/sci/ - Science & Math

sleeping*

This is the video: https://www.youtube.com/watch?v=XeSu9fBJ2sI
What do you think?

Picrel is also a similar question

>>15196068
>Are people who answer that the probability is 50% actual NPC
It's a Veritasium Video. Anyone who watched is an NPC regardless of their answer.

>>15196076
>It's a Veritasium Video. Anyone who watched is an NPC regardless of their answer.
He didn't create the problem, he just brought attention to it. So now that a lot of people have been exposed to it, it's relevant.

>>15196071
Can you paste the video transcript or something? My LAN battle station has firewall rules I crafted in 2003 to allow only traffic to 4chan. Anything important tends to trickle in eventually, and when I want the process expedited, I just put the kids to work.

>>15196081
Jesus

>>15196071
Is the answer 2/3 since this is the probability of the balls in the chosen box being the same color?

>>15196068
sneeding beauty
haha i just thought of that

>>15196081
lul

>>15196076
>anon chooses to virtue signal rather than answering the question

>>15196081
i'm permanently banned from all google products due a disagreement we had over some over computer networking protocols and how they're meant to function, so i can't look at any youtube links.

>>15196148
It's 2/3 yes, and an overwhelming amount of people say it's 50%

>>15196190
The question is this:


Sleeping Beauty volunteers to undergo the following experiment and is told all of the following details: On Sunday she will be put to sleep. Once or twice, during the experiment, Sleeping Beauty will be awakened, interviewed, and put back to sleep with an amnesia-inducing drug that makes her forget that awakening. A fair coin will be tossed to determine which experimental procedure to undertake:

If the coin comes up heads, Sleeping Beauty will be awakened and interviewed on Monday only.
If the coin comes up tails, she will be awakened and interviewed on Monday and Tuesday.

In either case, she will be awakened on Wednesday without interview and the experiment ends.

Any time Sleeping Beauty is awakened and interviewed she will not be able to tell which day it is or whether she has been awakened before. During the interview Sleeping Beauty is asked: "What is your credence now for the proposition that the coin landed heads?"

>>15196068
A fair coin is a fair coin. You can wake up a million times and that will never change.
>perspective
There's no perspective here. The question sleeping beauty is asked is "what are the chances the coin was heads" not "what are the chances this is the second time you woke up" and the answer to that is always 50% regardless of the circumstances of the experiment.

This shit legitimately feels like busywork mathematicians came up with so they look like their actually accomplishing something with their lives.

>>15196068
What's the probability that the coin "came up heads"? 1/2. What's the probability that, if you leave the coin alone after flipping it, it will be heads when she wakes up? 1/3. There. Solved this supposed philosophical conundrum.

The conditional probability that she wakes up on tuesday given that she woke up on monday with tails is 100%, whereas the conditional probability that she wakes up on tuesday given that she woke up on monday with heads is 0%.
Therefore waking up on Tuesday is completely dependent on the coin flaling on tails and does not affect the probabilities at play.
Therefore 1/2, /sci/ NPCs BTFOd

The real NPCs are the ones who can't see it both ways and are willing to argue about it.

It's simple bayes.The two questions "Depending on the action you'r woken up what is the probability the coin came up heads, and what is the probability the coin came up heads." are not the same. One gives 1/3 as answer the other on 1/2. The only ambiguity comes from the language used.

>>15196068
The video was crap tbqh. Very forced and I've never heard of this sleeping beauty coin thing.

>>15196068
No, they think she would answer 50% because she is a woman.

A hill troll goes to awaken her if its tuesday and heads. He asks her the same question nevertheless. The scientist tards never notice it tho, as hill trolls know enough magic to trick them and their security cameras.

Thus the cases are symmetrical 1/2 1/2.

A:1/2

I think this is a weird question, because to get it right you have to acknowledge the fallibility of your own conscious experience.

I think that more people would get this right from the frame of reference of an observer to the experiment, rather than the sleeping beauty themselves.

>>15196586
>I think this is a weird question, because to get it right you have to acknowledge the fallibility of your own conscious experience.
>I think that more people would get this right from the frame of reference of an observer to the experiment, rather than the sleeping beauty themselves
Consciousness-denier-tier post.

50% is correct because Tuesday isn't an independent event and therefore insignificant

>>15196068
Heads per flips: 1/2
Heads per wakeups: 1/3
The answer varies depending on whether you mean the probability of the experimenter observing heads after a flip or the sleeping beauty observing heads after waking up. You may delete this thread now.

>>15196168
truly hilarious anon

>>15196071
This is not a similar problem as unlike the sleeping beauty problem, you have knowledge of the first event that occurred.

>>15196389
So if I toss a fair coin and only ask you what your credence is that the coin landed on heads when it lands on heads, your answer is 50% even though you know that my asking you this makes it a certainty the coin landed on heads? LOL. You are unable to process information correctly.

>The question sleeping beauty is asked is "what are the chances the coin was heads" not "what are the chances this is the second time you woke up"
That would be 1/3, moron.

>>15196405
>What's the probability that the coin "came up heads"? 1/2.
From whose perspective?

>>15196415
>Therefore waking up on Tuesday is completely dependent on the coin flaling on tails and does not affect the probabilities at play.
Wrong. Since you wake up twice after tails, waking up makes it twice as likely tails was flipped.

>>15196651
Doesn't follow. It's twice as likely you were woken up after tails as it is you were woken up after heads.

>>15196747
The credence changes in your situation because experienced reality depends on the flip. In the given problem your experience is fixed so there is no new information gained. Your credence stays at 50%.

>muh balls
Not the same. You receive new information that reduces the possible states of the world to 3 of the original 6. The only reason you can change credence is because experienced reality differs.

>>15196747
>So if I toss a fair coin and only ask you what your credence is that the coin landed on heads when it lands on heads, your answer is 50% even though you know that my asking you this makes it a certainty the coin landed on heads?
Yes. If I play the lottery I have a 1 in 13,983,816 chance of winning and me winning doesn't mean I had a 100% chance of winning.

>>15196757
>>15196764
But you wake up twice because it flipped tails, it didn't flip tails because you woke up twice. Waking up on a tuesday does not influence the original act of flipping the coin so the probability stays at the normal 1/2.

>>15196753
"Came up heads" only makes realy sense from the perspective of the one who flips the coin, especially considering that the sleeping beauty gets to observe the result of a tails flip twice every time.

>>15196765
>The credence changes in your situation because experienced reality depends on the flip.
What does that have to do with probability? Probability changes when you are given information that changes what's possible. In my problem, the possibility of landing on tails is eliminated. The same thing occurs in the sleeping beauty problem. The possibility of it being Tuesday and the coin landing on heads is eliminated. Not that hard to understand.

Same problem as the original except they wake you up a quadrillion times. Also, one time when you wake up, they offer you 52 dollars if you can guess which of the quadrillion + 1 situations you're in. IE both the coinflip result and how many times you've previously woken up. You choose "tails" and one of the quadrillion wake-ups at random because all situations are equally likely.

>>15196772
>If I play the lottery I have a 1 in 13,983,816 chance of winning and me winning doesn't mean I had a 100% chance of winning.
After you won, the probability you won is 100%. The question is not asking for the probability before being woken up, it's asking for sleeping beauty's credence after being woken up. You're confusing prior probability with posterior probability.

>>15196791
Before you fell asleep the credence was 50%. Then you had exactly the same conscious experience until they ask you what your credence is. When did it change, exactlly?

>>15196780
>But you wake up twice because it flipped tails, it didn't flip tails because you woke up twice.
No one said otherwise.

>Waking up on a tuesday does not influence the original act of flipping the coin
Waking up on Tuesday means the coin landed on tails. I'm not sure why you're bringing causality into this when we're talking about probability.

>>15196783
>"Came up heads" only makes realy sense from the perspective of the one who flips the coin
No.

Sleeping beauty gains absolutely no new information when she is woken up. She knows exactly the same as she did before being woken up.

Therefore there is no logical reason for her to assume anything other than 50/50 odds

>>15196068
Suppose that they first tell her what day it is before asking her about the coin toss, what is the probability that it was heads given that it's Monday?

>>15196796
>Then you had exactly the same conscious experience until they ask you what your credence is.
Again, having the same experience is irrelevant since you already know it's impossible for it to be Tuesday and the coin having landed on heads. Why do you think you can ignore that information based on "having the same experience?" It's a non sequitur.

>When did it change, exactlly?
When you were woken up. Duh.

