All 3 of those are equally likely to occur.
1/3
>>708009062
The first coin isn't guaranteed to be heads. The situation is imagine the coins were flipped, and some guy tells you that there is at least 1 heads. Now given that's all you know about the result, what's the probability of both being heads. You aren't necessarily flipping the coins.
50%percents because the other coin doesn't count because us gonna be heads no matter what you do
>>708009327
>If the first coin is heads
>first
Question never says that.
1/3
50% we know one must land on heads so it's just the other coin we need to worry about which has a 50/50 chance
>>708009648
>It's the same
You're retarded.
>>708010177
> Uses mathematical theory
> is correct
> is wrong
>>708009327
The question says
>One of the two has to be heads
The question doesn't say
>Coin Nr.1 has to be heads
>>708009692
Learn to read. I did not say first coin. I said one coin. And also you are a retard for not agreeing to 50 %, witch is right.
50/100
>>708004281
It is 50% though. One already landed heads so you're just calculating the probability of the second coin.
>>708010326
are you legit retarded?
head tails and tails head are legit the same outcome. It doesnt matter which one landed first, it matter which one you get.
>>708009648
The question says "at least one of them landed heads".
You can't just assume it was the first one.
75%
>>708008387
So you're saying there's a 100% chance of getting Double heads?
>>708006072
Except there are only two possible outcomes this case GIVEN THAT ONE HAS ALREADY LANDED ON HEADS
Fucking retards. Its 38.937563 % Do you even math ?
>>708005673
This. Heads always wins.
>>708010481
A proof can be wrong even if the statement you are trying to prove is correct.
>>708010680
No. It's conditional probability. This is not how conditional probabilities work.
>>708006060
You're an idiot. When they're both in the air the chances of two heads are 1/3. When one has already landed heads it is now 50% for second one.
How have you got it the wrong way round?
>>708010809
Yes because there are 2 coins
1+1=2 there are two sides which is also 1+1=2so that means that there are 2 2ths when flipping the coins
>>708010680
Moron, there are 3 equally probable ways for at least one coin to land heads in a 2-coin flip
HH
or
HT
or
TH
HH is 1 of those 3
1/3
>>708004055
These luck situations are not undergoing basic laws of math. It's always 50-50, if you flip it 10/100/1000 times. It's always 50-50
>>708011209
What the hell are you talking about anon?
>>708010862
>GIVEN THAT ONE HAS ALREADY LANDED ON HEADS
So could be
heads, tails
or
tails, heads
or
heads, heads
1/3
>>708011371
Read the question carefully.
50%
25% otherwise
>>708011334
>>708011439
I understand now
>>708010611
00 - Ruled out (none are heads)
01 - 1 heads
10 - 1 heads
11 - 2 heads
1/3
We don't rule out either of the coins for "already being a heads"
We rule out the occurence of "double tails" because the question states that one of the two coins has to be heads in the final outcome.
75%..?
>>708004055
1/3, I know this riddle, similar to the monty hall "paradox"
HEY FAGGOTS IS NOT ASKING FOR THE PERCENT %
>>708004055
The answer to the stated question is one third.
The actual probability is one-quarter, but the query ignores some valid data, like the possibility that both coins come up tails. Probably written by liberal arts majors who think climate change is actually real, and any evidence that doesn't support this conclusion must be wrong.
>>708011439
but one is already heads no matter what, so we can take it out of equation.
Now it is just the other one, which is either a heads or a tail. 50%, no question about it.
It asks what the probability of both being heads, NOT how many possible ways can the coins land.
>>708011656
Welcome to the dark side.
>>708011334
What the fuck?
>>708011862
>but one is already heads no matter what, so we can take it out of equation.
Both coins are variable.
The only possibility that can't occur is both coins being tails (TT)
So
HH, HT, TH
are all valid possibilities and all are equally likely to occur.
1/3.
Prove me wrong.
>>708007199
I hope, for your sake, you're trolling and not actually a retard.
If I flip coin a and coin b, Coin a landing heads and coin b landing tails is NOT THE SAME OUTCOME as coin b landing heads and coin a landing tails. They are two, distinct, SEPARATE possibilities, therefore you can't count them as a single "case" for purposes of probability.
Simulation confirms 1/3
In the scenario we have there must always be a heads- see black box. There is only two possible options here, we get a second heads or a tails. 100/2=50, a 50/50 chance. The probabillity that we have It come up heads twice with no other stipulations is one 3rd that being said the probibillity of it landing on the same side without the side being specified is 50/50.
/thread
>>708011334
Then you multiply the mas of the sun and times the mass of the moon and add up all your living cells and the number of fucks i give to the second power and we get how much of a Faggot you are
>>708012010
ok.
Flip one coin, what is the possibility that it will land heads or tails? 50%
the other is always heads no matter what, doesnt matter if you choose which of the coins is heads or not, because regardless at anyway you look at it, you are only realistically flipping one coin. 50%.
