You should be able to solve this easily, Veeky Forums

>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.

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.

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?

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

>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

>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.

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

>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.

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?

>how can one apply it on the real world?

"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.

>No Country For Old Memes

>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.

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

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

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

>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.

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

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

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

Why don't you try the experiment yourself?

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?

3/8

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

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.

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.

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.

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

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

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.

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?

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.

50% it either happens or it doesn't

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.

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..

nice b8 m8

>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?

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

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?

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

>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

>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.

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.

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

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.

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?

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.

>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.

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

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

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

>You should be able to solve this easily, Veeky Forums
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.

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

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

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)

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.

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.

How are these always the biggest threads?

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.

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%.

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

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.

>It's really frustrating...
#Trolled

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

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

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.

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.

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

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.

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

>#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.

>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?

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

>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?

fuck off you stupid faggot

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)

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

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