/sci/ - Science & Math

why are people unable to grasp the concept of outcome sets?

2 coins with 2 possibilities = 4 possibilities
at least one is heads - therefore 3 total possibilities (ruling out tails tails)
there only 1 scenario where both flips have two heads.

answer is 1/3.

>>12040799

>>12040808
maybe with a weighted coin

a fair coin is 50/50

not posting all of these
>0.999...=1 or !=1
>monty hall problem
>gold ball vs silver ball
>basically anything relying on conditional probability
>graph showing IQ versus any factor
>anything involving race
>anything supporting/opposing gender science
>the word fluoride
>bill nye/NdGT
>climate change graphs
writing all of this out makes me realize how shit this board is

what am I missing?

>>12040820
yeah but where else can you call someone a nigger for not understanding something and not got perma'd

>>12040799
100% that one is heads
50% that the other is heads

50%

>>12040815
B. Doesn't matter what happens to the actual box when it goes through, the air which is swallowed up by the portal while it is moving towards the box will create a current on the other side will propel the box anyways.

>>12040828
this

If one is 100% heads we can remove that one from the equation. We are only caring about one coin. 50% chance because we are flipping one coin.

>>12040820
Covid stuff.

>>12040815
The block breaks into a billion pieces cuz magic isn't real

>>12040799

>>12040837
But what if we accidentally remove both? Is the probability 0 or 0/0 then?

>>12040871
0->0/0[000]

Old classic.

>>12040874
this one isn't so much anymore since mythbusters has an easy clip you can link

>>12040892
this is just the same trolley problem isn't it? whether you should do nothing and "kill" 5 people or flip the switch and kill one

>>12040958
But the number of people in the black box is set before the experiment. If there are people here, then they are killed, if there are no people, then no one is killed.

>>12040970
but there's no way to get out of this experiment without killing anyone because the predictor knows what you'll do.

33.3%

>>12040799
1/3

>>12040874
>>12040889
Mythbusters smartass it and claim the myth is a plane on a treadmill. The problem, left vague for trolling purposes, is that the wheels and treadmill go at the same speed, so no, it won't take off unless that propeller pushes enough air into the wings.

>>12040799

#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
#define TRIALS 1000000

bool coin_flip ()
{
return (rand() % 2);
}

int main()
{
int n = 0; int d = 0;
for (int i = 0; i < TRIALS; i++) {
bool coin1 =coin_flip();
bool coin2 = coin_flip();
if (coin1 || coin2) {
d++;
if (coin1 && coin2) n++;
}
}
printf("%f", (double) n / d);
return 0;
}

Answer: 0.33333

>>12041029
wrong

>>12040818
This brainlet.

>>12041039
Please leave.

>>12040818
hh ht
th tt

if at least 1 is heads, we're left with the options:
hh th ht

the chance for hh is then 1/3 and the chance for th or ht (aka not hh) is 2/3

>>12041039
you're not flipping two coins you fucking retard

Scenario 1: First coin was heads. Then 50%.

Scenario 2: Second coin was heads. Then again 50%.

But we are counting "twice heads" twice, so this need to be subtracted.

Therefore 50% + 50% - 25% = 75%

>>12040892
Ah yes, this is Pascal's wager, Rocco's basilisk all over again. The predictor doesn't exist, so this problem is m00t.

>>12040799
Everything is 50/50, it either happens or it doesn't. Realtime doesn't store information, that's human cope, so percentages are worthless.

>>12041039
wrong

>>12040808
"At least one is heads" could refer to a specific coin. It's ambiguous.

>>12040808
LOL! That would mean it has a 33.333333...% recurring, how is that even possible haha? Maths is made up.

>>12042642
it could also refer to a coin with heads on both sides. it's ambiguous.

>>12040874

>>12042645
https://en.wikipedia.org/wiki/Boy_or_Girl_paradox

>>12040815
B
it has been experimentally proven

Somebody post the flies weight problem

>>12042675
The ping pong abs steel ball in water

Clasique

>>12040808
first post instant derail, nice

>>12040799
2/3

>>12041029
>>12041039
Difference between C programmers and gay pythonistas

>>12040828
>that one
Which one?

>>12040874
>>12042646
Lift is created by the relative velocity between the wings and air. No relative velocity (as in this case), no dice. Put a giant fan in front of it though, and it could fly.

>>12042642
ambiguous for an illiterate retard like yourself maybe

>>12042615
No it isn’t. It works as long as the predictor has higher-than-chance accuracy, you just adjust the number of victims accordingly.

>>12042615
Also this has nothing to do with Pascal’s wager or Roko’s memelisk, those are completely different problems.

>>12042606
kek

>>12042606
those events are not disjoint though so you can’t just add their probabilities

>>12044015
Apparently the entire community of probability theorists are illiterate retards then.

https://en.wikipedia.org/wiki/Boy_or_Girl_paradox

>>12042646
1. The plane is moving forward
2. the wheels are touching the conveyor belt
3. speed of the conveyor belt = speed of wheels
4. speed of wheels = speed of conveyor belt PLUS absolute speed of the plane

This is a positive feedback loop, as soon as the plane starts moving (powered by the turbines), movement of wheels and conveyor belt will go to infinity.

>>12040799
It depends on which one is heads
Brainlets will disagree

>>12044590
yes, I thought this was already established

>>12040799
I flip your mom twice, at least one time she gives me head. What is the probability that she gives me head twice?

>>12040820
clamping

>>12044762
1/4. a mom flip has 4 outcomes: head, anal, vaginal, and a well cooked meal

The permutations:

HH
TT
HT
TH

Out of 4 possible outcomes, you can get heads twice(HH) only one time, thus it is 1/4 chance.

>>12045385
You've eliminated TT though by seeing one coin is heads, which leaves three remaining options.

