You should be able to solve this easily, /sci/

Yep, I solved it.

>>8209008
1/2

>>8209008
HH
HT
TT
TH

Given that at least one of the coins is heads, we have

HH
TH
HT

So 1/3.

>>8209018
>TH
>HT

the coins are indistinguishable senpai~

>>8209020
No they aren't.

How the hell can you know that the other is heads but not which one?

>>8209020
>flip two coins
>"the one on the left is..."
>"NO SUCH THING, THE COINS ARE INDISTUINGISHABLE"

50% ofc

If one is always HEADS then the second has a 50% chance to be HEADS.

>>8209025
flip two coins, look at all the times in which there are at least 1 heads, count how many times both are heads. easy experiment m8

>>8209034
>If one is always HEADS
There is no coin that has to be heads. Either could be heads and either could be tails, as long as at least one is heads.

>>8209026
>>8209021
You flip two coins, they land - one on the left and one on the right. Flip them both again - one lands on the left, one lands on the right. You have no idea if the right one in the second flip is the same as the right one in the first flip.

Monty hall problem is a ruse.
There is actually no problem.

It's a 50% of probability.

>>8209049
It doesn't matter if they're the same coin every flip, only that they're distinguishable every flip.

You go to a casino.
There is a machine there that accepts coins (pretend the coins are practically worthless)
It takes 2 coins to play. The machine flips them for you. Randomly and fairly.
-If you get 2 tails the machine gives you the coins back, and you just play again.
-If you get 2 heads you win 100 dollars.
-If you get Heads/Tails, you lose 100 dollars (go into debt)

You play the machine a trillion trillion times.
Will you be incredibly rich, incredibly in debt, or roughly break even?

>>8209008
Who gives a shit, and if, how can one apply it on the real world? Examples plox!

File: 1280x720-H7b.jpg (65KB, 1280x720px) Image search: [Google]

65KB, 1280x720px

>people keep arguing 1/3 vs 1/2
>decide I'll do an experiment
>start with one coin, then three coins, then six coins, then ten coins etc
>when I have a shitload of coins I notice something moving in the coins
>big nosed goblin gnawing on one of the coins
>mfw a jew tried to steal 1/12 of a coin from me

>>8209008
>more of these ridiculous questions.

>You flip two coins, at least one is HEADS
>What is the probability that both are HEADS?
First of all. You could look at this two ways:
The first line is a false statement which only serves the purpose of establishing that you are flipping two coins. And the question asked on the bottom when referring to "probability that both" you refer to a separate flip of the coins from the flip proposed in the first statement. (this yields an answer of 1/4 as each coin has a 1/2 chance of being heads: 1/2*1/2=1/4)

Or you could look at it as the coins flipped in the top statement and the question asked refer to a single flip of the coins. And the first statement established that one of the coins is heads. Then the question relies on the probability of the second coin being heads. (this yields an answer of 1/2 as the second coin has a 1/2 chance of being heads and it was established that the first coin is heads)(it doesn't matter whether you flip both at the same time or one after the other)

I give this question a 6/10 It was simple enough to not contain too much ambiguity and a young child could understand the question. However the relationship between the the first statement and the question asked is not too clear; with the only thing connecting them is the word "both." It could use some extra information relating them further. ie: saying "From the same flip: What is the probability..." or "You flip two coins. One of them is heads. What is the probability of the other being heads as well?"

Joint probability, I actually don't know much probability but I can tell you doing that shit for orbitals will not work otherwise we wouldn't be using all these spergy methods we have when dealing with systems that contain more than one electron.

>>8209093
Truly a terrifying tale of frights and spooks, thank you for posting your research.

>>8209114
>It could use some extra information relating them further. ie: saying "From the same flip: What is the probability..." or "You flip two coins. One of them is heads. What is the probability of the other being heads as well?"

>"You flip two coins. One of them is heads. What is the probability of the other being heads as well?"
This is exactly what OP's picture is saying. Granted, instead of saying "the other being heads as well" it just says "both are heads" which is completely justifiable and unless your first language is not english there should be no ambiguity.

>>8209114
I like how you tried to appear smart and still got the question wrong. It's 1/3.

Why does sci get memed on by this problem every single time, without fail? Don't you have one of these threads multiple times a week?

File: no-country-for-old-men.jpg (41KB, 640x302px) Image search: [Google]

41KB, 640x302px

>>8209060
>how can one apply it on the real world?

>>8209128
"The other being heads as well" would mean that "at least one coin is heads" refers to a specific coin. But then why say "at least"? The problem is not referring to a specific coin being heads, it's simply saying the number of heads in the pair is equal to or greater than one. There are three ways this could occur, and it does not imply that a particular coin must be heads:

HT
TH
HH

So the answer is 1/3 and the question you are answering is not the same as the question that was asked.