>>15196802
She can check the coin but that obviously doesn't count as a flip and doesn't correspond to a flip in a one-to-one manner. Asking her which side the coin came up on is asking her to assess it from the perspective of whoever flipped the coin, so it's 1/2. 1/3 is her odds of seeing heads if she goes to check it upon waking up.

>>15196071
Shit, I'm not immune to probability tricks.
Only after a 1-2 minutes of thinking I realised it's 2/3.

>>15196805
>Sleeping beauty gains absolutely no new information when she is woken up.
Wrong, she gains the information that it is not the Tuesday after the coin landed on heads. There is no logical reason to ignore this infornation.

>>15196821
But did you get to that answer just by luck? What if the first box had 10 gold balls, what would the probability be then?

>>15196806
1/2 of course. What's the probability that it was heads given it's Tuesday?

>>15196830
>1/2 of course.
I rest my case.

>>15196819
>Asking her which side the coin came up on is asking her to assess it from the perspective of whoever flipped the coin
No.

>>15196834
You didn't make a case, you just asked a question that doesn't even describe the problem. What's the probability that it was heads given it's Tuesday?

>>15196835
Sorry about your profound mental illness. Hiding all further posts from you. Kindergarten probability questions are great for weeding out nonhuman elements. :^)

>>15196837

>>15196814
respond to >>15196790

>>15196843
Trivial. Answer would just be 1/quadrillion.

>>15196840
Not an argument. Thanks for conceding.

>>15196838
See >>15196853

>>15196828
>What if the first box had 10 gold balls, what would the probability be then?

Still 2/3, it's about boxes, not the balls.

>>15196853
You're actually severely retarded. You must hear that a lot too.

>>15196849
1/(quadrillion+1)

>>15196861
You are correct.

>>15196849
So you believe the following:

You are given a chance to plan your strategy beforehand. You pick heads for a 50% chance of getting the money.

However, if you think of the same strategy after you wake up, and take the exact same actions as previously, you only have a 1 out of quadrillion + 1 chance to get the money.

That is mind bogglingly retarded.

>>15196860
See >>15196856

Thanks for conceding.

>>15196866
>You are given a chance to plan your strategy beforehand. You pick heads for a 50% chance of getting the money.
This is so vague it's meaningless. Strategy for what? What am I picking heads for? If you flip a coin then it doesn't matter what I bet. If you flip a coin and then give me information that tells me it's more likely you flipped tails, I will bet tails. You ignore that sleeping beauty is given the information that it's not the Tuesday after the coin landed on heads. Therefore it's more likely the coin landed on tails. Sleeping beauty would win the bet 2/3 of the time playing this game and guessing tails. It can't be exclusive any simpler than that.

>>15196882
You choose what to say when you wake up. Another way to phrase your belief:

If you write down "the coin was heads" you have a 50% to get money. If you write down "future self: say heads" you have a quadrillionth chance to get money.

The Sailor's Child problem, introduced by Radford M. Neal, is somewhat similar. It involves a sailor who regularly sails between ports. In one port there is a woman who wants to have a child with him, across the sea there is another woman who also wants to have a child with him. The sailor cannot decide if he will have one or two children, so he will leave it up to a coin toss. If Heads, he will have one child, and if Tails, two children. But if the coin lands on Heads, which woman would have his child? He would decide this by looking at The Sailor's Guide to Ports and the woman in the port that appears first would be the woman that he has a child with. You are his child. You do not have a copy of The Sailor's Guide to Ports. What is the probability that you are his only child, thus the coin landed on Heads (assume a fair coin)?

>>15196888
>You choose what to say when you wake up.
Yes, and choosing to say, "I bet money it's tails" whenever you wake up means you win money 2/3 of the time you are woken up. Please explain how this is possible if the probability is "actually" 1/2.

>If you write down "the coin was heads" you have a 50% to get money.
Again more vague nonsense. You would only win 1/3 of the time you are woken up, on the Monday after heads. On the Monday and Tuesday after tails, you'll lose.

>>15196902
It's not vague at all. You're retreating into being a pedantic fuckwit trying to imagine possible scenarios where what you're saying isn't retarded.

You can pay one dollar to play the following game: You wake up, say "heads" and if the coin was heads you get a trillion dollars.

Alternatively, they offer the following game for one dollar: You wake up and guess which of the quadrillion possibilities you're in. If correct you get a trillion dollars. The way to guess the first scenario is saying "heads". To guess any other possibility you have to get kicked in the balls so you'll inevitably say "heads".

You think the first game is worth playing but not the second. You think the expected result of this situation depends on which game you are playing, even if all the actions taken while playing the game are exactly identical. This is because you are stupid.

>>15196068
Its obviously 50/50 you dumbass. Every time she awakes, it doesn't matter what day it is, it only matters if the coin went heads or tails. Nevermind i remembered the other rule but im still posting it for full transparency

>>15196076
>Mindless hipster calling others an NPC

>>15196540
What's interesting is that conditional probability is always (as far as I have seen) supposed to restrict the probability space to a subset. However, in this question people are using it to expand the probability space. Specifically, people are using "given that you woke up" to expand the set of outcomes from 2 (H or T) to 3 (H monday, T tuesday, T wednesday). That approach doesn't seem valid to me. Are there any probability questions where that is known to give the correct solution?

>>15196931
>It's not vague at all
It is, since you're not specifying the context to determine what information is available to calculate the probability.

>You can pay one dollar to play the following game: You wake up, say "heads" and if the coin was heads you get a trillion dollars.
This would be a bad bet since on average you would lose (quadrillion-trillion)/(quadrillion+1) ~ $1 each time you played.

>Alternatively, they offer the following game for one dollar: You wake up and guess which of the quadrillion possibilities you're in. If correct you get a trillion dollars.
Same thing.

>You think the first game is worth playing but not the second.
No. You can't even formulate the problem correctly, let alone reach the correct answer. Moron.

>>15196981
You believe that playing the game "pay 1 dollar to bet on heads" has a different expected outcome than "pay 1 dollar to bet on heads in the future". I wish I was gambling with you.

My answer is correct. The really laughable thing is that you're pretending to know yours is. >>15196902
You haven't run the experiment. You have no mathematical proof. You just decided you know what would happen then tried to use that as an argument. You're just some dipshit who had the same vague connotative feeling when you saw two problems and decided that's what math is.

>>15196978
>However, in this question people are using it to expand the probability space.
You seem to be under several misconceptions. The sample space has to describe all possible outcomes. If the problem gives you a conditional that is not adequately described by your sample space, then you can't calculate the answer. The sample space is constructed to answer the problem, not to naively describe the problem without any conditionals.

>>15196068
Either one thing or another thing happens, this is always 50/50
Even if you flip heads 500 times in a row the probability your next flip will also be heads is still 50/50
statistics =/= probability

>>15196994
>You believe that playing the game "pay 1 dollar to bet on heads" has a different expected outcome than "pay 1 dollar to bet on heads in the future".
Again, this is nonsense since you aren't specifying what information is available in either bet. Why do you continually make these vague statements? Without any context, I don't see any difference between the two bets, so your claim is false.

>My answer is correct
What answer? You just ask vague questions and make incorrect claims about what I believe. LOL

>You haven't run the experiment.
No need, this a math problem.

>You have no mathematical proof.
Here's the proof:

P(heads|awake) = P(heads) P(awake|heads) / ( P(heads) P(awake|heads) + P(tails) P(awake|tails) ) = (1/2)(1/2)/((1/2)(1/2)+(1/2)(1)) = 1/3

Where's your proof?

>>15196071
it's 1/3 chance. there's only one box that lets you grab another gold ball. people saying 2/3 are small brained

>>15197020
Profoundly wrong. For one, the probability of the box with two silver balls is 0 instead of 1/3, since the first ball you picked up was golden, and that obviously is impossible if the box you chose had no golden balls.

>>15197034
okay then it's 50% because only 1 out of the 2 possible boxes will have another gold ball

1/3 - people who were successfully zogwashed in school
1/2 - people with free will
it's that simple

>>15197014
One bet is "it will be heads when you flip it in the future". Another bet is "after I wake up it will have been heads". Another is "I'll bet in the future after waking up and by the way I'm going to bet heads".

You think that which bet you take will magically control the state of the world even if every physical action after betting is exactly identical.

>P(awake|heads) = 1/2
P(awake) = 1. You are awake. You're doing some incoherent handwaving to justify setting the variable P(awake|heads) to something that makes you right. But you have no actual justification for your assignment.

>>15197041
It's twice as likely you chose from the all gold box side the other box only has a half chance of giving you a gold ball

>>15197014
>>15197064
Going to add that in P(heads|awake) you are clearly treating "awake" as the state of being awake at that time. Ie 1. You're not calculating "the probability of heads given the probability that the subject is awake at one of these two times which is being chosen randomly".