>>12045388
It is an observation of that current reality, but the true probability is 1/4.

>>12045394
>At least one is heads

This is a given

HT is equal to TH

Therefore 1/2

>>12045399
That is under the assumption that you will flip the coin as a separate event. The coins have already been flipped. It is making an observation of the current reality; at least one is heads. But that is noise, not the real probability.

>>12045404
What the the probability that 2 coins turn up heads if it is certain that 1 turns up heads

>>12044606
>This is a positive feedback loop, as soon as the plane starts moving (powered by the turbines), movement of wheels and conveyor belt will go to infinity.
No, as soon as the plane moves the wheels are moving at a different speed than the treadmill. Therefore, according to the question's premise, the treadmill is designed to keep the plane from moving. Therefore, the plane never takes off.

>>12045414
The coins have already been flipped, flipping another coin is meaningless.

You assume the first coin flipped is HEADS, which is not stated.

It could have easily been tails, thus logically it can't be 50%, you would have to treat it as noise, and find the true probability.

>>12045428
Lol either you're trolling or retarded

>>12045439
What is your IQ, you're arguing against logic here.

>>12045439
>HT is equal to TH
>Lol either you're trolling or retarded

>>12040808
No it’s actually 50/50 because one coin is guaranteed to be heads, you can basically pretend it doesn’t exist

>>12046104
You don't know which coin is heads, and they're flipped at the same time, meaning TH and HT are both probabilities, as well as HH.

>>12045385
Let's look at two different scenarios, both assuming both coins are flipped at the same time.

Scenario 1:
In this scenario, both coins are marked in a way that you're aware which is Coin 1, and which is Coin 2. You're physically shown the coin that is heads, meaning you can identify if it's Coin 1 or Coin 2. So, for example, if you see Coin 2 turned up heads, that leaves two possible permutations: HH or TH (HT can be eliminated). It becomes 50/50.

Scenario 2:
In this scenario, either you're told one coin has turned up heads after the flip, or you're shown the coin that turned up heads, but cannot determine if it is the first or second coin. In that scenario, there's three possible permutations: HH, HT, or TH.

Is my line of thinking correct?

>>12046855
>Scenario 2:
>In this scenario, either you're told one coin has turned up heads after the flip, or you're shown the coin that turned up heads, but cannot determine if it is the first or second coin. In that scenario, there's three possible permutations: HH, HT, or TH.
And just to elaborate, assuming I'm correct, I think this is where people are getting off track. If there's doubt over which coin is heads, then that means that there's always two outcomes where there's going to be one coin on heads, and one coin on tails. TH or HT. Without knowing which is which, both are in play, along with HH, which is why the odds remain 1/3. On the other hand, if you know which coin turned up heads, then the odds for that coin are removed, and it becomes a 50/50 flip of the other coin.

>>12045399
>HT is equal to TH
yeah, nope.

>>12040799
>>12040808
Congrats, thread derailed on the very first post. Oh well, let's do this.

>>12042642
Agreed. Language in general is a poor instrument for delivering thought. This is why communication is usually the first and the last problem in a given project / assignment / work. English is my third language, and the first thing I understood was that one of the coins was always heads. So it was a trick question, you're really only flipping one coin, making it 50/50.

But OP delivered, that's why pics like that derail threads everywhere they are. It's the same attribute most pictures, logic puzzles etc. share whether in media, or Facebook or where ever. People love to make it about misunderstanding the maths problem, when it's not about that. It's about trickery and purposefully confusing wording, designed to mislead.

Even the order of operations to a layman is a bunch of bullshit, for good reason. As a software engineer, I always use parentheses to separate the logical components of a formula so there is zero chance for misunderstandings when someone else later goes over my code (including myself). It's at odds with the fact that we read left to right, but then in some cases, are supposed to count right to left to center to right to further left and then finally left to right, depending on operators used. Maths majors get used to this, but the rest of us don't. It's an archaic process anyway, that doesn't serve its original purpose anymore since we're in the digital age, instead of having to worry about conserving ink and paper and type out our formulas as tightly as possible.

People will argue this. But that's what people - specifically the asshole subspecies of people - do. They are vain, petty little things. If they see an excuse to establish some meaningless pecking orders over trivial bs and claim superiority of someone else, they do it out of spite. Whether it's about obsolete maths, or a blue / gold dress. Assholes are like that.

1/3

sample size is 3, 1 is succesful

>>12040820
Fluoride is associated with drops in iq of around with points based on studies out of China. Guess why it may be so. (I know of a valid hypothesis). Criticism of fluoride is definitely no tin pot theory, unlike something like say, racial differences in iq :)

>>12046902
* 10 points

>>12040799
you never specified that order matters.

if it does then you have 3 possibilities.
otherwise ht = th and you're left with 50%

>>12046839
I see how flipping them both at the same time makes a difference. OP is ambiguous in that respect.

Still, though, if two coins are spinning in the air in front of you, and you know 1 will turn up heads, the probability that they're both heads still seems like 50% to me

>>12046870
But the odds of HH coming up are still 50% regardless of whether it's H_ or _H

H_ -> HT or HH

_H -> TH or HH

Half of the possible outcomes are HH

>>12040799
From the perspective before the first flip: 1/3
[math]P(H_1\wedge H_2) = P(H_2\, |\, H_1)\, P(H_1)[/math]
From the perspective after the first flip: 1/2
[math]P(H_1\wedge H_2) = P(H_1)\, P(H_2)[/math]

>>12046981
There is no need to specify whether order matters.

This isn't really a trick question; nor is it a twisting of language as some seem to claim. I can't think of a way of expressing the situation more clearly using English.

Try it experimentally. Flip two coins. Count each time that at least one of the two coins is heads. Also count each time that both coins are heads. Do that many times and see what the ratio is.

