I don't care about your math bullshit because I just tested this myself.
I had three coins. Coin 1, 2, and 3. Coin 3 was flipped to determine if coin 1 or coin 2 would be heads. The remaining coin was then flipped. I logged the results after 200 trials.
102 out of 200 trials resulted in Heads-Heads.
Other urls found in this thread:
en.wikipedia.org
twitter.com
0.5
obviously, there are only 2 outcomes:
mixed or head-heads, tails-tails is ingored
its 50-50
It's even easier to explain. The chances of the second coin being in state A or B is not influenced by the first coin.
It's not easier to explain because people still don't buy it. It's like you have to physically test something despite the proof
Yeah i guess. this is why scientific elites should run the world. fuck these idiots
I can never tell if Sup Forums is trolling or just stupid.
> Two coins were flipped
Outcomes:
H H
H T
T H
T T
> At least one was heads
Exclude T T
> What is the probability that both are heads
H H vs H T and T H
Clearly 1/3
Go back to school.
Logged
So is that why my coins landed heads Heads 50% of the time?
Way to fail at testing, but you know that so you'll just chuckle about having "trolled" me.lyford chartreux
To that logic you also need to exclude TH because you're clearly ranking them. It leaves HH and HT. 0.5, nignog.
H T == T H
Well the probability for a coin flip is 49.6 to 50.4 depending on the coin of course, a blank coin has 50-50 chance of landing on either side, but you won't know which side it lands on.
Also what if it lands on it's edge.
Well then instead of flipping a coins I would have to flip myself over a bridge
because of austism
No you're wrong. Didn't even reply to my fucking comment because you're too cuck.
they're not two ways to generate it. coin 1 being heads and coin 2 being tales is the exact same as coin 1 being tales and coin 2 being heads
HT is the same outcome as TH
(TH or HT) or (HH) = (50%) or (50%)
This is the boy or girl paradox. It's ambiguous so stop discussing it you retards:
No it's fucking normal logic
No it's fucking math
its not a paradox if you can physically prove the answer like stated in my OP
Because it depends on the randomization procedure, if you were to do it differently then it would have a different outcome.
Yeah but I tried to prevent the word math before all these fuckholes started to whine that OP didnt want math
no it wouldnt. that would only be true if HT =/= TH.
but
HT == HT
If you were to flip 1000 pairs of coins, take all pairs in which at least one coin landed heads, and compute the probability, it would be 1/3.
im op and i love math. when its used correctly.
the proper math is:
(HT or TH) == (HH)
when it comes to probability
the likelihood that I got a 102 out of 200 result would be beyond astronomical if that was correct
Then you are selecting wrongly.
yeah and it's 0.5.
However if you flip 1000 pairs of coins and from each pair select one random coin. If that coin is heads, the odds of the other one being heads if 1/2.
There is no correct answer because it depends on your interpretation of the question. It is a very famous problem in statistics used to teach about ambiguity.
the information can only be correctly interpreted one way however? it doesnt matter how often coin 1 or coin 2 is the one chosen for heads. it doesnt matter at all
yup
(0.5) == (0.5)
You are correct. If you test the problem the way you did, the odds are 1/2. However if another person understood the problem differently and tested it differently the odds would be 1/3. The paradox is that the question is phrased ambiguously so that you can't say which interpretation is 'correct'.
you say tested it differently but provided no example of how a different test would go. im sure if you gave me that example i can point out how it is incompatible with the rules provided
OP is flipping one coin (the "remaining") and is surprised that the result is close to 50%
kys please
Try to answer this:
I have tossed two coins and at least one of them is heads.' Given this information, what is the probability that the other coin is a heads?
I have tossed two coins and it is not the case that they are both tails.' Given this information, what is the probability that both coins are heads?
not surprised at all. what im surprised about is that i have to physically prove this to people
exactly 50%
>I logged the results after 200 trials.
>102 out of 200 trials resulted in Heads-Heads.
yeah but you have to discard the outcomes where neither of coin 1 and 2 landed heads, because that is a constraint given in the original text.
Another way to test it would be this:
Toss 1000 pairs of coins (2000 coins in total).
Take all pairs with at least one head and discard the rest of pairs.
1/3 of those pairs would have the other coin heads.