>>15197064
>One bet is "it will be heads when you flip it in the future". Another bet is "after I wake up it will have been heads".
Yeah, these are completely different bets since after waking up you know it isn't the Tuesday after heads. Information can change the probability. Sorry you don't understand this basic fact.

>You think that which bet you take will magically control the state of the world even if every physical action after betting is exactly identical.
No, both bets are fine and completely different. You can take both. Neither have any effect on the world. You're just spouting nonsense that has nothing to do with probability or math. Please stop.

>P(awake) = 1
Wrong. You cannot be awake on the Tuesday after heads. P(awake) = 0.75. Please learn basic probability theory before posting again. Thanks.

>>15197096
>Going to add that in P(heads|awake) you are clearly treating "awake" as the state of being awake at that time.
"Awake" means awake on Monday or Tuesday.

>Ie 1.
No, read the problem. You cannot be awake on Tuesday after heads.

>You're not calculating "the probability of heads given the probability that the subject is awake at one of these two times which is being chosen randomly".
That's exactly what I calculated. LOL

>>15197014
>P(heads|awake) = P(heads) P(awake|heads) / ( P(heads) P(awake|heads) + P(tails) P(awake|tails) ) = (1/2)(1/2)/((1/2)(1/2)+(1/2)(1)) = 1/3
Now prove this applies to reality and isn't just a random scribble of numbers

>>15196071
You pick a box at random.
It has a gold ball. That means you necessarily did NOT PICK the box with no gold in it.
So that means you picked box 1 or 2 in this example.
You are taking from the SAME BOX.
So you know it's 100% from box 1 that you would get another gold one.
And you know it's 0% from box 2 because you already took the gold ball.
So 50% is correct.

Now...if they stated the question different then you would get another answer.
The question of "what are the odds?" is posed AFTER you already selected a gold ball.

>>15197108
>Now prove this applies to reality
Logic about real things like coins and sleeping always applies to reality. Explain what you think is unreal about this.

If you can't understand basic math, then why don't we don't we play a betting game. We will flip a coin. We will then wait one minute and check it. If it's heads you will get $3. If it's tails I get $2 and we will wait another minute and check the coin again. If it's still tails I get another $2. You would play this game right?

>>15196221
See here and explain how this is wrong.
>>15197117
The question isn't "what are the odds that IF you select a gold ball the first time you then select a gold ball the next time.
It already dictated that you chose a box with gold in it.

Brainlets make it too complicated by trying to be smart.
The gold ball WAS ALREADY SELECTED.
Meaning you necessarily have either a 100% chance or a 0% chance respectively as you could not have taken from the goldless box.

>>15197117
>So 50% is correct.
Doesn't follow from anything you said. You incorrectly assume it's equally likely for you to have found the gold ball in box 1 or box 2 when it's twice as likely you found it in box 1 since it's all good while box 2 is only half gold. So it's twice as likely you are in box 1 and the answer is 2/3.

>>15197125
You are leaving out the part where you ALREADY selected a gold ball.
That means there is either a box left with ONLY a gold ball, or a box left with ONLY a silver ball.

You are starting from the beginning, but that's not where the question comes in.
The question comes AFTER you already have a gold ball in your hand.

>>15197124
>The question isn't "what are the odds that IF you select a gold ball the first time you then select a gold ball the next time.
Assuming you mean select the gold ball when you choose from the same box, that is the question. It gives you that information and then asks the probability. Why would you ignore information when answering the question?

>Meaning you necessarily have either a 100% chance or a 0% chance respectively as you could not have taken from the goldless box.
Yes, and the first is twice as likely as the second since you only had a half chance of choosing the gold ball from the second box.

>>15197132
Again, the question comes AFTER you already selected a gold ball.
So...AFTER you have a gold ball in your hand you have new data.

PRIOR ODDS NO LONGER APPLY.

>>15197128
>You are leaving out the part where you ALREADY selected a gold ball.
No, I'm not. I sourdough said you selected the gold ball. It's twice as likely you did so from the first box rather than the second. Please respond to what I said instead of making things up.

>That means there is either a box left with ONLY a gold ball, or a box left with ONLY a silver ball.
Yes, and the first is twice as likely as the second.

>You are starting from the beginning
No.

>>15197134
>Again, the question comes AFTER you already selected a gold ball.
Yes, and you're ignoring that is twice as likely that ball came from the all gold box. You correctly implemented the information that you didn't choose from the all silver box but then failed to use the information that you didn't choose the silver ball from the half and half box, making it half as likely you chose the gold ball from that box.

>>15197135
I know what you are saying.
But that is starting from previous odds.
After holding a gold ball.
There are only two boxes, you selected it from one. Necessarily leaving one at 0% and the other at 100%.
How can you argue with that WITHOUT using previous odds?

>>15197142
Again, the ball was selected already.
The odds of it being selected are irrelevant unless you are reasoning from the start, BEFORE selecting a box at all.

>>15196995
That's true, but you are mostly missing my point (which, to be fair, I expressed poorly). These posts get into the key issue:
>>15197014
>>15197064
which is what is P(awake | H)/P(awake | T) and what is P(awake)? Sleeping beauty will be awakened regardless of the outcome with probability 1. So what do those quantities actually mean?

>>15197143
>But that is starting from previous odds.
No, the previous odds were that you were equally likely to choose from either box. The new odds are that you were twice as likely to choose from the all gold box. You're the one using old odds!

>There are only two boxes, you selected it from one. Necessarily leaving one at 0% and the other at 100%.
>How can you argue with that WITHOUT using previous odds?
I didn't argue against either of those statements. You're making things up. I simply clarified that they are not equally likely possibilities, which you incorrectly assumed.

>>15197158
>you were twice
You are using past tense. Meaning you agree with me.
From the point of having a gold ball in your hand...it's 50/50.
Only from before selecting the ball at all can you make your argument.
Once the ball has been selected, it's likelihood of having been selected is irrelevant.

>>15197147
>Again, the ball was selected already.
Again, I didn't say it wasn't. LOL. Argue against what I actually said.

>The odds of it being selected are irrelevant
How can the odds the question is asking for be irrelevant??? Nonsense. The question is asking for the odds you chose from the all gold box. It's twice as likely you did so given you chose a gold ball since it's all gold and the other box you could have chosen from odds only half gold. If you don't get it then there's really no helping you.

>>15197103
>Yeah, these are completely different bets since after waking up you know it isn't the Tuesday after heads.
It doesn't matter what you know. How is knowing something later on supposed to retroactively change what it was? You're not even making a decision at that time. You're a chuuni larping as a time traveling esper. I'm starting to think you've realized you're retarded so now you're acting like you were just pretending all along.

>>15197107
>>You're not calculating "the probability of heads given the probability that the subject is awake at one of these two times which is being chosen randomly".
>That's exactly what I calculated. LOL
That's not the same thing as "the probability of heads given being awake", you moron. You said you were calculating some kind of objective measurement of the state of reality. What you calculated is not.

>>15197149
Awake seems to mean "being awake right now" when you're trying to use it to calculate the probable state of the world based on you being awake right now.

Maybe it means "the probability that the subject is awake at one of these two times which is being chosen randomly (prior to knowing whether heads will be flipped and therefore not even being dependent on the coin flip)" if you're insane.

>>15197169
>The question is asking for the odds you chose from the all gold box
Read the question. NO IT IS NOT.

>>15197149
>Sleeping beauty will be awakened regardless of the outcome with probability 1.
Sleeping beauty will not be awakened on the Tuesday after heads. That is what all halters miss. That is the information given by awaking that you continuously ignore.

>>15196068
So the question is how Sleeping Beauty would answer? How the hell should I know, she's an imaginary character.

>>15197165
>You are using past tense. Meaning you agree with me
Doesn't follow. I'm describing the chance of an event that happened, which is the same as the chance of an event in the future since one directly follows from the other.

>From the point of having a gold ball in your hand...it's 50/50.
No. When you have the gold ball in your hand, it's twice as likely you're in the all gold box. Why do you think they're equally likely? You will inevitably refer to their past odds.

>Only from before selecting the ball at all can you make your argument.
That's what I did.

>it's likelihood of having been selected is irrelevant.
It's likelihood of being selected from the all gold box is precisely what the answer is. You're not making any sense.

Prob(H|she's awake) is independent of her being awake, hence 1/2. This problem is NOT the same as the monty hall problem.