>>12047119

>Before the coin flips

You can roll a H_ or a _H, given OP's statement

If you roll a H_, you can roll a HT or HH
If you roll a _H, you can roll a TH or HH

HH = 50%, TH = 25%, HT = 25%

Where am I wrong?

>>12040799
You don't even need the first coin flip, it's a single 50% flip

>>12046892
If "at least one coin is heads" refers to a specific coin then there are only two samples.

>>12046902
Fluoride concentrations above safe levels are associated with low IQ. You're obfuscating.

>>12047000
>I see how flipping them both at the same time makes a difference.
It doesn't. They are two distinct coins regardless of when they are thrown.

>Still, though, if two coins are spinning in the air in front of you, and you know 1 will turn up heads, the probability that they're both heads still seems like 50% to me
You don't know one will turn up heads, it simply happens once. The ambiguity is that "at least one is heads" can refer to a specific coin or to the state of both coins.

>>12047116
Those are not disjoint, HH is in both.

>>12045385
is this a pasta
pls tell me this is a pasta

>>12040799
WRONG
they can be both not heads
OP is homosexual

>>12046885
WHERE DOES ONE LEPRECHAUN GO

>>12047129
>I can't think of a way of expressing the situation more clearly using English.
It's ambiguous. If the question stated that your friend looked at one of the coins and told you it was heads then it would be 1/2. If the question stated your friend counted the total number of heads and told you the number was greater than 0, then the answer is 1/3.

>>12047211
See >>12047298

>>12047368
Okay, but the second of those is the one that means the same thing as 'at least one is heads'. That terminology doesn't seem ambiguous to me.

>>12047397
To answer myself: Thinking it through, and after having asked a few real, meatspace people, it seems like 'at least one is heads' is being interpreted as 'this first coin I checked, at least, is heads'. To me this seems a weird and tortured way of treating the English language; but maybe I'm the weird one given how we've managed to derail this thread.

>>12047000
Let's try some examples to see if it can be more clear.

Let's say John and Joanna each flip a coin at the same time. Joanna let's you see her coin, it's heads. What are the odds that John's coin also turned up heads? It would be 50/50, Joanna's coin doesn't matter in this case, thus the odds that both coins are heads (after learning Joanna's toss) is also 50/50.

Now, John and Joanna each flip again. Joanna shows you her coin, it's heads (let's calls this 2H). However, they both turn their back to you and swap coins several times, then turn back around. At this point, you don't know who has the coin that turned up heads. So what are the odds that both coins are heads? We know one coin is heads, we labeled it 2H, but we don't know who has it, nor do we know whether coin 1 turned up heads or tails. The possible outcomes are:

Joanna : 2H, 1H, 1T
John : 1T, 1H, 2H

By introducing ambiguity, you can no longer rely on the 50/50 odds of one coin. Unlike the first scenario, there's actually a 2/3 chance John has a coin that shows heads (coin 1 could be heads or tails, and coin 2 has to be heads), and the odds that both coins turned up heads is 1/3.

>>12047339
Mathematicians average 130 IQ, the reason why you and most of /sci/ can't understand you're wrong is because your IQ is low. I'm sorry, but that's reality.

>>12046855
No, it is not, you assume you are flipping another coin.

The probability of it having been HH is 1/4, saying at least one is heads is noise. No where does it say the first coin flipped was heads, it could have been tails.

"If you flip two coins, what is the probability you will get heads twice?"

That's the real question.


You are just not smart, stop trying. IQ is real, you failed.

>>12045426
The only way to keep the plane from moving is through the wheels, and the thrust comes from the engines, not the wheels. So the conveyor really needs to match the engine thrust's force only by spinning the wheels. This is hard, because wheels are designed to be low friction. The only way to do it is to spin those wheels at fucking ludicrous speed until they blow apart and the conveyor can instead push against the plane's belly.
So the answer is the plane doesn't take off because the conveyor wrecked it.

>>12047742
I flipped one coin. It's not heads. What's the probability of it being tails? 1/2?

>>12047211
It depends on your interpretation
If I give you a coin (it doesn't matter whether its heads or tails) and I ask you to flip another coin, what are the chances the coin you flipped is heads? 50%
Now I ask you to flip your coin if mine lands on heads. What are the chances you get heads on any play? 33%

>>12047703
130 is so low

>>12047486
So the probability that both coins are heads = the probability that you draw the 2nd heads without knowing if it's the first heads, a tails, or the 2nd heads

>>12047788
I guess my issue is that I'm intepreting >at least one coin is heads
as an axiom and not a probabilistic event that needs to be taken into account

>>12047811
No it isn't, that's like 1 in 100.

>>12047742
>saying at least one is heads is noise.
It's not noise when it's explicitly stated in the question. You have to eliminate the TT scenario because of that, which changes it to 1/3, not 1/4.

>>12046855
Yes

>>12047397
They both mean that at least one is heads. Hence the ambiguity. The process for how that information is obtained determines what it means.

>>12047350
WHAT THE FUCK

>>12047751
>The only way to keep the plane from moving is through the wheels
No, the treadmill can (and must) be designed to put a force on the plane somewhere else. For example, an armature that extends towards the plane's nose and keeps it from moving forward.

>>12047703
You really would have to be a mathematician to believe in IQ

>>12040892
This is just the trolley problem with extra steps

>>12040892
Who is this predictor and how does he keep getting away with kidnapping people on a daily basis for these cruel tests? I would leave the switch and search for the predictor to kill this monster with my own hands

>>12040970
Because this line exists
>the predictor has never predicted incorrectly
It turns the problem into the trolley problem with extra steps
If you interpret it as
>the predictor is not wrong ever
then you know the exact outcome of each scenario.
If you interpret it as
>it may be outsmarted
then you can do whatever the hell you damn please, since past this point its all what-ifs

>>12047350
In the top picture, every leprechaun has a top part and bottom part across the horizontal line. This gives 28 leprechaun parts.