The answer to the problem would depend on how you understand the question, and there is not enough data in the question to have only one 'correct' answer.
that's wrong selection
coin 1 and 2 could not have both landed on tails. when i flipped coin 3 it determined if coin 1 or coin 2 was automatically given heads, thus making a tails tails outcome impossible
thing is, you tested something else, not what was written
if you did as it said, you would have gotten 1/3
That's the point I'm trying to make, the answer is different depending on how you understand the problem.
there is enough data in the question. infact it cannot be correctly interpreted any other way than one way
that is not true at all. if it was true please explain to be what the proper procedure is? otherwise i have to assume you're just trying to fuck with me
No it's not, you are just selecting all pairs with heads, a restriction given in the question.
>102 out of 200 trials resulted in Heads-Heads
So that mean 102% of time head?
There is no 'proper' procedure. This question has been studied for mathematicians smarter than you will ever be. It is ambiguous.
I really hope this is bait, because the alternate explanation is that you're a retard.
You flip two coins, like it is fucking written. why would you do anything else?
nigga you high?
This looks sound to me tbh.
smart people can make mistakes and if you assume that isnt true then anyone who has had success can never ever fail in your eyes.
please explain the flaw in my procedure
you dont flip two coins. thats not written. what is written is that you flip one coin and the other is heads.
this user gets it
There is no flaw. It just one of the two possible interpretations. The other interpretation would yield 1/3 as the result.
Try to be open minded, your perspective of things is not the only that counts in this world.
once again. you have stated there is another interpretation. i am certain if you explained that interpretation i can point out flaws in the logic
"Two regular coins were flipped."
Sure mate
I'm gonna explain the two ways you could understand this problem as there are some people who only seem to be able to see one of them:
1:
You toss 1000 pairs of coins (2000 coins in total).
You select all pairs with at least one heads (as it is a restraint given in the question.
1/3 of those pairs will have heads the other coin (thus being heads-heads).
2:
You toss 1000 pairs of coins (2000 coins in total).
You go one pair at a time. For every pair you choose one random coin.
If the chosen coin is heads, the odds of the other coin being heads is 1/2.
There is no 'correct' answer, just two different valid ones depending on the randomization procedure which is not specified on the question.
you can test this yourself if you dont believe us
that unfairly counts a bunch of HT and TH outcomes as a success (converts them into HH) though.
say you flip the 3 coins 200 times.
consider only the first two of the coins at first:
>25% will be HH
>25% will be HT
>25% will be TH
>25% will be HH
this is on average 50 results of the 200 to each outcome
now consider the result of the third coin.
>In the first case both are HH, so regardless increase success counter by one
>this will on average add 50 to the number of successes
>in the second case, 50% of the time it will be converted to HH, and 50% of the time it will be converted to TT.
>across the 50 outcomes, on average 25 will be converted to HH and 25 to TT
>this adds 25 to the successes, for a total of 75
>third case is same as second, this adds 25 to the successes for a total of 100
>regardless of what happens in the fourth case, it will never be HH because only one of the TT coins can be flipped by the third
>the number of failures is then 25 plus the (25+25) failures from case 2 and 3
so the outcome will always (on average) for 200 throws be 100 successes and 100 failures
I really do not get what you are trying to do with the third coin, all you have to do is look at the first two coins and decide whether at least one (any one) is heads.
And then increase the success count by 1 or fail count by 1 depending on whether both are heads
If neither are heads then it is not part of the constraint posed ("at least one"), so those TT-outcomes fall outside the hypothesis space of interest
even if 1/3 of those pairs have the other coin, no way of interpreting it changes the outcome that 50% of the time its heads-heads
>OP thinks performing a different scenario is "testing" a basic conditional probability question
Jesus FUCKING Christ. Ok Sup Forums I'm only going to explain this once so pay attention.
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
>25% will be HH
I physically tested this myself and this is not the case
HT = 25%
TH = 25%
HH = 50%
i tested this. that is all i should have to say.
Every one here seems to be missing the point.
There is the conditional and absolute (not conditional) interpretation of the question.
Everyone here is right, and also everyone is wrong. It just depends on how you see the problem.
% will be HH
>I physically tested this myself and this is not the case
before converting it using the third coin
>2:
>You toss 1000 pairs of coins (2000 coins in total).
>You go one pair at a time. For every pair you choose one random coin.
>If the chosen coin is heads, the odds of the other coin being heads is 1/2.
yeah but the text in the image says at least one of the coins is heads, not that a randomly chosen one is heads.
This is correct. Everyone else here is mathematically illiterate or trolling.