File: how much.gif (103KB, 480x270px) Image search: [Google]

103KB, 480x270px

>>8209152
>No Country For Old Memes

>>8209154
>But then why say "at least"?
Because saying "one coin is heads" instead of "at least one coin is heads" implies that ONLY 1 coin is heads, and the probability that both are heads would be 0. The picture is an attempt to get around this ambiguity. Whether or not it says "at least" makes no difference, either way it would not be referring to a specific coin being heads. If it was referring to a specific coin being heads it would say something like "the first coin is heads" or "the second coin is heads" and even if the problem did state this the answer would STILL be 1/3. I have no idea why you think the wording is vague, because in your first post you had nothing about the "at least" but now your second post is all about that. Make up your mind and try to keep your trolling consistent.

>>8209128
I admit; "You flip two coins. One of them is heads. What is the probability of the other being heads as well?" was not well thought out. And while writing my post I was debating on deleting it. i should have

>>8209133
Explain your reasoning behind your answer "1/3."

>>8209143
It's not even a trick question or anything though. All of the information you need is there, it just proves that the average /sci/ user doesn't even fully grasp high school level math.

>>8209172
>Because saying "one coin is heads" instead of "at least one coin is heads" implies that ONLY 1 coin is heads
No it doesn't, because you are then asked about the other coin. Why ask if you are told the other coin is definitively tails?

>Whether or not it says "at least" makes no difference, either way it would not be referring to a specific coin being heads. If it was referring to a specific coin being heads it would say something like "the first coin is heads" or "the second coin is heads" and even if the problem did state this the answer would STILL be 1/3. I have no idea why you think the wording is vague, because in your first post you had nothing about the "at least" but now your second post is all about that.
First of all you seem to be confusing me with some else. Second, your wrong. If the question stated that the first coin was heads then we would have only two possibilities:

HT
HH

So the answer would be 1/2

If the question was "at least one is heads, what is the probability that the other is heads" then we are not being asked about two coins, only one coin (the "other"). So we have:

H
T

Answer would be 1/2.

>>8209174
TH and HT both work. 1/3. Easy.

>>8209196
The second part is incorrect. The other would have a 1/3 chance of being heads if one of the two is heads.

>>8209197
That doesn't explain shit. "spoon feed me"

>>8209211
Why don't you try the experiment yourself?

https://www.random.org/coins/?num=2&cur=20-novelty.voting-2004

If you flip 3 coins, and one is heads and one is tails, what's the probability the remaining coin is heads?

>>8209216
3/8

You flip an infinite number of coins. What's the chance that you're lying?

>>8209206
How so? I just explained how its different. We are only being asked about the state of one coin, which is independent from the state of the other. In the original we are asked about the state of two coins which is dependent I the information that this state contains at least one head. So it's not the same.

>>8209225
The other coin implies it's a scenario which two coins are flipped and one is heads. In this case you eliminate the TT possibility from the flips are you are left with 1/3 for the other coin being heads, and 2/3 for it being tails.

>>8209197
>>8209206
Do you seriously think this is something like?:
TT
HT
TH
HH
These are the possible outcomes given. Choose one outcome randomly out of the outcomes that has one heads. Then tell me the probability that that outcome is the outcome with two heads.

>>8209216
1/2

If you flip three coins, at least one is heads and at least one is tails then the chance there are two heads is also 1/2

HHT
HTH
HTT
THH
THT
TTH

-1/12

>>8209236
I think it's how you described. Can you tell me why it's not how you described?

>>8209239
There's a subtly in the question. It is asking for the probability that both coins are heads given that one coin is heads. This is different then asking the probability of both coins being heads without the given.
The way you find a probability is by counting how many times it happens and dividing it by the total possible states. If I asked you:

What's the probability that both coins are heads?

You count the HH option as 1 and divide by the total states HH, HT, TH, TT 4 so the answer is 1/4. However, if I asked you:

What's the probability that both coins are heads if one coin is heads?

Then we still have the one case HH, but now, the given condition limits our total outcomes to HH, HT, TH (BUT NOT TT). There are 3 possible states instead of 4.

>>8209228
That doesnt answer the question being asked, nor does it respond to what I said. If we know one of the coins is definitively a head then there are only two options:

HT
HH

The other coin has a 1/2 chance of being heads.

You are saying TH is also an option. But it's not because that would mean we are not talking about the other coin. Again, the state of a single coin is independent so the answer must be 1/2 if we are only asked about one coin.

didn't you ever learn Bayes' Theorem?

>>8209252
The question doesn't say "one is definitively heads" it says "at least one is heads", if you say the "other" in the context than for TH the other would be tails, and for HT the other would be tails, making the other coin only have a 1/3 chance of being heads.

>>8209008
50% it either happens or it doesn't

>>8209252
But we aren't talking about the other coin. We are talking about both coins. Does the OP ever specify that the first coin is heads? It could be a situation where he flips two and one fell off the table out of view and the visible one is heads. But we don't know whether the visible one is the first (HT) or the second (TH). Nowhere in the OP does it even say anything about an "other" coin.