In the bottom picture, the 6th and 13th leprechaun are only made of one part each instead of two parts. So there are 15 leprechauns but still 28 parts. The trick is in the assumption that the number of leprechauns are preserved and not the number of leprechaun parts.

>>12040815
Trick question. The orange portal would go away since portals can only be out on stationary surfaces
>>12040799
1/2
>>12047350
Leprechauns are Irish Jews. They breed and die off so fast we don't notice the changes
>>12040874
No the plane will not be able to take off
>>12040892
I don't care I do 360 and walk away from lever

These are all too easy my dudes.
Give me a real challenge

surprised /sci/ doesnt know basic probability lmao

>>12040799
1/4

>>12048895
You must be new here.

what is the argument for flipping them one at a time changing anything exactly? i don't understand.

>>12049178
It's just dumb people talking about what they don't understand.

>>12040892
As I don't know the actual value of any of those people, I don't intervene, I do nothing.

>>12040799
Average IQ human here. It's more rare to get the same side two times straight, so it's less than 50%, perhaps around 25% or so, It should make no difference that they are two separate coins because what matters is the ocurrence of getting heads two times.

Prove me wrong

>>12049178
Retards confusing it with a scenario in which you know the first one is heads

>>12047000
The probability that coin 2 turns up head given that coin 1 is head is indeed just the probability that coin 2 turns up head, but that's not what is asked here.

>>12040799
1/4

>>12047000
>I see how flipping them both at the same time makes a difference.
it doesn't make a difference at all. difference would be if the wording said "FIRST coin is head".

>>12041039
><>J

>>12040799
well played

>>12041039
You're ignoring the cases where coin 1 is tails and coin 2 is heads.

>>12040799
why do you guys argue about this if you know there are two answers? is it just for autistic fun?
https://en.m.wikipedia.org/wiki/Boy_or_Girl_paradox

>>12040808

It's conditional probability.

P[heads|heads] = probability of heads excluding the trials where the first toss was tails. Tails in the first trial has no bearing on the outcome of the second toss. 50%

>>12053034
>he doesnt accept that the probability "theorists" are morons
ngmi

1/3
the outcomes are:
A:heads B:tails
A: tails B: heads
A: heads B : heads

Is that correct?

>>12046902
China Mexico Canada, over 11 studies sharing the same result. But as some anon said, only on a highr doses.

>>12040892
flip a coin for that 0.5 expected increase in the deathtoll

>>12040892
brainlet-proof trolly problem.

>>12053782
If "at least one is heads" refers to a specific coin (let's call it A) then the second outcome didn't occur.

>>12053893
I was thinking that aswell but I didnt wanna get fooled. And does that change anything? It's still 2/3 chance for either of them to be heads.

>>12053893
And if "at least one is heads" refers to a tribal dance performed in the Congo it gives us no information about the coins; but why not just take words at their plain meaning?

>>12053916
>It's still 2/3 chance for either of them to be heads.
What does that mean exactly? The chance of the pair containing at least one head given a specific coin is heads is 1. The chance of the other coin being heads is 1/2.

>>12053919
I don't see how "at least one coin" referring to a specific coin is not a plain meaning. If you can't handle other people interpreting an ambiguous phrase differently from how you first saw it, such that you feel the need to ridicule them with exaggerations, then you need to grow up.

>>12053929
Ah sorry I'm tired my thought got jumbled up you're right.

>>12040815
Real question is what would happen if blue portal was on the surface the box is on.

>>12040799
50%

No if coin 1 is tails and coin 2 is head this is the same as coin 1 being head and coin 2 being tail.

>>12054033
>Tail/Head
>33%

>>12054037
>coin 1 being heads is the same as coin 1 being tails

>>12042669
Fucking where? In Aperture Laboratories?

>>12045388
By seeing that one coin is heads, you've eliminated the possibilities to {HH, HT} or, equivalently, {HH, TH}. The coin flips are independent, so it's a 50% chance of getting HH.

>>12054984
>{HH, HT} or, equivalently, {HH, TH}.
They're not equivalent unless you can see where the heads is (left or right), otherwise both are available permutations along with HH.

>>12055000
If you've seen one coin is heads, you know that coin is heads. That has no bearing on what the other coin is, so you have a 50/50 chance of it being heads.

>>12055000
It doesn't matter if you've seen it, if the information given to you is based on looking at only one coin (i.e. "at least one coin" refers to a specific coin) then 1/2 is the correct answer. If it refers to either coin, then 1/3 is the correct answer.

>>12055013
>If you've seen one coin is heads, you know that coin is heads.
In your example, but that's not explicitly stated in the OP's example. If someone tells you one of the coins you flipped is heads, but you can't see it, then the probably that both coins are heads is 1/3 because you can't reduce the odds to a single coin.

>>12047486
How does the knowledge of which specific coin is heads change the probability of the answer to a question that doesn't ask about a specific coin?

>>12055031
>In your example, but that's not explicitly stated in the OP's example.
Right, I'm replying to >>12045388 who said
>You've eliminated TT though by seeing one coin is heads

>>12055191
>to a question that doesn't ask about a specific coin?
Exactly. If you know which coin is heads, then essentially that coin no longer matters, the probably becomes entirely based on the other coin, which is a 50/50 chance. If you don't know which coin is heads, then there's the potential coin 1 is heads, or coin 2 is heads (or both). You can't reduce the probability further than that. That leaves you with three possibilities, HT, TH, or HH (and TT, but this isn't in play).