>>708004055
>What's the probability that both landed heads given that at least one of them landed heads?
Can you next structure that sentence properly? Thanks.
Answer is 1/3 though.
>>708011862
But is not asking for the PERCENT
>>708011358
>assuming the order in which the coins land is important
One of them is heads, guaranteed. The other one either is, or isn't.
Heads and tails/ tails heads is the same outcome i.e. Both coins don't land on heads. The other option is that both coins do land on heads. It's 50/50.
>>708012206
But this is wrong you dumb fuck
>>708009066
01 and 10 are the same fucking thing, we already know there's a heads there, any other answer but 50-50 is mental masturbation
>>708012272
But hes asking for both coins not just one
>>708012206
I fucked up in the red box while drawing it, correct version here.
>>708012308
The sentence is structured correctly. It's using math terminology that you probably don't know unless you're studied probability.
"The probability of X given Y" is a very common structure.
to everyone saying 50%, it's the probability of both landing on heads, not the probability of the coin that is not definetly landing on heads landing on heads.
>>708012272
>the other is always heads no matter what
thats not what happens in OP question.
You're fixing a coin as heads. OP does not fix any coin. Either coin could be tails, just not both at the same time.
You fail at math.
1/3
>>708012469
01 and 10 are obviously not the same anon.
>>708012010
You're right but you forgot the question.
If it's HT did they both land on heads? No.
If it's TH did they both land on heads? No.
If the other coin lands on its fucking side are they both heads? No.
It really doesn't matter the method of it landing on heads or not, it's only the outcome. And the outcome for one coin is either heads, or not heads.
>>708012387
>Heads and tails/ tails heads is the same outcome
You're retarded.
quarter=heads, penny=tails
is not the same as
quarter=tails, penny=heads
Stay in school.
1/3
>>708012606
No, "What's the probability of both coins landing on heads given that at least of them has already landed on heads?" is better than what he said.
>>708012876
Goddamn, how can you be this retarded?
Please be trolling.
>>708011823
>given at least one is heads
>tails tails
Pick one
>>708012319
the probability of it being
10
01
11
1/3 probability is an illusion and doesnt technically work out because you need to have the 00 present, and that makes it 1/4.
Because if one is always going to end up heads no matter what, then the percentage is bumped to 50% because taking out the 00 fucks the probability up.
That is assuming both have the chance to land tails.
since it is
01 and 10.
If one is guaranteed to be heads no matter what, it would have to be selected which coin is going to end up heads.
so therefore, the probability would be 1/2
01
11
or
10
11
The whole "one is guaranteed to be heads" is what doesn't make sense. Because how can you guarantee it, if both of the coins have the probability to land on tails? Checkmate.
>>708004055
There are two kinds of people in this world:
People that think methodically and correctly arrive at the 1 in 3 result...
And people that "think" intuitively and assume it's 50/50 without giving any in-depth thought whatsoever.
50/50 people are the morons that believe in God, they're the saps that fall for pyramid schemes, homeopathy, anti-vaxer climate denial stupidity. They're reactionary, likely vote republican or democrat (one or the other, but ALWAYS that single party), hate gay people because they deep-down have homosexual feeling of their own, which they also hate. They probably also think traditions and "historical culture" are more important than progress and understanding.
People that think the problem through, and reach the 1 in 3 (correct) answer, are likely to vote for people, rather than political parties. If they do vote for any individual party, it's usually a third party. They consider themselves independent, libertarian or anarchist. They're disgusted by establishment politics and, skeptical of the media. They are openminded, but not gullible, so they don't fall for woo or superstitions. They recognize that God is just another holdover superstition, and that organized religion is a huge fucking scam. Tithing is like the lottery, a tax on the stupid.
And above all, they are SO FUCKING TIRED of being told by people who don't think methodically that they are the "weird/stupid/clueless" ones. They recognize that almost everyone around them thinks they're fucking brilliant and capable superstars, and that almost all of them are dead fucking wrong. They also know their own limitations and won't make stupid claims to knowledge they don't or can't have.
>>708004055
it's 1/3 isn't it?
the outcomes that count (given at least one H) are
H T
T H
and H H
both of them landing heads is 1/3rd of all the outcomes that count.
>>708012894
>implying the type of coin is now somehow important
Two unspecified coins, one is heads already. The chances of the second one being heads is what?
Go on, tell me, you're flipping one coin now, what are the odds of it being heads? Go ahead and say it's 1/3. Moron.
>>708013213
Try this then: "I flip a coin and it lands heads".
What is the probability it landed heads?