>>8209249
I agree with everything you said. What's the contradiction?

It's 50% FOR FUCK'S SAKE! AT LEAST ONE is heads. That leaves the other coin to decide the outcome with probability of 50% heads. Jizuz, dumbfags..

>>8209261
nice b8 m8

>>8209256
>You flip two coins, at least one is HEADS.
>What is the probability that both are HEADS?

It doesn't say you flipped them both at the same time. If I flip one coin at a time (it doesn't matter which). Its a given that I won't get two heads if the first one I flip is tails.

do you think the world would be a better place if anyone who failed to answer this question properly were burned in the gas chambers?

>>8209265
>*(it doesn't matter which one is first)

>>8209265
Not sure what your point is. The question asks to about when you get at least one heads.

Flip coin 1 and it's tails:

Flip coin 2, it's tails, doesn't fit the description of at least one heads, is discarded.
Flip coin 2, it's heads, fits the description of at least one heads, is counted into the odds.

Let's assume you flip them together, undiscernible: 1/2. Flip them separately: 1/3. Any mistakes?

>>8209272
Can you explain how you got 1/2 for the first one?

>>8209256
>The question doesn't say "one is definitively heads" it says "at least one is heads", if you say the "other" in the context than for TH the other would be tails, and for HT the other would be tails, making the other coin only have a 1/3 chance of being heads.
If one is not definitively heads then what does "the other" refer to in the case of HH?

If the first coin is the one referred to as heads

HT
HH

If the second coin is the one referred to as heads

TH
HH

Still 1/2

>>8209259
>But we aren't talking about the other coin. We are talking about both coins.
If you look back in the conversation instead of just butting in you will see we are in fact talking about "the other coin", not the problem originally asked.

>>8209277
You flip them both in the same time. Every time at least one (no matter which one) is heads. This leaves the probable cases to HH and HT.

>>8209283
TH also works for "at least one is heads" though. The only one that doesn't is TT.

>>8209272
If you flip them together there are still two coins. Discernible has nothing to do with the order you flip them in or any other detail. There are two physically distinct coins no matter how identical they are.

>>8209270
Flip coin 1: its tails
coin 2 doesn't matter
-try again
Flip coin 1: its tails
coin 2 doesn't matter
-try again
Flip coin 1: its heads
Flip coin 2: its tails
-try again
Flip coin 1: its heads
Flip coin 2: its heads
-you're done trying

You are a biologist travelling in the rainforest. You are bitten by a deadly venomous snake. You know that the antidote for the venom is secreted by the female of a certain species of frog found in this rainforest. The population of these frogs is split evenly between males and females, and they are visually indistinguishable from each other. You also know that the males have a distinctive croak and the females don't croak. You see a frog of the species in front of you. At the same time, you hear a male croak behind you. Turning around you see two frogs of the species where the croak came from. You only have enough time to run to the frog in front of you and lick it or to the two frogs behind you and lick them both before you pass out from the venom. Which choice maximizes your chance of survival and what is the probability of survival?

>>8209284
As I said, it has to be specifically mentioned that the coins are, let's say, A and B. In this case I assume the coins are A and A.

>>8209287
>Flip coin 1: its tails
>coin 2 doesn't matter
>-try again
If coin 2 is also tails then of course it matters as this does not meet the criteria of at least one coin being heads.

>>8209297
You cannot get two heads if you already have one tails.

>>8209301
So what is your point? This doesn't seem to help you calculate the probability of anything.

>>8209287
>>8209297
By the way. Those were all the possible outcomes in this order:
TT
TH
HT
HH

File: 6J9tnyS.jpg (68KB, 531x960px) Image search: [Google]

68KB, 531x960px

>>8209008
>You should be able to solve this easily, /sci/
67 responses, no clear consensus.
Surprise, surprise, the same board that doesn't believe in free will, extra-terrestrial intelligence (anywhere), or stochastic systems also can't into basic probability.
The answer is 1/3 btw.

>>8209301
you also cannot get "at least one heads" with two tails, so it actually does matter.

>>8209311
TT is not possible as we are told at least one is heads. I just said this.

>>8209301
You're not attempting to get two heads, you are attempting to calculate the probability of getting two heads if at least one of two coins you flipped is heads.

from random import randint

atLeastOneHead = 0
bothHeads = 0

for i in range(100000):
coin1 = randint(0,1)
coin2 = randint(0,1)
if(coin1 == 0 or coin2 == 0):
atLeastOneHead += 1

if(coin1 == 0 and coin2 == 0):
bothHeads += 1

print(bothHeads/atLeastOneHead)

>>8209315
Oh, there you said it.... It's BASIC probability. I have a riddle for you: 2+2=?

literally any "intro to probability" book will tell you that it's 1/3.