>>12048171
Based

>>12055244
Ah, I'm assuming that anon meant you know a coin is heads, not literally seen it (assuming they're working from OP's question), but that gets to the crux of a poorly worded question.

>>12040799
Let's consider two questions, the odds of two heads if we know the first coin flipped is heads and the odds of two heads if at least one is heads.

There are four ways to flip two coins
1: HH
2: TT
3: HT
4: TH

From question 1, we can eliminate situations 2 and 4, leaving a fifty percent chance of 1 and 3.

For question 2, we can only eliminate situation 2, giving us a 33% chance of 1,3, and 4. Thus, the answer to OP is 33%

> But there is no ordering of the coins in the question! Thus, we can arbitrarily choose the head flipped coin to be first and this becomes question 1.

To be fair, you'd have to randomly choose one of the coins to be first. 1/3 of the time this won't matter because you flipped two heads. However, in the other 2/3 of the time, you have a fifty percent chance of choosing a tails to go first. This, if we had the knowledge of question 1, we'd be able to eliminate that flip from our choices. This gives us a leg up from the knowledge we have with question 2. Thus, the probability of question 1 will always be greater than question 2.

>>12048458
EXCEPT FOR THE FUCKING NEUROSCIENCE ROOM IN PORTAL 2 WHAT THE FUUUCK WAS THAT
im still mad

>>12055824
ahem *NEUROTOXIN

>>12055485
>> But there is no ordering of the coins in the question! Thus, we can arbitrarily choose the head flipped coin to be first and this becomes question 1.
you can treat the coins as unordered (i.e. sample space is HT=TH and HH), but then the distribution is not uniform. two options don't necessarily imply 50/50 chance.

>>12055824
Can you link a video of that level? Been a while since I played portal 2

>>12040799
I never got a head, so I will say ZERO

How is the OP's question poorly worded? Is this thread full of ESL's?

>>12055894
>How is the OP's question poorly worded?
It's ambiguous.

"At least one is heads."

How do you know? You're the person flipping. If you flip both and look down at one coin and see that it's heads, then you know there's a 50% chance the other is heads. But maybe you caught the coins, closed your eyes, and asked someone else to tell you the result. They tell you at least one is heads, and ask for you to guess whether or not they're both heads. At that point you have a 1/3 chance of being correct.

>>12056012
Okay then the answer is 100% or 0% after you see the result then. The 50% claim makes no sense no matter what.

>>12056014
>Okay then the answer is 100% or 0% after you see the result then.
Not if you don't look at the second coin.

>>12056020
How would you know if at least one coin is heads then?

>>12056023
I just tried it. I flipped two coins, one in each hand. Caught each in the same hand. Opened my right hand to look at that coin, other coin is still in my left hand unseen.

I think the spirit of the question is meant to tell you one coin is heads, but you don't know which one. In that scenario, I suspect many people would still guess 50%, but as it's written, there's some excuse for ambiguity.

>>12040892
Flip the switch then quickly flip it back, bet it didn't predict this

>>12040808

This

>>12055249
Thank you

>>12056027
This doesn't answer my question though. If you flip 2 coins, look at one, and let's say it's tails, how do you know if one of the coins is heads or not?

>>12054017
https://youtu.be/0TZd95BCKMY

>>12055894
>Of all sets of two flipped coins containing at least one heads, what percentage have two heads?
1/3
>You flip two coins, one rolls under the couch. You look down and see that the visible coin is heads. You proclaim "At least one of them is heads". What are the odds both are heads?
1/2

>>12056058
>If you flip 2 coins, look at one, and let's say it's tails, how do you know if one of the coins is heads or not?
Just make it a scenario where you ask what are the odds both coins land on the same side, so the orientation of the coin you look at doesn't matter. In the OP's scenario, it doesn't tell us how we know at least one coin is heads, that's the entire point. Maybe you looked at one coin (which happened to be heads), maybe someone told you, maybe you have a really weird version of clairvoyance.

>>12040837
>If one is 100% heads
Bad assumption. It says 1 of your coins landed on heads, not that this outcome you start with had a 100% chance of happening.
If 1 coin lands on heads as a result of a normal 50/50 coin toss then the probability your other coin is also going to be heads is 33.33%. You can prove this like the anon here did:
>>12041029

>>12056204
that isn’t a proof. computers aren’t agents they can’t prove anything. sorry!

>>12056162
>In the OP's scenario, it doesn't tell us how we know at least one coin is heads,
^This. Anons get tricked by this trick question by assuming the 1 coin you start with as heads must have a 100% chance of ending up that way in the beginning when in reality the question says no such thing about the odds of your starting observation.
By analogy if I say "suppose you're a doctor and you find out your patient has pancreatic cancer" you would be completely wrong to try to calculate the odds of other events happening for this cancer patient by assuming he had a 100 % chance of getting that cancer. By knowing he has cancer you know he was part of some sub-100% outcome and other events like responses to medicine will conditionally depend on that fact he got this kind of cancer and that it wasn't a 100% odds having happenstance.

>>12056214
It's OK that you're wrong.

>>12056234
I agree with the 1/3 answer I just wanted to continue bumping the thread as is tradition on /sci/.

>>12056239
Don't give in to troll's remorse. Stay in character.

>>12047274
Someone needs to be slapped.

>>12056239
>I agree with the 1/3 answer I just wanted to continue bumping the thread as is tradition on /sci/.

>>12056269
Whom?

>>12041039
You fixed the first coin so your assuming th == ht
and that's not the case.

>>12041029
>Chad C programmer cutting through the bullshit with elegant truth
>>12041039
>Python fag exactly as low IQ as you would expect

It's 0.25

>>12056422
>coin2 = 1
Oh no, it's retarded.