>>15197170
>It doesn't matter what you know.
That's the dumbest thing you could possibly say. Probability is a measure of what you know.

>How is knowing something later on supposed to retroactively change what it was?
It doesn't retroactively change anything. The probability of a coin landing on heads is completely different from the probability a coin landed on heads given you are awake.

>You're a chuuni larping as a time traveling esper.
Can you translate this from schizo to English? You're not making any arguments, so thanks for conceding.

>>15196068
>Are people who answer that the probability is 50% actual NPCs?
No, but you are.

>>15197170
>That's not the same thing as "the probability of heads given being awake"
Yes it is.

>You said you were calculating some kind of objective measurement of the state of reality.
You're lying. I said no such thing. Probability is completely dependent on the information available to the person calculating it.

>>15196821
You are retarded.

>>15197170
>Awake seems to mean "being awake right now"
As opposed to?

>Maybe it means "the probability that the subject is awake at one of these two times which is being chosen randomly (prior to knowing whether heads will be flipped and therefore not even being dependent on the coin flip)"
Those are the same thing since you don't know what day "now" is.

>>15197173
>Read the question. NO IT IS NOT.
It is. Explain what you think the difference is.

>>15197122
>>15197122
>Logic about real things like coins and sleeping always applies to reality.
You're not using logic, though, coinflips are completely random

>>15196747
>That would be 1/3, moron.
You're the only imbecile here, along with every other cretin who answered 1/3, which includes the Veritasium imbecile. I would like to remind you that most people are stupid, and the majority opinion is 1/3. Congrats brainlets, you fail at math.

Chat GPT btfo'd NPCs such as OP.

>>15196757
>, waking up makes it twice as likely tails was flipped.
LMAO, imagine believing future events influence past results. You are literally braindead.

>>15197215
>Prob(H|she's awake) is independent of her being awake
LOL, you just wrote the probability dependent on her being awake is independent of her being awake. What you meant to write is P(H) is independent of her being awake but that's still wrong since being awake tells her it's not the Tuesday after heads, which means it's less likely to be heads.

>>15197014
>P(heads|awake) = P(heads) P(awake|heads) / ( P(heads) P(awake|heads) + P(tails) P(awake|tails) ) = (1/2)(1/2)/((1/2)(1/2)+(1/2)(1)) = 1/3
This is - 1 = 1 tier logic. You're a moron. You don't understand a single thing you're talking about.

>>15197122
>Explain what you think is unreal about this.
Future actions do not modify past events.
QED.

>>15197274
I notice my question wasn't completely accurate to the actual problem, since I didn't specify a coin was tossed again. But even copying the question from one of the articles, Chat GPT still correctly answers 1/2.

>>15196068
Correct answer: 1/2.

>>15196071
Correct answer: 2/3.

>>15196764
Yeah but tails days gets only 1/2weight

1/2+1/2(1/2+1/2)=1

>>15197308
If 85% of articles says its 1/2, in what propability a dumb machine that mixes their results answers the same. Hmm

>>15197271
>You're not using logic
I am.

>coinflips are completely random
I didn't say they weren't. In fact P(H) = 1/2 is right there in my proof. It's clear you have no response. Thanks for conceding.

>>15197308
That reasoning makes no sense, as is to be excepted obviously

>>15197272
Not an argument, thanks for admitting the answer is 1/3.

>>15197276
>LMAO, imagine believing future events influence past results.
The conditional probability of an event is not a past result, moron. It's the likelihood an event occurred with your present knowledge. If you look at a coin and see its heads, then the probability it landed on heads is 1, not 1/2. Retard.

>>15197295
>This is - 1 = 1 tier logic.
How so?

>You don't understand a single thing you're talking about.
Nice projection.

>>15197302
>Future actions do not modify past events.
Nothing I said implied they do. The probability of an event is not a past event and is affected by new information. So please explain what is unreal about what I said.

>>15197308
>whether she is being awakened for the first time (in which case the coin came up heads)
This is trivially false. She would be woken up for the first time on Monday whether the coin was heads or tails.

>>15197317
>Correct answer: 1/2.
Proof?

>>15197331
>Yeah but tails days gets only 1/2weight
This is gibberish. What is "tails day?" It's equally likely that you are woken up the Monday after heads, the Monday after tails, or the Tuesday after tails soccer you are woken up both days after tails. There is no half weight because it's not one or the other, both occur.

This is the dumbest shit ever. If you flip a coin and ask somebody the odds 10 times in a row the odds of a coin toss if it's tails and 20 times if it is even it doesn't matter how many times you ask them it's still 50%.

>>15197103
>>One bet is "it will be heads when you flip it in the future". Another bet is "after I wake up it will have been heads".
>Yeah, these are completely different bets since after waking up you know it isn't the Tuesday after heads.
What happens over many iterations when one person makes one bet and a second makes the other bet on the same coinflips?

"thirder" is one of the dumbest category someone would want to self-insert into. Holy fuck.

>>15197495
>categories
Fixed.

>>15196861
There is 0% chance that you pick the box with 2 silver balls because the problem specifically tells you that you picked a box with a gold ball in it.
Consider this problem instead:
There are two boxes with two silvers balls and one box with two gold balls.You pick a box at random and you reach into it to find a gold ball, what are the odds the other ball in that same box is gold as well?

>>15197428
>If you flip a coin and ask somebody the odds 10 times in a row the odds of a coin toss if it's tails and 20 times if it is even it doesn't matter how many times you ask them it's still 50%.
Wrong. The more times you are asked, the more likely it is the coin landed on heads. If you've been asked 11 times then it's a certainty the coin landed on heads.

I love it when retards prove their own retardation.

>>15196068
It's 50%. The logic behind 1/3rd is that there's 3 scenarios she could be in, 2 of them are from the tails result, and therefore only 1/3rd is from the head result. But the 3 scenarios are actually not equal. The reality is there's a 50% chance she's in the heads scenario, 25% chance she's in tails Monday, and 25% tails Tuesday.

>>15197490
The person who makes the first bet will win 50% of the time and the person who makes the second bet will only win 1/3 of the time since they are awakened twice when the coin lands on tails. It's not that hard to understand.

>>15197526
2/3, since it's half as likely you chose the good ball from the box that is only half gold. The third box is irrelevant.

>>15197549
They're betting on the same coinflips. The same coinflips are determining when they're waking up.

>>15197538
>The reality is there's a 50% chance she's in the heads scenario, 25% chance she's in tails Monday, and 25% tails Tuesday.
No, she is awakened on both days after tails. You're calculating it as if she is awakened on a random day after tails.

P(H and M|awake) = P(H and M) P(awake|H and M) / P(awake) = (1/2)(1/2)(1)/(3/4) = 1/3

P(T and M|awake) = P(T and M) P(awake|T and M) / P(awake) = (1/2)(1/2)(1)/(3/4) = 1/3

P(T and Tu|awake) = P(T and Tu) P(awake|Tu and M) / P(awake) = (1/2)(1/2)(1)/(3/4) = 1/3

>>15197268
It literally does not ask what you said it asked.
Read the question.
Where is your phraseology?

>>15197566
>They're betting on the same coinflips.
Yes. So what? If you see the coin landed on heads you are betting on the same coin flip as everyone else, but you will always bet heads and always win. Again, you're confusing the event with the probability of the event. The probability of the event is dependent on what information you have.

>>15197556
Either trolling or retard.

>>15197606
>It literally does not ask what you said it asked.
It literally does, and you can't tell me the difference, so even you know you're wrong.

>>15197611
Not an argument, thanks for admitting the answer is 2/3.

>>15197556
Nope.
After you have a gold ball in your hand there necessarily only either a box with a gold ball or a box with a silver ball.

Why do brainlets INSIST that prior odds affect future odds?

>>15197556
Read my post again.

>>15197608
They both win the same fraction of times. Is that fraction approximately 1/2 or 1/3?

>>15197620
Read my post again retard.
There is only one box with gold balls the other two have silvers balls only.
Same as the original problem but this time with only one box.
Based on your room temp IQ the answer to this should be 1/3 when it's obviously 100%.

>>15197615
It asks "What is the probability that the NEXT ball you take from the same box will also be gold".
That is not the some, nor does it have the same implications as asking whether you INITIALLY chose the box with two gold balls.
Your assumption that it's the same is your error.

You assumed question starts at the beginning. But the question starts in the middle, after already have a gold ball.