File: 1467838720428.jpg (99KB, 1000x664px) Image search: [Google]

99KB, 1000x664px

>>8209315
p.s.: classical mechanics was known to be completely wrong about a hundred years before QM was codified, yet most of you cling to it the way a Chad clings to a set of D-cup boobs.

>>8209008
How are these always the biggest threads?

>>8209332
They are the best for honing one's trolling ability. Convincing others that your wrong answer is actually the right answer is quite the troll.

>>8209337
That doesn't explain why there are always 5 people posting their brute force Python scripts to figure out the answer.

If you flip both at the same time or verify the result after flipping both (i.e. you flip while blindfolded) 50%.

>>8209340
I've done that before.
It's really frustrating when you know you're right and half the people here just refuse to understand.

>>8209344
The order of flipping is irrelevant. And you don't have to blindfold yourself either. Getting a head and a tail counts as at least one is heads but not both, and getting a head and a head counts as at least one is heads and both are heads. The latter will occur half as often as the former.

>>8209337
>>8209347
>It's really frustrating...
#Trolled

>>8209331
>classical mechanics was known to be completely wrong
I swear nobody seems to understand the idea of a theory being correct

>>8209352
It undeniably makes the two mixed (TH/HT) outcomes indistinguishable.

>>8209373
it makes them seem indistinguishable, but they aren't indistinguishable. They are two actual seperate events and in order for them both to happen they need to be distinguishable. The universe doesn't care if you blindfold yourself, it's still going to behave the way the non ignorant people have observed.

>>8209373
Let's say I blindfold two people and have them fire a gun at you and your father simultaneously. They don't know who is firing at whom. One of you dies, but since the gunmen are blindfolded, it's indistinguishable -- you dying and your father dying are the same outcome.

>>8209008
I read somewhere that coins are more likely to land on a specific side

>>8209373
Of course not. Let's say you flip two completely identical coins at the exact same time. They are still two physically distinct coins. The point is not that you can tell which coin is which after every flip. the point is that there are two physical coins every flip. If you don't believe me, try flipping two coins yourself. You'll see that getting a head and a tail is twice as likely as getting two heads.

>>8209008
>You flip two coins, at least one is HEADS.
>What is the probability that both are HEADS?
>>8209326
Explain to me where it asks what the probability of getting two heads IF you have at least one heads is.

File: wKEKRTr.jpg (138KB, 745x785px) Image search: [Google]

138KB, 745x785px

>>8209353
>#Trolled
Are you suggesting the "50-50" crowd here all understand the answer is 1/3 but pretend otherwise?
Nah, if anybody is trolling, they're doing so from within a crowd of the genuinely ignorant.

>>8209387
>muh reality

You have a discrete random variable the inclusion [math]X:\{0,1\} \to \mathbb R[/math] with PDF the constant function 1/2. You take two samples and sum them, and the result is at least 1. What is the probability it is exactly 2?

>>8209399
dude
there are two possibilities
1) it happens
2) it doesn't
so in any case - it's, 1/2, or 50%

>>8209396
>Explain to me where it asks what the probability of getting two heads IF you have at least one heads is.
Right here:

>You flip two coins, at least one is HEADS.
>What is the probability that both are HEADS?

>>8209008
fuck off you stupid faggot

>>8209408
kek.
>IF so and so happens
(the problem tells you so and so happens)
>what is the probability that such and such happens
(the problem asks what the probability that such and such happens)

>>8209441
If I am a man what is the probability I am not a man?

>>8209451
50-50 you either are or you aren't.

It's 1/3 you retards

>>8209408
>You flip two coins, at least one is HEADS.
>What is the probability that both are HEADS?

>given(flip two coins: one or more = heads)
>probability of(flip two coins: both = heads)
If I flip two coins and its assured that one or more is heads. Then either one or more of them always gives heads or you only consider the outcomes of the coins IF one of them is heads. OP doesn't give an IF relationship between the statement and the question. If OP said; "If you flip two coins and at least one of them is heads. Then what is the probability that both are heads?" then I'd agree with you.

>>8209473
>If I flip two coins and its assured that one or more is heads.
Nope, wrong. The question doesn't say it was assured, it say that it simply happened. Try again. Before you answer you might want to look up "conditional probability".

>OP doesn't give an IF relationship between the statement and the question. If OP said; "If you flip two coins and at least one of them is heads. Then what is the probability that both are heads?" then I'd agree with you.
That's because it's saying that something happened, not asking what the probability would be IF something happened. The answer is the same for both though.

>>8209480
>The question doesn't say it was assured
>You flip two coins, at least one is HEADS.

>>8209488
>You buy a lottery ticket, you win.
Oh I guess that means the lottery is fixed.