Pic Related: 1/3
NO why does everyone think this when HH comes on top 50% of the time?????
why do all these math heads completely ignore physical trials?? tell me a scenario where i can test this and get heads heads 33% of the time. please tell me when in the physical world this is possible because i did it myself
chance that neither is heads is 25%, so knowing that at least one is means you already know you're within the other 75%. our specific info reduced this 25% to 0 though, so this 75% becomes 100%. every 0.03% of it is now worth 0.04%, because we excluded 25% of possibile scenarios.
for every three throws that we did not exclude, one results in two heads.
you can test it this way - throw two coins and if both are tails, it's against our knowledge, so it doesn't count. of the rest, you will havve 1 double heads per every 3 throws, on average.
>i tested this. that is all i should have to say.
You're retarded. For a 2 coin flip you will get
HH= 25%
HT = 25%
TH = 25%
TT = 25%
If at least 1 coin landed heads only TT is no longer a possibility. The other 3 outcomes are all possible and EQUALLY probable.
HH
HT
TH
HH is 1 of those 3.
1 of 3
1/3
>You toss 1000 pairs of coins (2000 coins in total).
>You select all pairs with at least one heads (as it is a restraint given in the question.
>1/3 of those pairs will have heads the other coin (thus being heads-heads).
i reject the small sample argument because even with 200 trials the chance of getting 102 is astronomically high if the true chances were 1/3
As others have already said,
> For every pair you choose one random coin.
is not equivalent to
> Given that one of them is heads
You are just trying to be a fancy faggot
one trial:
>throw two coins
>check whether at least one is heads
>(it does not matter which one, as long as at least one is heads)
>is neither coin heads? Discard the trial. Forget it ever happened; it was a condition that at least one coin turned up heads.
>Did at least one of the two coins come up heads?
>Increase the success counter if both are heads
>increase the fail counter if not both are heads
afterwards the success:fail proportion should be 1:3
the mistake is to even consider the case TT
>I had three coins. Coin 1, 2, and 3. Coin 3 was flipped to determine if coin 1 or coin 2 would be heads. The remaining coin was then flipped.
Nobody else sees what's wrong here??
If coin 3 was flipped, which of the last 2 coins is the "remaining coin" and what happened to the other coin?
Okay the thing about this is the two main camps are looking at the problem differently. One mathematically, one physically. One side views it as HH HT TH and the other as HH HT/TH. The way the question was posed favors the second side, as the outcome realistically is either its heads, or it is a mixed. One side views them differently, when in this situation they are not, and the other views them together, not mathematically correct, but physically and realistically correct
your fault is not realizing that TH and TH are the same outcome. and that outcome is 50%
It could be interpreted either way.
If you choose one random coin for every pair and it is heads. Then you have 'given that one of them is heads' and the odds of the other one being heads is 1/2.
You have been given the information that one of them is heads, there isn't any contradiction with the question.
I am not saying that this is the correct answer, I'm only trying that people can see other's points of view.
this
to add to this, this is actually the problem with running trials (even simulated ones on computers) in cases where the conditional probability is really small
say you want to test something about lottery winners named John Doe who live in Alaska born in 1950
as an example let us say you are interested in the probability that they have brown hair.
because the condition is so restricted, the number of lottery winners you have to throw away because they do not match the description makes it take forever to get enough trials worth considering.
it doesnt just favor the second side, it is the only way it can be interpreted without logical fallacies
I hope you're a troll, otherwise gtfo retard
yeah
like yeah you could probably track down people specifically, so I guess that might be a bad example/analogy, but I hope it still shows the main idea
You retarde faggot there is LITERALLY 2 WAYS to get a heads - tails outcome and ONE WAY to get heads-heads
HH (This is 1 possible outcome)
HT (This is 1 possible outcome)
TH (This is 1 possible outcome)
All 3 of those possibilities are EQUALLY probable.
HH is 1 of the 3
1/3
>your fault is not realizing that TH and TH are the same outcome.
Your problem is that you haven't thought about using a penny and a quarter to prove to yourself that HT is NOT the same outcome as TH.
1/3
they are not equally probable
HT = 25%
TH = 25%
HH = 50%
But "given that one is heads" means "given that some coin is heads", and not "given that one coin, that I chose randomly from the pair, is heads"
unless I learned english and math wrong
if you honestly believe using different sized coins changes the outcome from 50% to 33% you're not worth talking to
Yes but ht and th are the same outcome. IN this test, You either have two heads, or a combination of heads and tails. 1/2
>HH = 50%
what?
heads heads came out 50% of the time in my physical trial
Nice trips, just proves that the correct answer is 1/3
You're a moron. Never have kids.
There are 3 possible outcomes, but they are not all equally likely. HH will happen 50% of the time, and TH/HT will happen 50% of the time, or if you prefer, TH will happen 25% of the time, and HT will happen 25% of the time
Then your problem is counting, not frequentist or Bayesian probability