50%
it's given that one of them landed heads, and the other is 50/50 to also land hands
>>708013284
WOW
>assumptions
>lumping people in arbitrary groups
>muh high IQ euphoric atheism
you fucking fedora wearer, go buy some cheetos and mountain dew you shitnugget
>>708013381
50%
The first one is given you retarded assholes so it doesn't factor at all may as well say we never flipped it
Fifty fifty
This is the be all end all post ITT
Stop being retarded
>>708013213
>Because if one is always going to end up heads no matter what
But that's not what's happening, you fucking retard.
>>708013327
It is one third you gigantic faggot.
>>708012712
This question is a double trap
Trap 1: Oh it's obviously 50-50
Trap 2: Oh wait it's 1/3 because HT and TH
Reality: Wait it's 50-50 because any conclusion about it being 1/3 is just masturbation and an olympic stretch in interpretation
>>708013461
It's 100%. I told you it landed heads. Are you really this dense?
>>708013505
It doesn't say first one. Read the question.
>>708006158
you forgot 01, faggot.
That's why there are 3 possibilities (and why it's 1 in 3) 00 is not a possibility, because it is disallowed by the problem itself (at least one is heads.)
01
10
11
>>708013588
An anon coded a simulation. It's 1/3.
>>708012094
>>708013327
I wasn't implying that, you retard.
I was using a penny and quarter to illustrate to morons like you that HT is NOT the same as TH.
Kill yourself.
1/3
Flip 2 coins. At least 1 landed heads, so you could have
coin1=heads, coin2=tails
or
coin1=tails, coin2=heads
or
both coins = heads
All 3 of those are equally likely to occur.
1/3
>>708006722
>"Given that the first landed heads".
That's not what it says. it says "that at least one of them landed heads". The first one might as well have been tails, if the second one is heads that throw is still part of the group of throws we have to take into our calculations of probability. Meaning we have to consider what is said in >>708006296
>>708013673
Explain why the order of the coins matters
>>708013505
>The first one is given you retarded assholes
No it isn't.
1/3
>>708013512
This is a grammar problem then.
"Given that one of them landed heads"
Which says that one already landed heads.
It is 1/3
00
10
01
11
and we take 00 out because it said one of them landed heads.
>>708013673
God damn it
Brb physically flipping coins and recording data now
>>708013588
>1/3 is correct answer using Bayes' theorem Math
>hurr durr answer is 50-5-
You're retarded.
1/3
>>708013912
Saying "the first one is heads" gives more information than "one of them is heads".
>>708013959
I originally thought it said, one is always going to end up heads no matter what.
instead of, one of them landed heads.
that fucked me up.
>>708013443
>muh high IQ
Where did I say anything about IQ, faggot?
One group knows how to think, one group makes stupid assumptions like you just made in your post...
IQ has NOTHING to do with it. Knowing how to think methodically has nothing to do with how high your IQ is or isn't. It has everything to do with knowing your ass from a hole in the ground. (which, clearly, you don't)
>>708013964
Easier to code it.
See: >>708012094
>>708013674
01 and 10 are the same thing. Together they make up a 50% chance of occurring. The only reason to display them as different results is to attempt to bend the interpretation of the question. The only way anyone could end up at 1/3rd is if they're furiously masturbating mentally.
>>708005803
> It is heads already, no matter what
That is literally not true. Either coin could land tails. All we know is that it wasn't both.
>And now on to coin number two.
No. We consider both coins together.
>>708006722
>Given that the first landed heads
>first
This would be an excellent troll if we didn't have this thread every other day. Unfortunately we do, so no one is falling for it.
>>708007199
>HT and TH is redundant
OK, then lets combine those into one term. We'll call it HT/TH.
HT/TH is twice as likely to occur as HH. 1/3.
>>708008416
You are a gentleman and literal scholar.
>>708009062
>>1 already landed on heads
>ok, that's out of the way then
No it isn't
>>what's the probability of the second coin?
You are asking the wrong question, we are considering the probability of both coins. Either one could have landed on tails, there isn't a specific one we know landed on heads. We only know that it isn't the case that both landed on tails.
>>708009327
>If the first coin is heads
It isn't. Or rather, we don't know if it is or is not, same goes for the second coin. We only know that we are only considering cases where there is a coin that lands heads, not that one coin is already heads. 1/3 of such cases land with both coins as heads.
>>708009648
>There are only two posibilities left. HH or HT
While it is possible to combine HT and TH into one term as HT, you must remember that as there are then two ways for HT to occur, HT is twice as likely to occur as HH.
> The first coin is a H. The second is H or T.
That is where you are wrong.
The first coin is H or T. The second is H or T. The only condition is that you can't have both as T. There is no specific coin that we know landed heads.
>>708009812
The order of the coins does not matter as each coin is equivalent to the other. However, a result with one head and one tail (interchangeable with one tail and one head) is twice as likely to occur as HH.