>>8209491
If you're going to make assumptions and assume that the coins have an equal chance of being heads or tails. Then why not make it easy on yourself and assume that both of their probabilities of being heads is 1?

>>8209498
>If you're going to make assumptions and assume that the coins have an equal chance of being heads or tails.
They do in idealized probability questions. Anything else would be an arbitrary choice.

>>8209507
Assuming that this is an idealized probability question was an arbitrary choice.

Hard mode:
how do you argue against 1/2 without resorting to combinatorics? i.e. why is it false to view the unknown coin having landed both heads and tails with a 1/2 probability without providing the solution to 1/3?

>>8209511
No it's not.

>>8209512
Because both coins are unknown.

File: 0ecc55e519cc9f7feef1c295734848066c2e38b2fdc4778bb3a207aa89029151.jpg (60KB, 625x508px) Image search: [Google]

60KB, 625x508px

>>8209516
Come back to me when you find "The coins each have a probability of 0.5 for being heads and a probability of 0.5 for being tails" written on OP's image.

You flip 2 coins, you look at 1 of them which happens to be heads and you cover the other one with your hand. What are the odds you discover the second coin is heads if you take your hand off of it?

Is the question identical to the one in OP?
Why is the problem not the same as gambler's fallacy?

>>8209538
>You flip 2 coins, you look at 1 of them which happens to be heads and you cover the other one with your hand. What are the odds you discover the second coin is heads if you take your hand off of it?
1/2

>Is the question identical to the one in OP?
No.

>Why is the problem not the same as gambler's fallacy?
Because while the result of each coin is independent from each other, the result of two coins is not independent from the fact that the two coins contain at least one head.

>>8209512
There are three possible outcomes. You're asking someone to explain why something is true without using the reason it is true.

>>8209054
Hmmm. Let's see. My odds are as follows
TT - 1/4
HT - 1/4
TH - 1/4
HH - 1/4
In the eyes of the machine, HT and TH are equal, so really the odds become
TT - 1/4
HT/TH - 1/2
HH - 1/4
In other words, every time you roll you have a 50% chance of losing $100 dollars, but only a 25% chance of making $100. So after a trillion rolls, you will be in a huge amount of debt.

>>8209008

>You flip two coins,

>at least one is HEADS.

>What is the probability that both are HEADS?

>You generate the sample space
>1 HH
>2 HT
>3 TH
>4 TT
>Where all outcomes are equally probable

>You rule out TT

>What is the probability that the outcome was HH?

One in three. Would have been one in four if TT wasn't ruled out, which squares with 0.5*0.5=0.25

>>8209296
>As I said, it has to be specifically mentioned that the coins are, let's say, A and B. In this case I assume the coins are A and A.

Even if you flip the same coin twice, you can then discern them.

So you're back at HT and TH, but instead of them being left/right, they're first/second flip.

I get really worried when I see posts on /sci/ like this with anything more a few posts saying the answer. How can this break 100 on a fucking science and math board??

>>8209749
welcome to /sci/

>>8209749
Monthy Hall got PhDs riled up against each other arguing over the answer, some of them admitting their mistake only after witnessing simulations.

A confident approach is not a good one for these kinds of problems.

>>8209762
Finally a legit post.

ITT: gambler's fallacy.

>>8209762

I don't understand your post.

It's logically ambiguous.

Stop implying implications.

What is your point?

https://betterexplained.com/articles/understanding-the-monty-hall-problem/

>>8209766
The state of two coins is not independent from the fact that at least one is heads.

If one is -always- heads, it's just the probability of the other coin being either heads or tails. Obvious 50/50.

>>8210204

Yes. Yes it is.

>>8209766
ITT: People who don't know probability

>>8210527
Sure, but that's not what the question says. It says at least one. Either of the two can be one.

File: coin_math.png (24KB, 766x968px) Image search: [Google]

24KB, 766x968px

When you flip a coin it has two possibilities, heads or tails. But with the assumption that one IS heads it adds a third possibility or a combination thereof of the possibilities.

So, flipping a SINGLE coin gives you two possibilities. Heads and tails.

So we know one coin will be heads. (H).

Now the thing is, since we have two coins, and we don't know which is heads, it adds a possibility that either coin 1 or coin 2 could be the guaranteed heads. But we do not know which. (H*n)

Since we do not know which, it adds a looping possibility with having the two coins. What does all that mean? If you assume Coin 1 is tails, then Coin 2 MUST BE heads. And if Coin 2 is heads and Coin 1 is tails that means a negative probability outcome for the answer, so we need modulation. (H*n(H*n)

If Coin 2 is heads then Coin 1 is in a state of either being heads or unflipped, and if coin 1 is unflipped, it must be modulated to see its outcome. (H*n(H*n))H*n) So this goes on and on... unless you solve this problem with a bit of logic.