>>15197428
The question is asked from the perspective of sleeping beauty, from her perpsective it's 1/3, from your perspective is 1/2.
Halfers like you get it wrong because they misunderstand the question asked.
She not asked what the probability of a future coin toss is she is asked what she think the probability of the coin toss was before

OP here
So basically after reading through my thread, I've understood that; Yes, these people are actual NPCs, and aren't able to conceptualize perspective. I've gotten my answer
It's the same with three gold balls problem, same with frog riddle, same with two dice question, same with monty hall
Seeing these people explain their thought pattern of how they're going about the questions... really shows....
NPC meme is real...

>>15197640
Hi OP you forgot to answer this question. >>15197626

>>15197640
You are correct that it's 1/3 but in the case of the ball problem it is not the same.

>>15197621
>After you have a gold ball in your hand there necessarily only either a box with a gold ball or a box with a silver ball.
Exactly, and it's twice as likely that gold ball came from the first box.

>Why do brainlets INSIST that prior odds affect future odds?
Why are you insisting is equally likely you chose from either box when those are the prior odds, not the odds after you find a gold ball?

Why do retards always project their mistakes into others?

>>15197642
That question wasn't asked of me, that's someone else
>>15197646
It is the same. If you repeat the experiment IRL, you will get 2/3 chance for 2nd gold ball. There's 3 gold balls you can pick, out of 3, 2 of them return true

>>15197649
What's the answer, though?

>>15197650
If you would repeat the sleeping beauty experiment IRL, you would get an answer of 1/3 heads

>>15197626
>They both win the same fraction of times.
No, the person being woken up and betting on heads only wins 1/3 of the times they are woken up. They lose twice when the coin lands on tails.

Picrel - Life lesson regarding the gold ball problem

>>15197622
I don't care about your problem, the answer is 2/3 regardless of the third box.

>>15197628
>There is only one box with gold balls the other two have silvers balls only.
Not what the problem says. Irrelevant. The answer is 2/3.

>Based on your room temp IQ the answer to this should be 1/3
How so?

>>15197651
>>15197653
You repeat sleeping beauty with two people who wake according to one coin. One gets a dollar every time the coin is heads. The other person gets a dollar every if they guess correctly after waking up, and always chooses heads. Do you believe they eventually have a different number of dollars? If not how many dollars are they expected to both have?

>>15197647
How do you not see that the "twice as likely" only applies AHEAD of taking the ball.
After it's a done deal. You have it in your hand.

>>15197632
>It asks "What is the probability that the NEXT ball you take from the same box will also be gold".
That's the same thing. If you choose from the all gold box your next ball from the same box will be gold. LMAO.

>That is not the some, nor does it have the same implications as asking whether you INITIALLY chose the box with two gold balls.
It literally is the same. The probability of having initially chosen the all gold box given you chose a good ball, the information given in the problem. You still haven't told me the difference.

>You assumed question starts at the beginning. But the question starts in the middle, after already have a gold ball.
You're lying. I literally said it's after you chose a gold ball:

>The question is asking for the odds you chose from the all gold box. It's twice as likely you did so given you chose a gold ball since it's all gold and the other box you could have chosen from odds only half gold.

>>15197667
>How do you not see that the "twice as likely" only applies AHEAD of taking the ball.
How do you not see it's only twice as likely you chose from the box with two gold balls AFTER choosing a gold ball? You're literally projecting your own mistake onto me. You assumed the two boxes are equally likely when they are only equally likely before choosing a good ball. R - E - T - A - R - D

>>15197649
>There's 3 gold balls you can pick, out of 3, 2 of them return true
You don't get to pick balls you get to pick boxes with balls in them and you are guaranteed a box with a gold ball in it, the third box does not matter.
Since there's only two boxes that you could have picked now we have 2 scenarios.
1.The second ball is silver.
2.The second ball is gold.
In conclusion chance is 50%.
How are you failing at this one which is even simpler than the sleeping beauty one.

>>15197663
>One gets a dollar every time the coin is heads. The other person gets a dollar every if they guess correctly after waking up, and always chooses heads.
If they don't lose anything then this has nothing to do with betting or the posts you're replying to.

>>15197688
That you happened to pick a gold ball this time doesn't mean you'd pick one every time. It's not some universal law that guarantees you'll always get a 1st gold ball. The question states: "you pick at random" and it states: "you can't see into any of the boxes"
Your hand is more likely to be in the first box when the conditions of the question are met, because in the second box you have to restart the experiment 50% of the time

>>15197684
The third box does not matter because you can never pick it, it's included in the problem to filter retards like you.
The chances of picking the box with 2 gold balls is the same as the change of picking the box with 1 gold ball.

>>15197688
>In conclusion chance is 50%.
That doesn't follow from anything you said. The two scenarios you listed are not equally likely, side is twice as likely you got your gold ball from the all gold box.

He does a more or less good job in explaining that the 1/3 answer arises when you try to optimize being right, after waking up.
It's basically a solved issue.

>>15196168
nice

>>15197694
I declare they both lose a 50 cents each round. Did that make them have a different number of dollars?

>>15197684
>CHOSE
>PAST TENSE
It's already happened dude.
There are no odds on that anymore.
They do not effect anything anymore.

Once you have a gold all in your hand, the fact that one box was more likely to yield a gold ball isn't in play anymore.

>>15197701
If you happen to pick the third box, you restart the experiment
If you happen to pick the second box second ball, you restart the experiment
That's why it's more likely your hand is in the first box when the conditions of the experiment are met

>>15197701
>The third box does not matter because you can never pick it, it's included in the problem to filter retards like you.
Where did I say anything about the third box being relevant? Not only are you a projecting retard, you can't even read. I only talked about the first and second box. Just stop posting, you're only embarrassing yourself.

>The chances of picking the box with 2 gold balls is the same as the change of picking the box with 1 gold ball.
Those are the prior odds, not the odds after choosing a gold ball. Why do brainlets INSIST that prior odds affect future odds?

>>15197495
protip: "Third positionist" is just sugar coating for neo-nazi

>>15197705
>I declare they both lose a 50 cents each round.
Each round of what? Sleeping beauty is giving her credence whenever she wakes, not for each coin flip.

>>15197698
>That you happened to pick a gold ball this time doesn't mean you'd pick one every time
It's literally stated in the problem that you pick a gold ball, the question asks what the probability of the next ball is given that the one in your hand is gold.

>>15196814
>she cant know when she wakes up
>she doesnt retain information from the previous day
if she remembers being woke up and having another set of dreams, then her creedence will be 100%, otherwise it would always be 50%. Otherwise she would always have no idea how many times you wake her up, and you could even test for this in the study.
>>15196389
>This shit legitimately feels like busywork mathematicians came up with so they look like their actually accomplishing something with their lives.
pretty sure vertasium gets off to making his videos seem like theres content but actually its entirely nothing or even outright wrong

>>15197710
>>CHOSE
>>PAST TENSE
>It's already happened dude.
Yes, that's what I said, illiterate retard.

>There are no odds on that anymore.
There are, since you don't know the outcome. LMAO, are you 8 years old? You don't even understand what odds are. And you claimed the odds are equal for each box, when you already choose the box, so you aren't even being consistent in your retardation.

>Once you have a gold all in your hand, the fact that one box was more likely to yield a gold ball isn't in play anymore.
It's ONLY in play once that occurs. You're the dumbest retard in this thread, and that's saying something.

>>15196068
She is asked the question, "What are the odds that the coin was heads?" Anyone, whether it's her or someone else must answer 50% because those are the odds of a fair coin flip. If she were asked "Was the coin heads?" And the question was "What are the odds she is correct," Then the answer would be 1 in 3.

>>15197720
Right, so there's 3 scenarios in which your first ball is gold

>>15197730
If you were woken up you have to say the odds are 1/3 tails, as you're told how the experiment was conducted.

You don't know in which one of the 3 possible awakenings you are.

>>15197727
You choose a gold ball. ESTABLISHED.
That means you are in one of two boxes that were known to contain a gold box.
>this where you are when the question is asked.
If you got it from the two gold ball box then it's 100%.
If you got it from the one gold one silver box the odds are 0%

>>15197717
The lose 50 cents once per coinflip.

Another question for you. Sleeping beauty is off doing whatever bullshit she wants. I, a person who is not sleeping, start paying 1 dollar to gain 2 dollars if her coinflips are heads. Do you believe I am losing money making this bet on fair coinflips?

>>15197741
there's two gold balls in the two gold ball box
you could get either

>>15197738
The question isn't "Which way did the coin land?" It's "What are the odds?" He even changes the question at the end when he talks about the soccer game with Canada. In that one he asks, "Who won?" not "What are the odds?" One question depends on perspective, the other doesn't.