>>708014090
Congratz on proving that theorem useless then
>>708014487
Bayes' Theorem
Useless
>Pick one
There are two ways to go about this,
first, if it's perceived as such: we take 1 of the flips away because it's always going to be heads, so we only flip 1 coin basically so it's 1/2 chance
second, if it's perceived as such: we flip coins, and take out only the flips that end up with 0 heads. so it's going to be either 11 01 or 10, and it's 1/3 chance
bottom line, the starting statement didn't have accurate enough description. so we can't ever know the real answer
>>708014611
"at least one of them landed heads" is unambigously the second interpretation.
>>708014407
It literally makes no difference as to whether the first or second coin landed heads, that heads basically exists in a void as a constant truth. Coming to 1/3rd as the answer is just people manipulating the interpretation with bullshit theoretical maths.
>>708005803
Almost - with the way this question is worded you need to take account of which coin landed first.
So we know at least one will land heads, but not which. Here is what we could get:
H_T
T_H
H_H
All have at least one coin landing heads, so p=0.33
IT IS 1/4 FUCKING RETARDS!!
BECAUSE NO MATTER IF ONE LANDED HEADS OR NOT, THE PROBABILITY BOTH WOULD MAKE HEADS/HEADS IS 1/4.
JUST BECAUSE ONE MADE HEADS AFTER THE FACT THAT YOU FLIPPING IT, DOESN'T CHANGE THAT THERE WAS A 1/4 PROBABILITY!!
/end
>>708014565
Okay I pick useless?
Was that hard?
>>708014487
>mathematical theorem
>useless
Holy fuck, you're retarded
>>708014399
>01 and 10 are the same thing
No, they're not. You can't just assume to distinct cases count as one because "1 is heads and 1 is tails for both" or whatever.
Let's say coin 1 is being used to see who kicks off at a football game. Coin 2 is being used by some faggot in the stands. Now, are 01 and 10 the same case?
If you can find ANY SITUATION where a case can be differentiated into two distinct possibilities, then they aren't the same fucking case. Use your fucking head, shitforbrains.
>>708014399
>01 and 10 are the same thing.
Kill yourself.
>>708014730
>bullshit theoretical maths
No, it's just math. Labeling it "bullshit" because you're too stupid to understand it says nothing about math and everything about you.
>>708013284
I am all for trashing on those who believe that the answer is 50/50, but I have arrived at 1/3 while simultaneously believing in God.
Point being that you are attributing a bit much to this exercise.
>>708014751
Questions like this that ask for "probabilities" are taken to mean "conditional probability" by convention.
This is some sorry ass autismal shit. One is heads no matter what. Doesn't matter if flipped first second or simultaneously. This is one flip. The answer is fifty fifty.
Fuck you geeks in the neck of all impractical knobslobbing theorem
I reworded the question a bit different to help you all understand.
Is it 0%? Or is it still 1/4 since they HAD the chance to be heads before you flipped them, but didnt end up being heads.
>>708014751
>what is conditional probability?
>>708015029
The entire argument for it being 1/3 hitches on the idea that HT and TH are two separate results with equal probability of occurring. Meanwhile in REALITY they are the same result which together have a 50% chance of occurring.
I agree with the people who said the same.
If OP wanted TH and HT considered different outcomes, it'd be 1/3.
If OP wanted the to count as the same outcome, it'd be 1/2.
Right?
I'm stupid though, so I try to take that fact into consideration.
>>708015183
It's 0% you stupid fuck.
See: >>708015119
>>708010687
you can consider them to be equal outcomes all you want, if you try this out and do 100 throws with 2 coins, count only the throws that have at least one head in them, approximately 66% (and not 50) of these counted throws will be HT/TH.
>>708015029
Exactly.
HT
HH
TH
1/3 niggers
>>708015269
conditional probability is a lie. because it could either be 1/3 or 50% if you disregard that TH and HT are different outcomes and count it as one.
>>708004055
"What is the possibility that both landed heads?"
Depends on if they land heads or not.
If they both land heads, the possibility was 100%. If they don't, the possibility was 0%.
This isn't rocket science. If a thing happens, it has 100% likelihood. If a thing does not happen, it has 0% likelihood.
>>708015298
Wow, apparently the proof that I'm an idiot is quite infallible given the immense amount of typos here.
For anyone who thinks the answer is 50%, answer pic related.
Then try to explain how it's different to the OP question.
Protip: Answer to both is 1/3 (same question, asked 2 different ways)
>>708015450
Yes, ex-post probabilities are different to ex-ante probabilities.
I bet you're fun at parties.
>>708014703
well, think about it. if we flip two coins. Then we just look at one of the coins, and assume that the other coin that we aren't looking at is heads. because it's a given heads. then it's 1/2
it goes a lot more theoretical, but it's actually correct.
To all the retards saying HT and TH is the same. Let's do it this way: HH - no one gets shot. HT- the guy next to you gets shot. TH- You get shot.
Yes, you can say 1 person got shot but if you want to be more correct you have to think that they are different.