There are two possibilities that a coin has not been flipped. Assume Coin 2 is unflipped and we do not know Coin 1's outcome. That puts us in a state of 6 possibilities. C1=UF C1=H C1=T C2=UF C2=H C2=T. However, if one must be heads then it changes the others possibilities as shown in the chart.

Therefore If Heads (H) must hold 1 positive value and we are calculating for (H) to have two positive values out of an unmodulated 4 possibilities, that puts the entire problem in a state of point floating. If you modulate it, (H) Can be true once or twice, and Tails can be true once and unflipped can be true once. If further modulated assuming (H) is true for 1 and (T) is true for 1, it begins to modulate itself. Thus giving 5 possibilities.

>>8209093
Now THIS is /sci/ shitposting

>>8210593
No. It's not.

>>8209216
The important part is AT LEAST. If coin #1 and #2's states are given, obviously coin #3 will go 50-50. But if you know that AT LEAST 2 coins are heads, without specifying which coins these are, then you're in the court of conditional probability. You choose a state out of
H H H
H H T
H T H
T H H
and the probability for coin #3 being heads is evidently 3/4, not 1/2.

>>8209272
Explain the mathematical difference between the two cases.
Protip: you can't

>>8209288
Frog in front gives me straight 50/50.
Behind, I know that at least one frog is male - possibly both. If both are male, I have a 100% chance to live. The probability that both are males, given that I heard a croak, is 1/3.
The complementary probability, that on is female, is therefore 2/3. In that case, I have a 50% chance of survival.
Turning around and picking a frog at random therefore gives me a 1/3*1+2/3*1/2=2/3 chance of survival.

File: autism191992.jpg (24KB, 277x296px) Image search: [Google]

24KB, 277x296px

>>8210701
Sure, whatever you say, anon....

Bayes' Theorem

[math]P(2H|1H) = \frac{P(1H|2H) P(2H)}{P(1H)}[/math]

[math]P(2H|1H) = \frac{1 \cdot 0.5 \cdot 0.5}{0.5}[/math]

[math]P(2H|1H) = 0.5[/math]

>>8209008
Explain heads. Are you fucking with me?

The answer is 1/3

Here's a simulation to prove it.

https://repl.it/Cddc/0

Click "run" and see for yourself

>>8213636

1) Define your terms

2) Once you've defined your terms, I'll tell whether you're wrong because you've calculated wrong, wrong because you assigned wrong probabilities or wrong because you misunderstood OP.

>>8213636
P(2H) = 1/4. Probability that both coins are heads. 1/2 * 1/2
P(1H) = 3/4. Probability that at least one coin is head. 3 possibilities: TH, HT, HH, out of four possible.
P(1H|2H) = 1. If both coins are head, then it is certain that at least one is head.

P(2H|1H) = 1/3

>>8209051
I though the same, try it again with 20 doors, remember the hoster opens every door expet yours and the prize door.

>>8209258
Obligatory meme.

>>8209762
This is not Monty Hall.
The ambiguity doesn't lie in the unintuitive mathematics but the interpretation of the wording.

File: monty.png (50KB, 374x382px) Image search: [Google]

50KB, 374x382px

>>8209051

>>8209051
Monty hall problem is unsolvable if you don't know what the person would prefer. A person already having 10 cars or whatnot might actually get an increased standard of living with a 'lil goat his kids could pat or whatever.

>>8209017
this

≈ 1/2

Yep, there's a little probability that the coin remain blocked on its board.

File: severed-head.jpg (19KB, 400x300px) Image search: [Google]

19KB, 400x300px

>>8209008
What a dumb question! How could a coin turn into a head?

>>8209008
50/50

Either they are, or they're not.

>>8209093
>>8209093
> not "-1/12"

1/9.

File: 1466788577197.jpg (143KB, 1280x720px) Image search: [Google]

143KB, 1280x720px

Holy shit /sci/ is dumb. The question is flawed, because there is an ambiguity. It's either read as:
>You flip two coins, one lands as heads, what is the probability that both are heads?
or
>You flip two coins, one will land as heads, what is the probability that both are heads?
The answer is 1/2 and 1/3 respectively, for the reasons given by people in the thread.

1/2 in the first case since the coins are independent, and 1/3 in the latter case because you rule out TT in the table of possibilities.

>>8217414
>You flip two coins, one lands as heads, what is the probability that both are heads?
>You flip two coins, one will land as heads, what is the probability that both are heads?

The fact that the answer to these two questions is not the same has some intricate philosophical and probably physical meaning that I have yet to grasp.

>>8217414
>>You flip two coins, one lands as heads, what is the probability that both are heads?
Answer is 1/3 still

If you don't know which coin did it, the answer is 1/3

>>8217416

The pyshical is retards don't get english. It is not the same question

File: aba5f42ddc28dceadc36e88d0c5b02e6.jpg (78KB, 600x692px) Image search: [Google]

78KB, 600x692px

>>8217417
No, it's really not. Because the question in the OP is ambiguous. Here's an unambiguous version of the question with 1/3 as the answer:
>Suppose I flip two coins without letting you see the outcome, and I tell you that at least one of the coins came up heads. What is the probability that the other coin is also heads?
Here's an unambiguous version of the question giving 1/2 as the answer, with motivation:
>I will flip two coins, and one of the coins will always come up heads, what is the probability that both will come up heads?