>>12040799
HH
HT
TH
TT

1/4 = 0.25%

HH
HT
TH
TT Impossible

1/3 = 0.333% repeating

Why did this take an entire thread lmao?
Are you people retarded?

>>12056430
Ye I could have ignored that outcome. But it still doesnt invalidate the result

>>12056431
>Why did this take an entire thread lmao?
It was answered in the second post.

>>12040799
A brief solution.

>>12056440
No, ignoring the result would be as dumb as forcing the second coin to be heads. You don't understand probability at all.

>>12056462
OP says that one coin has to be heads.
If the first coin is tails, the next one HAS TO be heads.

>>12056469
>OP says that one coin has to be heads.
No, OP says one coin is heads. This doesn't mean a coin was forced to be heads. Do you understand the difference between something randomly happening and something being guaranteed? Your simulation should generate all outcomes and ignore those that don't meet premise of the question, or at least generate the possible outcomes in the correct proportion. Your failed to do both. Better yet, learn basic probability theory and solve the problem in 30 seconds without writing a retarded simulation.

>>12056489
rude

>>12056422
this is wrong because in the case there is a 50% chance that the first coin is tails, and you're forcing all of that 50% to be a TH, when in reality only 25% of that would be a TH and 25% of that would be TT and disgarded.

>>12056489
>No, OP says one coin is heads.
"Is" doesn't mean "has to."
If I flip a coin and it lands heads then one coin is heads and this result didn't have 1/1 odds of happening. Having a premise of a particular outcome already happening means exactly that: an outcome happened. Not that the outcome you're starting with had no chance of not happening.

>>12056527
I understand now, ty

>>12040799
50% chance the first time, then 50% chance of the left over 50%, which is 25%. 50% + 25% = 75% so, 75% chance you get heads twice.

>>12040815
A

Where am I fuking up my logic here and what do my percentages mean?

It doesn’t matter if you don’t know which coin is heads if you just pretend:

If you pretend coin 1 is heads —> then coin 2 is 50% heads or 50% tails

If you pretend coin 1 is tails —> then coin 2 is 100% heads or 0% tails

So you know HH is 50%
HT is 50%
TH is 100%
TT is 0%

This makes the most sense to me yet I can’t make sense of it

>>12041039
kys faggot

>>12056547
Thanks for agreeing with me.

>>12056585
There's nothing wrong with your logic per se, it's just a convoluted way of doing it and it's unfinished. What is the probability of the first coin being heads given at least one coin is heads? 2/3.

HH = (2/3)(1/2) = 1/3
HT = (2/3)(1/2) = 1/3
TT = (1/3)(1) = 1/3

None of this was necessary because it's easy to see all the possible outcomes were equally likely to begin with, thus they must all have probability 1/3.

>>12056624
I do agree with you. Replied to your post by accident. Was orignally writing it as a response to this one:
>>12056469
But then I think when I reloaded the page because my connection cut out I got confused and replied to your post instead.

>>12056245
I don’t feel remorse.

>>12056585
You're doing a more intelligent version of falling for the same trick the other 50% answer anons did. It's good you're thinking in terms of actual a/b chances, but you're assuming one coin heads is always guaranteed instead of merely being what you happen to observe for the sake of this question.
So the real chances are:
HT, HH, TT
With each being 1 possible result.
TT is not what you observe per the question, but that doesn't mean it wasn't a possible outcome before you observed heads on one coin.
Because it's possible you find the odds of HH as 1 outcome out of 3 possible outcomes (HH, HT, or TT).
If you get heads on at least 1 coin = if you got HH or HT for an outcome. Your starting outcome had a 66.67% chance of happening, and it's a premise of the problem that this 66.67% result has happened. Now from that result only 1/3 out of the 2/3 premise has heads for the other coin, so it's 1/3 to get that result.

derailed own thread

doesnt it depend on how you learn how one coin is heads? i imagine for instane, if you flip two coins with your eyes closed. and someone tells you that one of them is heads but doesnt tell you the other one. to me it seems that the answer would be 50% because all that matters is the probability of the coin you dont know the result of.

>>12058311
>derailed own thread
thematically appropriate

>>12046885
>software engineer
*125 IQ retard

>>12040799
Based OP, showing a proof of concept. Not only did he post an image that derails threads, but he showed it works by derailing his own thread with it.

>>12042615
who?

>>12056585 here

I ended up doing this IRL. Just flip two coins, and record if it was a TH, HT, or HH. If it’s TT you can just not record (or not count it in the final tally/real calculation).

Ho Lee Fuk. You don’t need to get many flips in to see the one-heads counter be Around double the two-heads count. The HH accounted for around a third of flips when I was bored after 60 flips.

I think the easiest explanation for those struggling is that the one-heads flips can happen twice as easy as the two-head flips

>>12040799
100%, because both coins are head on both sides.

>>12040799
>Implying order matters
It's always 50% anyone who says it's 1/3 skipped combinations

>>12041029
>hides bad logic behind sepples

https://pastebin.com/gEcc573T

>>12041029
>hiding bad logic with sepples
https://pastebin.com/KTKEUuZd

>>12061071
Three possible outcomes, all equally likely:

GG
GS
SG

1/3

>>12060829
Order doesn't matter, the fact that there are two distinct coins does.

>>12060128
wat

>>12061108
Thanks ESL retard. It's even written in fagscript.

>>12061130
>writes a simulation that doesn't even solve the problem when he could have gotten the answer with 5 seconds of logic.
Typical CS retard.

>>12061135
kys, stats is even lower than cs.