>>708008512
You're a faggot.
>>708015602
It doesn't say we only look at one coin.
>>708015275
No, they aren't. This has been tested, fagboat. You can test it, too. Take 2 coins, start flipping, and write down the results. Flip until you have 100 results of at least one of the coins landing on heads. You'll end up with somewhere near 33 (usually within five or so) HH results, and a around 67 HT/TH results.
Try it, if you don't believe me.
>>708004055
"The answer is man OP."
>>708015538
It isnt the same question.
You are basically restricting the coins from ever getting tails - tails, which basically is impossible realistically and is 100% for them both to be heads if such a scenario was true. Otherwise, tails - tails would have to be an option and the probability would be 1/4.
>>708015538
Heads-tails or heads-heads
That's two things that could happen
Fifty fifty
Stop being a retard
>>708012216
K, it's not my fault that you don't learn math
>>708015720
it doesn't say we look at either coin.
>>708014407
Look. One of these coins is guaranteed to be heads, so it's best to imagine it as a coin that has heads on both sides. Even if that isn't literally the case, it may as well be - it's an absolute certainty that one will be heads.
Therefore we consider the odds of the second coin joining it on heads - 50/50
>>708015756
Don't bother. This guy wrote a program to simulate it in one of these threads a while ago.
It really is 1 in 3.
This was worded in a really retarded manner. I thought the first coin i flipped was heads guaranteed, not that one of them are going to be heads. 33% is correct.
>>708015275
HT and TH are different outcomes.
"one head and one tail" is an event, consisting of HT and TH.
Read some basic math on Probability Spaces.
>>708015936
You forgot tails-heads, faggot. Doesn't say "the first coin flipped is heads," it says ONE OF THEM is heads, so tails heads is a valid possibility. It's 1 in 3 not 50/50.
>>708015936
you forgot tails heads.
If you think HT and TH are the same, see: >>708016079
>>708015432
You're a fucking idiot. The answer doesn't change because you're an idiot.
The answer is 1/3.
1/3 is the only correct answer.
>>708016062
It's worded in precise mathematical language.
You're just a retard.
This is retarded.
How can you all discuss fucking school maths here?
Go read a school book and keep that shit out of b.
>>708006072
Right answer, wrong explanation
There are 4 outcomes to start with (h = heads, t = tails)
(h,h)
(h,t)
(t,h)
(t,t)
Now, one coin already lands on heads, which removes the last option.
So, the chances of (h,h) is one in three.
im gonna find some coins and check brb
>>708007930
you are double counting an outcome if TT was eliminated, TH must also be eliminated
>>708015880
>You are basically restricting the coins from ever getting tails - tails
No, I'm not.
tails-tails is possible, it just wasn't the outcome. Same as OP question.
>>708015936
Or tails-heads
1/3
>>708016263
THE PROBABILITY IS STILL 1/4 OMFG
JUST CAUSE ONE LANDED HEADS DOESNT MEAN THAT THE PROBABILITY CHANGES!!
>>708016327
Shut up.
>>708016349
If tails-tails wasn't the outcome, THEN IT IS STILL 1/4!!!
P(1/2 * 1/2)/P(1//)
P(1/4)/P(1/2)
P(1/2)
50% chance
>>708016527
You defined A and B wrong. Next.
>>708016374
Yes, it does. It's disallowing consideration of one of the 4 outcomes, meaning you only have 3 possible outcomes, meaning the answer is 1 in fucking 3, like every non-idiot in this thread has said from the very fucking beginning.
>>708016128
But if the first coin flipped is tails, you don't need to flip another coin because you already know the result.
Therefore the flip of only one coin is what matters and that can only have 1/2 outcomes.
>>708008632
What else is being smart than learning something from someone else?
>>708015119
"conditional probability" my fucking ass.
You aren't going to get a different probability after the coins already fucking landed.
It is 1/4. You flipped the coins, and one landed on heads. The probability was 1/4. How the fuck is it going to change to 1/3 just because one of the coins is heads? The coins are already landed. You cant reroll them, if you do, it is back to 1/4 again.
fuck your conditional probability shit, it is common sense.
>>708016327
>TH must also be eliminated
Incorrect.
TH is valid as it contains at least 1 heads coin.
HH
HT
TH
All equally likely. All contain at least 1 heads
1/3
>>708016454
If you take 1 of the 4 outcomes away, the probability that both landed heads cannot still be 1/4, dumbass.
That's why it's called CONDITIONAL probability.
The condition is AT LEAST 1 COIN LANDED heads
1/3
>>708016646
>bases argument on information about first coin
>question says nothing about first coin
kys
1/4
>>708016619
YOU CANNOT DISALLOW CONSIDERATION OF ONE OF THE OUTCOMES, THATS NOT HOW PROBABILITY WORKS.