>>15197721
>if she remembers being woke up and having another set of dreams, then her creedence will be 100%, otherwise it would always be 50%.
No, it would be 0 and 1/3. She only knows it is not the Tuesday after heads, and all other days/flip combinations are equally likely to be true.

P(heads|awake) = P(heads) P(awake|heads) / ( P(heads) P(awake|heads) + P(tails) P(awake|tails) ) = (1/2)(1/2)/((1/2)(1/2)+(1/2)(1)) = 1/3

>>15197741
>You choose a gold ball. ESTABLISHED.
No one said purveyor, illiterate retard.

>That means you are in one of two boxes that were known to contain a gold box.
Yes, and it's twice as likely you are in the first box since the second box is only half gold. Just like it's impossible you are in the third box since it has no gold. R E T A R D

>>15197742
>The lose 50 cents once per coinflip.
This is irrelevant to the problem. Sleeping Beauty is asked her credence whenever she wakes, not once per coin flip.

>I, a person who is not sleeping, start paying 1 dollar to gain 2 dollars if her coinflips are heads.
Who cares? Her credence is still 1/3.

>>15196753
Anyone's, including hers. Fair coin = 50%.

>>15197759
It's twice as likely BEFORE you have the gold ball.
After, YOU HAVE A GOLD BALL ALREADY.
jesus fucking christ
>>15197749
Doesn't matter. You ALREADY got one.
Based on already having one it's irrelevant.

>>15197750
They both depend on perspective.
You're asked about the probability in your reality, not the original reality.

>>15197767
>Doesn't matter. You ALREADY got one.
Based on already having one it's irrelevant.
Let me rephrase the question to make you understand it better: "There's 2 boxes. One of them has 2 gold balls, and one of them has 1 gold ball and 1 silver ball. You can't see into any of the boxes, and you don't know which one's which, and then you pick a box at random. Now that you've picked a box at random, pick a random ball. If the ball is silver, restart the experiment. If the ball is gold, continue. Now that you've got a gold ball, how likely is it that the second one from the same box is also gold?"
This is the correct understanding of the question, and this amounts to the result of 2/3.
When this experiment is repeated IRL, you'd get 2/3. There's no other argument.
"It's a gold ball" doesn't mean some universal law that makes you always get a gold ball every time you try, no, it's a condition for the question. This case, you got a gold ball. The question says: "you pick AT RANDOM", and it says: "you cant SEE into any of the boxes" for a reason

>>15197765
>Anyone's, including hers.
Wrong. Once she's awake, she knows it isn't the Tuesday after heads, so it's twice as likely the coin landed on tails. You ignore that information, so you get the wrong answer.

>>15197771
Sleeping Beauty, I just woke you up. What are the odds of a fair coin flip? 1/2

Sleeping Beauty, what are the odds that you were woken up because the coin landed heads? 1/3.

>>15197785
meant to greentext 2nd sentence

>>15197767
>It's twice as likely BEFORE you have the gold ball.
No, it's equally likely to choose either box before before you have a gold ball. Read the problem. After you have a gold ball, it's twice as likely you chose it from the all gold box. Illiterate retard.

>>15197789
Yes, and those two are the same thing.
She doesn't know in which of the 3 possible awakenings she is. There's no way for her to know.
Can't you understand?

>>15197798
I mean:
"Sleeping Beauty, I just woke you up. What are the odds the coin we flipped earlier was heads?"
and
"Sleeping Beauty, what are the odds that you were woken up because the coin landed heads? 1/3."
Are the same thing

>>15197762
>>The lose 50 cents once per coinflip.
>This is irrelevant to the problem
That is true. But someone seemed to think it was relevant for some reason. Since you understand it isn't maybe you can answer the question?

If I bet on the coinflip beforehand, and she makes the same bets afterwards, do we win a different number of times? How many times are we expected to win?

>>15197798
Perhaps the second question is the actual problem and this guy fucked up the wording for this video.

>>15197803
>If I bet on the coinflip beforehand, and she makes the same bets afterwards
This is too vague to answer. Just state what the bet actually is. Or better yet, just answer the original problem.

>>15197814
You repeat sleeping beauty with two people who wake according to one coin. One gets a dollar every time the coin is heads. The other person gets a dollar if they correctly guess the coin position, the first time they wake up after a flip. They always guess heads.

Do you believe those two people eventually have a different number of dollars? If not how many dollars are they expected to both have?

>>15196822
>Wrong, she gains the information that it is not the Tuesday after the coin landed on heads
This is wrong, you midwit.

She is not told ANYTHING about what day it is. She is ONLY woken up and asked what day it is.

She gains absolutely NO information post-waking up. If it's Tuesday, SHE DOES NOT REMEMBER THAT SHE WAS WOKEN UP ON MONDAY AND SHE DOES NOT KNOW THAT IT IS TUESDAY. AGAIN, SHE IS ONLY WOKEN UP AND ASKED WHAT DAY IT IS.

IF IT IS TUESDAY, HER CREDENCE IS THE *EXACT* SAME AS IT WAS ON MONDAY AND ON SUNDAY BECAUSE SHE DOES NOT GAIN ANY NEW INFORTMATION AFTER BEING WOKEN UP.

Anyone answering 1/3rd is severely retarded and thinks they are smarter than they truly are.

>>15197787
That's answering the question "What are the odds the coin landed heads this time?" not "What are the odds of a fair coin flip?"

>>15197827
Again these problems have nothing to do with the original problem.

>>15197845
Does that mean you're incapable of answering?

>>15197847
stfu homo

>>15197834
>This is wrong, you midwit.
It's right, projecting retard. Since she is awake, she knows it isn't the Tuesday after heads. You will never disprove this.

>She is not told ANYTHING about what day it is.
She is told beforehand that she will not be woken up the Tuesday after a heads. She doesn't need to be told anything else. Maybe retards like you who can't add 2 and 2 together need to be TOLD this explicitly when woken up, but you're retardation is not part of the problem.

>She gains absolutely NO information post-waking up.
She gains the information that it is not the Tuesday after heads. LMAO, you lose.

>Anyone answering 1/3rd is severely retarded and thinks they are smarter than they truly are.
Amazing projection.

So for the people that say 1/2 is correct here is a slight variation of the problem taken from
>>15196222

Would you still say 1/2 in the following case?

>Sleeping Beauty volunteers to undergo the following experiment and is told all of the following details: On Sunday she will be put to sleep. Once or nonce, during the experiment, Sleeping Beauty will be awakened, interviewed, and put back to sleep with an amnesia-inducing drug that makes her forget that awakening. A fair coin will be tossed to determine which experimental procedure to undertake:
>If the coin comes up heads, Sleeping Beauty will be awakened and interviewed on Monday only.
>If the coin comes up tails, she will be never be interviewed.
>In either case, she will be awakened on Wednesday without interview and the experiment ends.
>Any time Sleeping Beauty is awakened and interviewed she will not be able to tell which day it is or whether she has been awakened before. During the interview Sleeping Beauty is asked: "What is your credence now for the proposition that the coin landed heads?"

>>15197842
>"What are the odds the coin landed heads this time?"
As opposite to what? It's always "this time" when she is awakened. LMAO

What you retards can never seem to grasp is that probability is not objective. It is dependent on what information you have. If you see the coin lands heads then the probability the coin landed heads is 1, not 1/2.

>>15197870
>If the coin comes up heads, Sleeping Beauty will be awakened and interviewed on Monday only.
>>If the coin comes up tails, she will be never be interviewed.
>>Any time Sleeping Beauty is awakened and interviewed she will not be able to tell which day it is
Wrong.

>>15197847
It means your question doesn't replicate the problem, which is the only answer you need.

>>15197637
>The question is asked from the perspective of sleeping beauty, from her perpsective it's 1/3,
Incorrect, retard.

Sleeping beauty's perspective can only logically be 1/2 as she gains no new information after being woken up. Her credence post-waking up is the exact same as before she was woken up.

>>15197877
Stop beeing pendantic.

Also the week she is woken up is not specified, so the the last sentence is still correct

>>15197890
>Sleeping beauty's perspective can only logically be 1/2 as she gains no new information after being woken up.
Wrong. She gains the information that it is not the Tuesday after heads. Thanks for admitting the answer is not 1/2.

>>15197890
The information she has is how the experiment is conducted.
She doesn't know in which of the 3 possible awakenings she is now, but,
She KNOWS she's currently more likely to be in the sequence of awakenings, that contains more awakenings

>>15197897
>3 possible awakenings
>sequence
There are only two possible outcomes for the coin toss, heads or tails. There could be a million day long sequence after landing tails and It would still have zero relevance to that coin toss.