>>12061145
this is a probability question not a statistics question. they are qualitatively different

>>12053041
what do you mean the "first toss was tails"? nobody said anything about a sequence of flips, it says two coins were flipped. they may have been flipped at the same time

>>12047350
the top leprechaun parts will be integers, the bottom will be letters
>top picture
the leprechauns are 1A, 2B, 3C, 4D, 5E, 6F, 7G, 8H, 9I, 10J, 11K, 12L, 13M, 14N
>bottom picture
the leprechauns are
10A, 11B, 12C, 13D, 14E, F, 1G, 2H, 3I, 4J, 5K, 6L, 7, 8M, 9N

so ya, as the other anon said, 2 of the leprechauns lost "half" their body and didn't get a replacement. im still a little confused though honestly. 6F lost only his hair, and 7G lost only some fabric from his robe...

>>12040799
1/4

>>12058786
your intuition is off

>>12056455

>import java
stopped reading there

>>12040799
In case of a doubt just write every possible equally likely outcome

heads + heads <--- only this one has both heads
heads + tails
tails + heads
tails + tails <--- this one is excluded

so it's 1/3

>>12040815
if you think A you're a legit brainlet

>>12040892
I do nothing and call the police

>>12041029
based, although your lack of srand() triggers my autism even if it's irrelevant

>>12041039
lmao, people who don't code in C don't code in C because they're too dumb to code in C

>>12042646
The belt goes so fast that the wheels blow apart and the plane pretty much explodes

>>12047211
/sci/ is really filled with brainlets. You count the same outcome twice, which would be obvious if you weren't so dumb lmao.

>>12053034
>boy or girl odds
>assumes that the sex ratio at birth is 1.000000
lmao

>>12056422
>if coin1 == 0:
>coin2 = 1
how do retards even come up with such ideas?

>>12061071
>>12061108
it says randomly but it doesn't say equally likely

>>12040799
ntma

>>12040815
Neither. It would remain still in the middle of the blue portal.

>>12061968
Depends on the timing really. Are we talking about flipping one before the other or both at the same time? The wording is ambiguous regardless.

>>12040892
1. The trolley can break the glass box but it will only push the opaque box or just crash into it if its fixed on the ground.

>>12062025
this. using a fleshlight doesn't make your dick fly off from the thrust.

50%. Can we just give these shitly worded variable change threads a rest once and for all?

>>12061571
Your intuition is off.

>>12061825
if "at least one coin is heads" refers to a specific coin then the third outcome is also excluded.

>>12061846
Doesn't matter how fast the belt goes, the treadmill is designed to keep the plane from moving at any speed.

>>12061917
Correct, but using a flat prior gives the same result.

[math]P(both are heads \| atleast one is heads) = \frac{P(atleast one is heads \| both are heads) \cdot P(both are heads)}{P(atleast one is heads)} = \frac{1 \cdot \frac{1}{4}}{\frac{3}{4}} = \frac{1}{3}[/math]

>>12062560
If "at least one coin is heads" refers to a specific coin then P(at least one is heads) = 1/2 instead of 3/4.

>>12040874
The treadmill goes stupid fast and either the wheels explode from overspeed or the plane takes off from headwind induced by the treadmill.

Probably exploding wheels.

>>12053893
>If "at least one is heads" refers to a specific coin
learn english

>>12062936
I already speak it. If I flip a pair of coins, look at one of them and see heads, then I tell you "at least one is heads," what is the probability both are heads?

>>12062948
>I already speak it
Learn english

>>12062688
Different cases where atleast one is heads are: HH, HT and TH.

Total number of different cases is four, therefore chance that atleast one is heads is 3/4.

>>12062985
>Different cases where atleast one is heads are: HH, HT and TH.
If "at least one coin is heads" refers to a specific coin then the different cases are HH and HT.

Total number of different cases is four, therefore chance that atleast one is heads is 2/4.

>>12062949
Not an argument.

>>12062033
Why would that matter?

>>12062463
Yeah my intuition says 50% so you're right.

The wording isn't even ambiguous. People are just trying to justify their 50% bullshit after the fact by intentionally misinterpreting it. Literally no native English speaker would interpret it the way you faggots are. Like if someone said "I have 5 coins under 5 cups, at least one of the coins is a penny" do you really think people would interpret that sentence to mean "the first cup has a penny under it"? Arguing in bad faith.

>>12063883
Introductory probability questions are iq gated. It’s a mixture of bad actors and actual idiots.

>>12063885
It's like when someone messes up the order of operations and instead of saying their wrong they go on a rant about how stupid PEMDAS is.

>>12063889
And there is a word for that, a powerful one often abused and misapplied but which still captures the full pathetic glory of this behavior...

>>12040827
You will not post the following outside of /b/:

-Racism.

>>12040799
50% (assuming fair coins).

The question uses a fake scenario where 1 coin is guaranteed to be heads.

You nerds try to twist that into a real event.

It's a fixed event or a fake magic scenario.

One coin is always heads. Order, etc... has no bearing.

all you are dealing with is the 'other' coin.

interesting thread though, considering you guys mostly abstained from /pol cult stuff.

>>12063866
It's ambiguous.

>>12063883
>>12063885
>>12063889
>>12063900
https://en.wikipedia.org/wiki/Boy_or_Girl_paradox

>>12063953
In a real world event if you flipped two coins you would already know the answer, so it would either be 100% or 0%. Never would it be 50% though. Stop trying to twist that into a real event.

>>12063976
wow very cool

>>12063883
>Like if someone said "I have 5 coins under 5 cups, at least one of the coins is a penny" do you really think people would interpret that sentence to mean "the first cup has a penny under it"?
No, but plenty of people interpret it as a specific coin. If I only look at one coin but don't tell you which coin then I can say "at least one is heads." If I look at all the coins and see one or more heads then I can say "at least one is heads." Both lead to the same sentence so there is no way to say that that sentence can only be interpreted one way. It's ambiguous, get over it.

>>12063953
>The question uses a fake scenario where 1 coin is guaranteed to be heads.
Wrong. Try again.