>>708008387
This
fuck you guys. I'll get two quarters and actually test this shit
>>708004055
the wording of the question is deliberately ambiguous and the answer depends on the reader's interpretation. Anyone who provides an answer is retarded.
>>708004055
The coin has no heads neither a tail you fucking moronic mongoloids.
>>708016745
Wrong
See >>708016301
I did the experiment and it's actually 1/9
you all suck if you want to know the answer flip some coins and see for yourself
>>708016691
nah it's 1/3 because of the conditional property that made the dual tails flip an impossibility.
>>708008387
I don't even know how to respond to this
>>708017123
ya all got rekt by science
>>708015936
I found a massively fucking genius way of explaining this shit.
You toss two coins. You are keeping track of which is which. You toss them together 1000 times.
250 times, coin 1 is heads and coin 2 is heads.
250 times, coin 1 is heads and coin 2 is tails
250 times, coin 1 is tails and coin 2 is heads
250 times, coin 1 is tails and coin 2 is tails
We remove the 250 times they both landed tails.
Now we have 500 times where the coins landed on one heads and one tails, and 250 times where the coins landed on two heads.
Get it? You have to think mathematically.
Oh and by the way, if you're thinking about doing it as "Either it's Heads Heads, OR one haeds and one tails, OR two tails, and they all have a third chance of happening, SO IT HAS TO BE A HALF RIGHT??" you're wrong.
I know this is confusing, but think about this...
There's ONE FOURTH chance that the coin is heads heads. There's ONE FOURTH chance that the coin is tails tails. There's TWO fourths chance that the coin is one tails one heads. Remove one of the options, the tails tails option, and then, bear with me, there's ONE THIRD chance that the coin is heads heads, and TWO thirds that the coin is one heads and one tails... Get it? Do you get it?
There IS a lower chance of both coins landing on the same side than one landing on a different side than the other. That's mathematically easy to prove. 0.5*0.5 = 0.25. So only 25% of the time will the coin land on either Heads Heads or Tails Tails. The other 50% of the time, the coin will land on one heads and one tails.
Do you get it now?
There is ALWAYS.
NO MATTER what you say
A higher chance for the coins to land on different sides than the same side.
No, one of them does not automatically land on heads.
That is not true.
GIVEN that AT LEAST one of them lands heads does not mean that one automatically lands heads. It simply means, remove the 250/1000 times it landed on tails tails from the equation.
>>708014730
I agree that it makes no difference if a first coin or a second coin lands on heads.
With the information that we have, however, the results of both coins are unknown to us. Both coins have a chance of being tails. Therefore, we cannot say "one coin is already heads, we should only consider the other coin", because NEITHER coin is already heads. Both coins have been flipped, the reality has been chosen.
What the question is asking of us is to take the information we have, that being:
>at least one coin landed heads
And use that to determine a new probability for HH based on what we know.
The question does not state that we saw a coin. If we had seen the coin then we would know for certain that particular coins outcome. We didn't see it, so we don't know either coin's outcome. We don't have enough information to say that this coin or that coin landed heads.
Thusly, our three results
HH
HT
TH
Now, let's choose a coin. the left one sounds reasonable. (note, we could choose the right one as well, if you want to follow along for the right coin, simply swap left with right in the following explanation)
Within our three results, we see that the left one hits heads 2 out of the 3 times. Both coins can only land heads if the left coin lands heads, so we are then considering within the 2/3 chance of the left coin landing heads. Within that 2/3 chance, the right coin has a 1/2 chance of landing heads (HH or HT). So 2/3 * 1/2 = 1/3. The reason that the right coin being heads in this case is calculated as 1/2 when it occurs in 2/3 of all cases is that the probability of right landing heads intersects with the probability of the left landing heads and that intersection was accounted for when we treated left as a 2/3 chance. So don't try to get cheeky and say that it must be 4/9.
>>708016646
2 outcomes do not mean they are equally likely, fuckwit.
There either IS or there IS NOT a gorilla with a lightsaber under your fucking bed. Is that 50/50 too?
Heads tails is one in three
tails heads is one in three
heads heads is one in three
Tails heads =/= heads tails
They are not the same fucking case, no matter how many times you insist they are.
We're talking about two coins landing on different faces. How could they NOT be considered seperate cases for probability. That's like saying "My friend wrecked is car, or I wrecked my car... it's the same thing, one car is wrecked and the other is not!"
Obviously it matters whose car was wrecked. It also matters which coin was heads. THEY ARE SEPARATE CASES WITH EACH BEING A 1 IN 3 CHANCE.
>>708016527
B = at least one heads = 3/4
Correct your mistake.
1/3
WTF is this ? Why is it even on /b ? I'm an autist and even I wouldn't care to have a long-ass discussion about this.
Is /sci raiding us ?
>>708017270
tl;dr sorry
>>708016235
>It's worded in precise mathematical language.
Mate, it didn't even have any numbers in it.