The question she is asked is "What is your credence now for the proposition that the coin landed heads?" Not "What day do you think it is".

There is no new information gained after she is woken up.

Thirders fail at basic reading comprehension and critical thinking.

>>15197880
I'll answer for you since you're incapable. You either believe 1/2 = 1/3 or you admit that no matter what sleeping beauty believes, they will both of X/2 dollars, where X is the number of trials.

>b-b-but we're not talking about reality, we're talking about this random number she pulled out of her ass
Does she think she has X/3 dollars? Does she care about the random number and think it has some connection to reality? If the answer to either question is yes then she is an idiot, as is anyone modeling their thought process after hers.

>>15197870
>>15197892
If she is interviewed she knows it was heads. If her credence is something other than 100% she's just stupid.

>>15197928
Halfers fail at basic ability of theory of mind
When you wake up, do you know what day it is? No. Do you know the result of the coin? No. Do you know the rules of the experiment? Yes. So can you guess what the result was based on amount of awakenings each? Yes.

>>15197928
>There are only two possible outcomes for the coin toss, heads or tails.
Yes, and it's twice as likely the coin landed on heads when Sleeping Beauty wakes up, because she then knows it is not the Tuesday after heads. You incorrectly ignore that information and get the wrong answer.

>There is no new information gained after she is woken up
Wrong.

Since you are unwilling to listen to reason, here is the mathematical proof:

P(heads|awake) = P(heads) P(awake|heads) / ( P(heads) P(awake|heads) + P(tails) P(awake|tails) ) = (1/2)(1/2)/((1/2)(1/2)+(1/2)(1)) = 1/3

Now fuck off.

>>15197938
Try again, timmy.
Read it slower this time.

>>15197947
You're woken up.
What would you guess the coin toss resulted in?

>>15197936
>they will both of X/2 dollars, where X is the number of trials.
So what? It's irrelevant to the original problem.

>b-b-but we're not talking about reality,
We're both talking about reality, you're talking about a different problem. Sleeping Beauty's credence that the coin landed heads is 1/3, because she only knows it is not the Tuesday after heads and it's equally likely that it is the Monday after heads, the Monday after tails, or the Tuesday after tails.

>>15197951
You're almost there
Was it heads or was it tails?

>>15197952
Define credence and explain why anyone should give a shit about it. It apparently isn't because it helps you make accurate predictions about the future or the state of the world.

>>15197960
I would guess tails and have a 2/3 chance of being right.

>>15197958
I would guess that it was tails, as I don't know anything other than
>I am woken up
and, the procedure

>>15197958
I would guess tails and have a 2/3 chance of being right

>>15197960
>Define credence
A measure of belief that something is true.

>explain why anyone should give a shit about it.
That's what this thread is about. You're free to not post here and embarrass yourself further.

>It apparently isn't
Isn't what? LMAO, retard.

picrel relevant to this thread - the last part

>>15197969
>I would guess tails
And have a 50% chance of being right, as the sequence of events that follows after tails has zero physical or logical effect on that heads or tails cointoss.

>>15197997
>And have a 50% chance of being right, as the sequence of events that follows after tails has zero physical or logical effect on that heads or tails cointoss.

The following events don't have an effect on the cointoss, the cointoss has an effect on the events. If the coin is tails, there's 2 subsequent realities, if it's heads, there's only 1.
You have no way to tell which one out of the 3 you're in when yo wake up.

>>15197999
>the cointoss has an effect on the events
Which isn't relevant to the question being asked of Sleeping Beauty as that question is only concerned with the 50/50 coin toss, not what happens after.

>>15198004
She's not asked "if we throw a coin now, what's the probability it's heads?", she's asked: "now that you're awake, and you know the rules of the experiment, what's the probability the coin WAS heads?"

>>15197785
There are only two boxes.
Higher likelihood ahead of time does not convert to higher likelihood post facto.
You still insist on starting your reasoning before selecting the gold ball.
After selecting the ball, the prior odds are irrelevant.
The odds WERE 2/3. NOW they are 50/50.

>>15198006
>now that you're awake
And she knows no more than she did before she was awake

>and you know the rules of the experiment
That give her no new knowledge about her state

>what's the probability the coin WAS heads
50%

I'm glad I could walk you through this

>>15197997
>And have a 50% chance of being right
OK, so I will give you $3 every time I'm wrong and you'll give $2 to me every time I'm right. Sound good right?

>>15198011
>And she knows no more than she did before she was awake
She knows she's in 1 of the 3 awakenings
>That give her no new knowledge about her state
She's got the knowledge that she's more likely to be in the sequence of 2 awakenings rather than the single awakening
>50%
1/3

>>15198018
>1 of the 3 awakenings
There are only two possible outcomes to the coin toss, heads or tails.

Read the problem again. Slowly, this time.

>>15198011
>And she knows no more than she did before she was awake
Wrong, she knows it's not the Tuesday after heads. When she was asleep, it could have been the Tuesday after heads. Thanks for admitting the answer is not 50%.

>>15198008
Right, so you select a random box, and a random ball.
What are the possible scenarios?
- Box 1 Ball 1
- Box 1 Ball 2
- Box 2 Ball 1
- Box 2 Ball 2
- Box 3 Ball 1
- Box 3 Ball 2

In which of these does the question apply?
- Box 1 Ball 1
- Box 1 Ball 2
- Box 2 Ball 1

In which of these, out of the 3, do you get a 2nd gold ball?
- Box 1 Ball 1
- Box 1 Ball 2

2/3

>>15198022
>There are only two possible outcomes to the coin toss, heads or tails.
Yes, and tails is twice as likely as heads when she wakes up, because she knows it's not the Tuesday after heads.

>>15198022
If the outcome of the coin was heads, she's awakened one time. If the outcome of the coin was tails, she's awakened two times.
She doesn't know in which one of the 3 awakenings she is, when she's woken up.

>>15198029
See >>15197928

>>15198033
See >>15197938

>>15198036
See >>15198022

>>15198040
See >>15198029

>>15198042
You have not reread the problem.

Read the problem again, slowly.

>>15198044
I have read the problem, slowly

>>15198045
And still can't grasp the very basics of it. Meaning you clearly have a learning disability.

I accept your concession.

>>15198044
You have not responded to the fact that waking up tells her she is not in the Tuesday after heads, which makes it twice as likely the coin landed on tails. Thanks for admitting the answer is 1/3.

>>15198050
You can't grasp how perspective works.

>>15198050
>>15198052
As I said, you lack theory of mind.

>>15197936
So you do admit to beeing a brainlet.

The question is fundamentally still the same. Either you argue 1/2 or you say it's 100%.

If you say it's 100% it logically follows that in the other case the probability is 1/3

I'm so fucking annoyed by these types of questions.
What's the probability that they rolled a tails? THERE IS NO ANSWER. These are meaningless questions. Might as well ask what is the probability that I went to supermarket yesterday or the probability that my hair is yellow.
STUPID MEANINGLESS QUESTIONS.
Questions about probability are only meaningful in the context of:
- Pure mathematics, where you have a well-defined sigma algebra and a measure.
- Scenarios where you precisely understand all the moving variables in a way that you can translate the problem into a closed computer simulation, and then ask what is the probability of getting a particular outcome in that computer simulation model.
IN ALL OTHER CASES IT IS STUPID AS FUCK AND MEANINGLESS.
FUCK VERITASIUM

>>15198062
Probability means: how often does it happen?
In this question, the coin is heads 1/3 of the time.
If you throw a dice, it's 6 1/6 of the time.

>>15198027
Again, you started from the beginning.
We are starting from the middle dude. kek
One of your three options is gone already. IT'S IN YOUR HAND.
There are only 3 gold balls. ONE IS IN YOUR HAND.

So that necessarily means that there are two boxes it could have been.
The gold ball IN YOUR HAND means one possible box has only silver in it.
The other box has only gold in it.

>>15198065
What makes you assume that the first box only has one gold ball, that you could have picked, and is currently in your hand?

>>15198068
I'm not assuming.
AFTER having one in your hand, here are two possibilities.
You were in box 1 and thereby there is another gold ball to be picked and you will pick it 100% of the time because it's the only ball left.
Or, you were in box two and there is only a silver ball left and therefore you will pick gold 0% of the time because the ball is silver.
You don't know which box you chose, so it's 50/50.

>>15198068
I read you again. Because that's the way the question is worded.
This other brainlet keeps starting as if the question is asked at the start of it all.
It's not.
The question is asked after you are already holding one of the gold balls.

>>15198077
>if you throw a dice, the probability of it being 50%... because... it either is, or it isn't.