>>12063990
the wording precludes the interpretation.

>>12063982
?

>>12063997
How? The same wording can result from either situation. You are just mad that your first reaction to the question was not the only possible one, you don't even have a reason why.

>>12040815
How far the cube flies depends on the speed of the approaching orange portal.

>>12063990
The image doesn't mention looking at a single coin. It only states at least one is heads. That is the information you are given. Given that information, you are to deduce the probability. If they said "one coin is heads and the other coin is tails" you could know with that information with certainty that there is a 0% chance, however the reason probability exists in the first place is because of lack of information. It's an estimate on the likelihood of something occurring without knowing with certainty. This is a probability question and you are given limited information. The information just says "at least one is heads", there is no reason to add extra nonsense to it like "I saw one coin and it was heads". There is no ambiguity.

>>12064005
No I just have a high verbal iq and can tell the cases apart.

>>12062560
>the chad Bayesian statistician

Someone rolls two dice and tells you that at least one of the dice is a 5. What is the probability that both of the dice add up to 6?

>>12040892

>>>/b/835094945

/b/ actually smarter than /sci/ lmao

>>12064012
"At least one is heads" would hold true if you saw one coin (which was heads) but not the other, which changes the probability of both coins being heads to 50%. If you see neither coin, leaving the potential that either coin could be heads or tails (but at least one must be heads), then the odds of both being heads becomes 1/3. The language is ambiguous.

>>12064052
The image describes the second scenario. The first only exists in your imagination.

>>12064012
>The image doesn't mention looking at a single coin.
The image doesn't mention looking at both coins either.

>That is the information you are given.
In order to be informative, that sentence has to be interpreted. You interpret it one way and others interpret it a different way. It's not about adding information to the problem (interpreting it as referring to a specific coin is actually less informative than your interpretation). It's ambiguous.

lmao all these 50%ers trying to justify their wrong answers LOL actual cringe

>>12064015
If you can't explain then you don't understand it.

>>12064019
If he's referring to a specific die then it's 1/6. If not, it's 2/11.

>>12064061
LMAO at all the idiots beating their chest that their interpretation of an ambiguous problem is THE BEST.

>>12064055
>The image describes the second scenario.
No, it doesn't. "At least one is heads" leaves multiple possibilities open. Without telling you *how* you know at least one is heads (did you look, did someone tell you, are you psychic?), then 1/2 or 1/3 could be correct.

>>12064055
>same result with no way to distinguish between them, but I know it's the second

>>12064075
How do you know one is heads? Because the image tells you one is heads. That's how you found out. Are you stupid?

https://en.wikipedia.org/wiki/Boy_or_Girl_paradox
https://en.wikipedia.org/wiki/Boy_or_Girl_paradox
https://en.wikipedia.org/wiki/Boy_or_Girl_paradox
https://en.wikipedia.org/wiki/Boy_or_Girl_paradox
https://en.wikipedia.org/wiki/Boy_or_Girl_paradox
https://en.wikipedia.org/wiki/Boy_or_Girl_paradox
https://en.wikipedia.org/wiki/Boy_or_Girl_paradox

>>12064085
It also told me I flipped two coins, but I'm sitting here and I didn't flip two coins. Are you stupid? It's clearly creating a hypothetical situation, and in that hypothetical situation where I flipped two coins, I had some way of discovering one of the coins is heads. It would take very little to make the image unambiguous (which would stop the arguing, which is why it's intentionally made ambiguous).

>>12064085
a specific coin is heads -> one is heads

the total number of heads in the pair is greater than 0 -> one is heads

Which one is it?

>>12064099
the "at least" makes it unambiguously the second

>>12064190
I give you two containers of food. You peek in one and put them away. Someone asks you what's in the containers. You say "at least one is a hamburger."

>>12064190
At least could refer to either. Do you have any actual reasoning?

>>12064206
Yeah and the person who asks me at that point in time only knows the information that "at least one is a hamburger". That means either container could contain it, as I didn't specify anything further. You are assuming more information that what was given.

>>12064267
Exactly. Now let's assume the person who gave you containers asks you to give them the one with the hot dog. You now know which one has the hamburger, so you can pick the one with the hot dog without needing to look. The point being, "at least one" is perfectly reasonable to use as a non-specific, or specific phrase.

>>12064085
>Because the image tells you one is heads.
It also shows you one coin is heads, and one coin is tails, so the answer to the question is 0%.

>>12064267
Yes, either container could be the one you are referring to. That doesn't affect the interpretation. It's like if you hear a male frog croak behind you and turn around to see two frogs. Since you know a specific frog croaked (but not which one) the chance that both are male is 1/2, not 1/3.

>>12040818
This in reality is the correct answer as there are only two specific outcomes you can expect, whether or not which coin flips heads is irrelevant when one is always guaranteed to be heads the final result can only ever be two heads or heads and tails.

The outcome to the question isn't changed by which coin flips heads or which coin flips tails.

There are only two possible outcomes.

the hh/ht/th is retarded.

>>12047294
>They are two distinct coins regardless of when they are thrown.

Which is not part of the equation but more a pedantic point ht = th the order is irrelevant as the probability of the outcome is the same when at minimum one coin is guaranteed to be heads.

>>12064070
Ad soon as he tells you one of the die is a five then he has already specified that one die is a five, if there are only two die then the odds of the other die being a 1 is 1/6.

>>12056489
rude

>>12064355
No, if a specific coin is guaranteed to be heads and the other is unknown then the probability is 1/2. If neither is guaranteed then it's 1/3.

>>12064379
>Ad soon as he tells you one of the die is a five then he has already specified that one die is a five
No, if both are 5 and he sees both are 5 then which one is "the one die that is five?" Neither. The only way it can refer to a specific die in all cases is when he only sees one die.