>>708017182
If it made it impossible to get tails, then it is 100% heads every time. What do you not understand?
It only works mathematically to 1/3 because you took out the 1/4th chance it has to get tails-tails, which we both know realistically would NEVER happen. Just because it works on paper doesnt mean thats how it works in real life dumbass.
>>708005468
Say you got a coin in each hand. You flip them.
What all could happen?
>Left coin lands heads, right coin lands heads.
>Left coin lands heads, right coin lands tails.
>Left coin lands tails, right coin lands heads.
>Left coin is tails, right coin is tails.
FUCK THAT LAST ONE. We're assuming at least one of the coins landed heads!
So out of those three, how many had both coins landing heads?
One, right!
There's your answer.
Happy to do your homework for you, kid.
>>708016841
>YOU CANNOT DISALLOW CONSIDERATION OF ONE OF THE OUTCOMES
Yes, you fucking can. If you flip TT, you just ignore the results and start over again. Where are you getting this retarded "rule?" Your ass?
>>708008387
>>708008387
i havent laughed this hard in a while. thanks anon
>>708004055
33.3333....% heres why
I will mark H for heads and T for tails. Here are all ur options
H H
H T
T H
T T
We remove T T because it doesnt meet the requirement at least one of them landing heads.
So you have 3 options and only 1 of them is the one you need!
>>708016007
>One of these coins is guaranteed to be heads
No, no it isn't. Both coins simultaneously have a chance of being tails. The two coins must both be considered as possibly being tails.
>>708016374
You must be troll.
2/10 for making me respond.
>>708005468
Someone said bayes theorem, but you don't even need that, just conditional probability for this case.
Probability of A given B is the probability both A and B occur, divided by the probability B occurs. So, the prbabolity 2 heads occur is 0.25, proability at least one is (1-0.25)=0.75, so the probability in OP's picture is 0.25/0.75=1/3
Also anyone who answers with percentages is wrong because the probability is strictly between 0 and 1
>>708017035
>>708004055
Interpretation Method A: There are two possibilities- Heads Heads or not Heads Heads
Interpretation Method B: There are three possibilities- Heads Heads, Heads Tails, and Tails Heads.
The whole thing hitches on whether or not you think Heads Tails and Tails Heads are two different results or the same result.
>>708017465
WELL THERE IT IS!
YOU FUCKED UP THE REAL PROBABILITY OF THE COIN BEING ABOUT TO BE 1/4 AND ARE PLAYING THIS GAME BY YOUR OWN RULES!
"Im going to ignore the probability of it being tails/tails so my math will always be 1/3rd to prove that i am right"
>>708016691
If at least 1 landed heads, tails-tails is no longer a possible outcome, retard.
Do you understand now?
That leaves 3 possible outcomes, each of which is equally likely.
heads-heads
heads-tails
tails-heads
1/3
>>708008387
>>708017377
250 times is HH, 250 times is TH, 250 times is HT, 250 times is TT
Ignore the TT. 500/750 times is TH or HT, 250/750 times is HH. It's 1/3. Get it?
>>708016691
You must be troll
2/10 for making me respond.
>>708017379
math is only numbers
Holy shit, let us know when you get out of 6th grade, bro. In the real world, math is more than simple arithmetic.
How is headstails and tailsheads not the same
One is heads and one is tails both ways and it doesn't mention which one first or if simultaneously or why the coins are being flipped who's flipping them and the physics behind the motions
There is no truth fuck you die in a coinflipping accident
everybody's wrong
the only way to be sure is to experiment
just toss some coins grab a pen and paper
then count
>>708005959
so 25%... I was right then?
>>708008416
dude ur a fucking retard. 1 coin is 50 50. how can two coins be 1/3. its 75% ur graph is right there!
>>708016841
When did you first realise you had autism?
>>708017598
>You don't need Bayes' Theorem.
>Uses Bayes' Theorem in next line.
Just kys
>>708017599
Hold up, you can totally consider HT and TH to be the same result and still come up with 1/3. You just have to realize that HT(or TH, if you want to call it that) it twice as likely occur as HH.
>>708017484
It is
1/4.
You cant declare result 1 to be impossible, you can only ignore it. And by doing so, your probability is 1/3 but realistically, the coin flipping is 1/4 for each combination including the ones you are choosing to ignore.
>>708017744
Yes his graph is right. 3 Outcomes
TH, HT, HH
You need only HH so your probability is 1/3 or 33.333(3)%
Test it on excell table with 100, 1000 or whatever rolls you want
>>708004055
How fucking idiotic you have to be
>>708004886
>>708004975
>>708005668
>>708006060
>>708006072
>>708004281
>>708004224
Can you morons read? two coins WERE (AS IN PAST TENSE) flipped. What is the probability that both landed heads GIVEN THAT at least ONE OF THEM LANDED (ALREADY FUCKING LANDED) HEADS. So lets break it down fuckers:
1. Possible outcomes: H T OR H H because one of them is already heads. So IT CANNOT FUCKING HAPPEN THAT THERE IS T T OR TH FUCKING MORONS
2. WHAT IS THE PROBABILITY OF 1 OUT 2 HAPPENING?? 50%
>>708017916
You obviously can ignore the outcomes that the question told you didn't happen.