The difference is whether or not the coins have been flipped yet or not. I don't care about the question in the OP and its semantics.

Why does it matter if they've been flipped? Because if they have you do the table with the HH, HT, TH, and TT. If they have not been flipped you have to take into account that one of the coins (You don't know which) will always be heads, regardless. In the first case where they have been flipped it just happened to be that case, if they haven't been flipped it HAS to be that case, making the table of possibilities:
(Imagine a coin with heads on both sides to visualize the case of unflipped coins with one always landing heads)
H_1, H
H_2, T
H_1, H
H_2, T

or simplified:
H, H
H, T

50/50 or 1/2.

Again, it matters if the coins already have been flipped or not, since it affects the possible outcomes we need to consider.

>>8217433
To clarify the part that makes those questions unambiguous are the "came up" and "will come up".

In my first post:
>>8217414
I didn't make this distinction clear enough, since English isn't my first language.

>>8217414
How is "at least one" ambigious?

File: Jj1Feuq.jpg (34KB, 674x750px) Image search: [Google]

34KB, 674x750px

>>8217433
>the question in the OP is ambiguous
It really isn't.

>Here's an unambiguous version
>>I will flip two coins, and one of the coins will always come up heads, what is the probability that both will come up heads?
Except that isn't what the OP is asking.
The 1/3 vs 1/2 thing hinges on "at least one coin" vs "one particular coin", and the OP clearly states "at least one".

>>8217709
>The 1/3 vs 1/2 thing hinges on "at least one coin" vs "one particular coin"
No it doesn't. This version of the question:
>I will flip two coins, and at least one of the coins will always come up heads, what is the probability that both will come up heads?
still has 1/2 as the answer, for all the reasons I mentioned.

File: goalPosts.jpg (63KB, 574x328px) Image search: [Google]

63KB, 574x328px

>>8217739
>No it doesn't. This version of the question:
>This version of the question:
>This version
https://en.wikipedia.org/wiki/Moving_the_goalposts

50%

File: don.gif (398KB, 480x238px) Image search: [Google]

398KB, 480x238px

>>8217776
That's not moving the goalpoast. Both that version and the one in this post:
>>8217433
Have 1/2 as the answer. I was clarifying YOUR mistake for YOUR benefit, mr rude man.

File: 1352993537191.jpg (91KB, 350x437px) Image search: [Google]

91KB, 350x437px

>>8217820
I'm not following...
First, how was I rude?
Secondly, you didn't "clarify" anything.
I'm ultimately addressing the claim that the OP question is ambiguous.
The only rebuttal you offered related to alternate versions of the question, not the OP at all.
The OP's question is unambiguous, and the answer is 1/3.

>>8209715
wait so since 1/2 and 1/4 are the only options and 1/2 is double 1/4 are the new odds 2/3 and 1/3

>>8217830
Sure, that's true. I was trying to explain how people might be confused. As I said earlier: "I don't care about the question in the OP and its semantics."

Sorry for any confusion.

>>8210701
This beautiful kind of autism is exclusive to /sci/, that's why I like lurking here.

So we have four possible outcomes if you flip two coins: HH, HT, TH, and TT.

Flipping in sequence: you flip the first coin, log the result, then flip the second coin. In this scenario, HT and TH are different. If you flip one coin and it lands heads, you can eliminate scenarios TH and TT because the first flip wasn't tails. From here, your remaining options are HH and HT. The second coin thus has a 50% chance of landing heads, which is logical because the second flip is independent of the first.

Flipping coins in parallel: you flip both coins and the result is known to you simultaneously. In this scenario, HT and TH are equivalent because the order doesn't matter. In this instance, if you are informed that one of the coins has landed heads, you can only rule out TT as an option because the only states available are HH, HT, and TH. Since you know you have one coin that's landed heads, the remaining coin must be H,T, or T. That gives you a 1/3 probability of getting heads. This is because the two probabilities are dependent and the events simultaneous.

>>8209008
25%?

this shit screams "semantics" problem

>>8209008

Did I know one of the coins was going to be heads before I tossed them, or is it after the fact?

>>8213636
This poster is almost correct. Except P(1H) refers to the probability that one of the coins is heads but not ONLY one of the coins is heads. So instead, P(1H)=.75 and you get .25/.75=1/3

>>8209008
binomial distribution, that's it.

>>8218967
Just use the info in the OP. You know at least one is heads after you flip them.

>>8218960
Maybe if you don't understand probability.