>>708017716
only good method
>>708017270
>already arranged, so 1 coin has already been arranged as heads?
words man...
>>708017611
>BY YOUR OWN RULES!
not my rules, fagboat. those are the rules set forth in the problem. You don't like the rule of the problem, take it up with Joseph Bertrand. He's the one that came up with this shit in 1889. You'll need a time machine, and fluent French, though. The guy that literally wrote the book on calculating probability says you're fucking wrong, though.
>>708018008
Possible outcomes include TH. 1/3
>>708010477
care to explain why he is retarded or are you gonna throw out insults like a retard?
>>708018018
SEE, HERES THE THING:
The question never said ignore the probability of tails- tails.
The question simply stated one of the coins landed was heads (future tense)
THAT MEANS, THE COINS HAD A 1/4 PROBABILITY OF BEING BOTH HEADS! LEARN TO READ
>>708018050
Use a math dictionary.
>>708017711
>How is headstails and tailsheads not the same
Allow me to explain for simpletons.
You and me are in a room. I have a loaded gun and 2 coins (a penny and a quarter)
I tell you to flip the 2 coins.
If the penny lands heads and the quarter lands tails, I'll shoot you in the head.
If the penny lands tails and the quarter lands heads, I'll shoot you in the ballsack.
If they both land heads or both land tails, I'll let you go free without shooting you.
Can you see how they are different?
1/3
>>708018008
answer is 0.5 because 1 coin always lands the correct side up 100% :)
>>708017711
See
>>708017297
It most certainly isn't the same
Alright, let's go through this logically.
If the first coin is heads, there is then a fifty fifty chance of them both being heads.
If the first coin is tails there is no chance of both being heads.
If however they land simultaneously, but we have the knowledge that one of them is heads, then the odds of them both being heads are fifty fifty.
Also if we're only throwing the coins once, we know one is heads, the other one is either heads or tails, that's it. Fifty, fifty.
Finally, we aren't throwing the coins in theory, we're throwing them in reality. One of them IS heads, that only leaves room for the other to be one of two things.
The answer is fifty fifty.
>>708018008
>WHAT IS THE PROBABILITY OF 1 OUT 2 HAPPENING?? 50%
You assume they are equally likely. They are not.
Twice as many possible scenarios lead to one heads-one tails result as will lead to HH result. Coin A could land on tails, coin B could land on tails. Both scenarios result in a HT combination.
Only one scenario leads to HH, that is no coins land on tails.
It's 1 in 3.
>>708017744
You best be trollin, son.
1/3
>>708018172
Sir, I am not certain if you are aware, but probabilities change when you add evidence to suggest or disclude possible outcomes.
>>708018127
Probability spaces are defined over outcomes.
See: >>708016079
>>708018377
>>708018008
>H T OR H H
Or TH
1/3
Damn, you're dumb as shit. Are you a nigger?
>>708017856
That's not Bates theorem dumbass, Bates theorem says P(A|B) = (P(B|A)P(A))/P(B)
You normally use this when it's easier to evaluate P(A) and P(B|A). What I gave was the correct definition of conditional probability. Maybe you should read proper textbooks next time you dangus.
>>708017716
No it is not, because most coins aren't perfectly balanced to give you a 50/50 probability.
>>708018300
The problem doesn't say the coins are different though faggot stop trying to like your way into a smartass answer
Retard
>>708004055
the coin don't have no say. it's just you
>>708017735
No, exclude the last result and the odds are 1/3
>>708017375
i've seen these threads for four years on a weekly basis
>>708018645
*kike your way
>>708018377
yes. "given that one of them landed heads"
doesn't matter if 1st or 2nd landed heads, who gives a shit hehe
this ppl here so dumb, u can look up all formulas u want but if ur brain is too small to think this simple logic u still gonna be a dumb bitch lul
>>708018465
NO. NO. NO,
What the question suggested was that, you flip two coins, and one happened to be heads.
Before you knew it was going to be heads, the coins had a 1/4 chance to be both heads.
One obviously ended up heads. It doesn't matter what the other coin is, they are already flipped. If you want to know what the probability is of both of them at that exact moment of being heads heads, it is either 100% or 0%, because they are already fucking flipped.
If you want to flip them both again, it is 1/4
>>708005468
>mathematical evidence
>evidence
It's called a proof, this isn't some shitty science like physics or chemistry where there are no definites. Everything that can be proven/disproven is definite in mathematics because we invented the rules.