>>8209008
Coin flipping a meme, it's counter-intuitive. Are the coins identical? Is the physical space thrown at "equal"? How do we know the coins will always be 1/2 outcome. So many questions...

>>8220471
All of those questions are answered if you weren't autistic.

>>8209008
>>8217709
>>8217739

i get the feeling that a lot of fuzz derives from the fact that the OP didn't explicitly state that both coins are fair (i.e. 1/2 prob for either H or T) and independent - something that I as a non-native english speaker would have boldly assumed.

Sorry to beat a dead horse but the answer is 1/3.

Three possible outcomes each equally likely:

HH
HT
TH

P(HH) =1 /3

Using Baye's theorem:

A = probability of HH
B = probability of at least one is a head

HH
HT
TH
TT

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

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

Wow look at that. The answers are consistent! Go figure.

So this can work in two different ways according of how the "at least one coin is heads" statement works?

I mean, if I flip both coins, without knowing what I got, and the condition "at least one coin is heads" works first, showing me a heads in one of the coins, the chance of both coins being heads is 50% because only depends on the other coin I haven't seen yet. And, if I flip both coins right away, I have four different cases that are TT, TH, HT and HH, and then the condition "at least one coin is heads" works in 2 ways (acting either in the first or the second coin) in each different case, I have then cases of:
HT, TH, HH, TH, HT, HH, HH, HH, having also 50% of both coins to be heads.

But, if I flip both coins right away having the again the first four cases: TT, HT, TH and HH, and the statement "at least one coin is heads" means that only will work if one of my coins is not a tails then I will have always three cases that TH, HT, HH and in that case cahnce of both being tails is 1/3.

Sorry for my mediocre english.

>>8221044
>look how smart I am
>cant comprehend basic english sentences

lol nigger. Two coins are flipped and at least one is heads. i.e first coin doesnt matter nor does it affect the probabilty of the next coin flipped.

The problem can also be "I flip 10,000 coins, at least 9,999 of them have to be tails, what is the probability that the 10,000th coin is heads"

dumber nigger is dumb

X~B(2,½)
Let the event A be such that X≥1
Let the event B be such that X=2

P(A)=1-P(X=0)=¾
P(B)=¼

P(B|A)=P(A^B)/P(A)
B is a subset of A so their intersection is B
P(B|A)=P(B)/P(A)
P(B|A)=⅓

>>8217414
>Holy shit /sci/ is dumb. The question is flawed, because there is an ambiguity. It's either read as:
>You flip two coins, one lands as heads, what is the probability that both are heads?
or
>You flip two coins, one will land as heads, what is the probability that both are heads?
>The answer is 1/2 and 1/3 respectively, for the reasons given by people in the thread.

Either the first one means "at least one" when you say one, in which case they're both 1/3, or it means "exactly one" in which case it's 0%.

>>8221044
>Bayesian Statistics
You do realize it was completely discredited, right? That it tries to make use of the inductive fallacy and probability fallacy based... on... eachother? And it completely rejects deduction?

50%

You can ignore the "always lands on heads" coin since this is 100% chance of happening. Only concentrate on the other coin, which only has a 50% chance of being head. So ultimately it's 50%.

>>8222170
And the result is consisted with numerical simulations! >>8213652

Go fuck yourself.

>>8221715
The answer to that question is really close to 0%.

>>8222199
When does it mention a "always lands on heads" coin?

>>8216068
Remove the actual incentive and just have "the car" turn into "the desirable outcome" and "the goat" turn into "the undesirable outcome."

>>8209008
I have two pennies. I take these pennies, manage to put them on both thumbs, and flip them simultaneously onto a table. At least one is heads, for whatever obscure reason, right?

The first outcome: one is heads, one is tails. Ok.
The second outcome: one is heads, one is tails, but they are in different places than the first outcome. Essentially, this is the same outcome we got the first time, because the order in which they landed on the table is entirely irrelevant to the problem. We're looking for two heads...

The third outcome: one is heads and so is the other. A different outcome this time -- the desired one.

HT = TH

0.5

>>8209018
>TH
>HT
Pick one.

>>8222633
Imagine the two coins landing in different rooms

Ran an experiment, got 7/30.

>>8217321
Well he is stealing it, so that's a net gain of -1/12

Question is phrased ambigously.

>>8221715
>lol nigger. Two coins are flipped and at least one is heads. i.e first coin doesnt matter nor does it affect the probabilty of the next coin flipped.

Coins are not labeled "I am number 1" and "I am number 2". The way the problem is worded you can assume they are tossed at the same time and a third party looks at them and tells you "at least one is heads". You have not seen the coins for yourself.

>>8217277
I like the way you think

>>8216457
With the help of a moslem, it seems possible.

>>8222724
How so?

>>8209017
this
op is retarded

>>8209008
-1/12

>>8209046
>>8214622
What's this have to do with pie?