>>15198081
A die has six side retard.
Try actually refuting me, or just admit I'm right.

>>15198084
>A die has six side retard.
yes, and this question has 3 gold balls you can pick

If you repeat the gold ball experiment, IRL, you will get 2/3

If she thinks it is Monday when asked, it could be heads or tails.
If she thinks it is Tuesday when asked, it could only be heads.
If it is Wednesday, she is not asked.

So for Sleeping Beauty, if she is asked, she has one probability distributions to assess: is it Monday or a Tuesday. She cannot asses the probability of the coin, because it has already been tossed. From that probability distribution of Monday or Tuesday, she must decide the chances of heads. She has to see FROM the probability of what day it is TO the probability of the coin toss. She cannot see FROM the coin toss to what day it is because, if she is being asked, that means the coin has already been tossed, and she cannot know whether the probability of heads is 0% or 100%. There is no story where it is both. Therefore, she can only Enumerate all of the outcomes, and count heads.
So that is HT on Monday, but only H on Tuesday. But she does not know whether it is Monday or Tuesday, so she has to look at the TOTAL distribution for both days. The total for both days is HH and T. That makes it 2/3 heads and 1/3 tails.

Critical thinking requires understanding that the narrator’s position changes the story being told. That is why racists cannot understand CRT. It is impossible to assess the coin toss that has already been made, if you cannot see it. Therefore, from Sleeping Beauty’s point of view, the coin toss is still stochastic, and if asked to bet on which story she is in, of all the multiple stories she could be in, she would be best betting on heads, because that is the one with the highest chance of being the one she is in.

>>15198087
After you have one in your hand there are only TWO gold balls.
lamo fucking retard.

>>15196071
I wrote an easy to understand to simulation so you can stop fking arguing about this. Copy the code, press f12, paste it in you console, and press enter to run it on your machine.

let box1 = ["g", "g"];
let box2 = ["g", "s"];
let box3 = ["s", "s"];

let boxes = [box1, box2, box3];

let firstBallWasGoldCount = 0;
let nextBallWasSilverCount = 0;
let nextBallWasGoldCount = 0;

let numIterations = 1000;

for(let i = 0; i < numIterations; i++){
let chosenBox = boxes[Math.floor(Math.random() * 3)];
let chosenBall = chosenBox[Math.floor(Math.random() * 2)];

if(chosenBall == "g"){
firstBallWasGoldCount++;
if(chosenBox[0] == "g" && chosenBox[1] == "g") nextBallWasGoldCount++;
else nextBallWasSilverCount++;
}
}

console.log(`Times ran: ${numIterations}
Times first ball was gold: ${firstBallWasGoldCount}
Times next ball was gold: ${nextBallWasGoldCount}
Times nextBall was silver: ${nextBallWasSilverCount}\n
P(nextBallGoldGivenFirstWasGold)=${nextBallWasGoldCount/firstBallWasGoldCount}`);

>>15198093
This again, does not account for having already drawn a gold ball.
The question is posed AFTER you already have a gold ball chosen.
Lot of work for nothing.

>>15198065
You started from the beginning by assuming the boxes are equally likely to be chosen. They aren't one you have a gold ball. You have no argument.

thread tl dr
veritasium watching onions boy chooses contrarian answer to a riddle image that involves probability to feel smart, gets proven wrong and can't even use semantics to defend his ridiculous position

>>15198093
https://archived.moe/b/thread/887074895/#887083432

>>15198102
>you pick a box at random
>you pick a ball
>IT WAS GOLD
Now the question is posed.
IT STARTS AFTER THE GOLD BALL WAS CHOSEN.
The first choice has no effect anymore.

If they asked "What are the odds that you chose and gold ball AND THEN choose another gold ball?" you would be correct.
But that's not what the question indicates.

>>15198113
>But that's not what the question indicates.
It is tho

>>15198114
No, it gives the exact things that happen to start.
Those aren't up to chance. It tells you they happen.

If they were up to chance, you would be correct.
They aren't up to chance. The question dictates them.
BRAINLET.

>>15198100
>>15198102
The problem specifies that you selected a box at random, so, I selected a box at random, and ignored events where the first ball chosen wasn't gold. What's the problem?

>>15198114
the question says you've already picked a gold ball so the part before is irrelevant. you are wrong.

>>15198119
>>15198123

They're conditions for the question, not some magical universal law that makes you always get a gold ball. The question says: "YOU PICK AT RANDOM" and it says: "You cant see into the boxes", for a reason

>>15198120
But it gives you the outcome.
So the question is not based on this randomness. It's best on a set of already settled events.

>>15198100
>This again, does not account for having already drawn a gold ball.
It does, you're desperately lying. The times the next ball was gold is about double the times the next ball was silver.

>>15198128
It is based on randomness.
If you do the experiment, and you don't get a 1st gold ball, you simply restart the experiment, until you do.

>>15198123
Finally. Thank you.
They insist on counting the already settled portion. There is no chance to the first part. It's settled already.

>>15198127
the question says you pick at random and then get that as a result making the first part irrelevant

>>15198131
>it's based on randomness
>the question automatically bypasses this "randomness"
okay

>>15196068
>Are people who answer that the probability is 50% actual NPCs? It seems like they're incapable of conceptualisering perspective, they just can't grasp it.
Another potential NPC test is to ask people what they think of Hellie's vertiginous question. If they give an answer that's something like "the question is meaningless" or "if you were someone else, you wouldn't be you", they are an NPC.

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

>>15198135
How come YOUR 1/2 answer requires almost half of the question to be overriden and contradict itself, and isn't based on reality, as if you repeat this IRL you'd get 2/3
While MY answer of 2/3 makes complete sense and doesn't require the removal of parts of the question?

>>15198135
That's called a hypothetical. Are you a woman?
They don't get hypotheticals very well.

It literally tells you the outcome. That is NOT based on chance. It's predetermined.
You are not thinking clearly.

>>15198113
>IT STARTS AFTER THE GOLD BALL WAS CHOSEN.
Yes, it's now twice as likely you're in the all gold box AFTER you chose the gold ball. The first choice has no effect anymore, so your assumption that the two boxes are equally likely is wrong. Thanks for admitting that.

This thread is helping me accept the NPC meme.
I've acknowledged that there's differences in peoples minds & their thinking, but that's still pretty unbelievable.

>>15198120
>The problem specifies that you selected a box at random, so, I selected a box at random, and ignored events where the first ball chosen wasn't gold. What's the problem?
Nothing. If you actually did that you would see there are three equally likely events where you chose a gold ball and two of them are in the all gold box. But you didn't do that.

>>15198147
kek
I'm being trolled I guess.

>>15198153
Not an argument, thanks for admitting I'm right again.

>>15198151
>But you didn't do that.
This is his sticking point.
He read the word "randomly" and insists that it happened randomly. But the question clearly determines ahead the outcome, thereby making it not random.

>>15198151
Yeah I did, and I got 2/3?

>>15198157
You just keep insisting it's random from the start. The question says "randomly" but it's not. The question predetermines the outcome. That's NOT random.
The only way it's 2/3 is starting from the beginning. All your arguments start at the beginning.

>>15198159
It's still random, it states that in this scenario, 1st is gold, that doesn't mean you'd always get 1st gold. It's a condition for the question to be asked.

>>15198159
It did happen randomly, the question literally says that it happened randomly.
I don't know how else to say that the scenario explicitly states that it happened randomly.

>>15198165
In Monty Hall, the common pitfall people fall for is viewing the situation from the perspective of someone who's just walked into the room, who wasn't there since the beginning, and that's why they get it wrong. It's a cognitive DISORDER. You're just stupid, or pretending.

>>15198178
But the question NECESSITATES you start in the middle.
It literally MAKES YOU start in the middle.

>>15198171
>>15198166
>it's random if I predetermine the outcome
lamo
I guess /sci/ is really just teacher pet, swallow anything they read, types

You could be hustled very easily. Just stack the deck and tell you it's random ahead.
kek

>>15198182
Yeah, so to run the experiment, you keep picking balls until you're in a scenario where the first was gold, and you are now in the exact same situation as the question

>>15198186
Running the experiment after I've selected gold already or before?

>>15198188
You just restart the experiment if the 1st isnt gold.
That's the condition outlined in the experiment.

>>15198186
Read you wrong.
Yes, from that point it's 50/50 because I have a ball in my hand already.
There are no longer better odds of it coming from a certain box.

>>15198191
>there's no way previous events affect the probability of future events!

>>15198190
It's the IF you select gold part that makes it 2/3.
The reason is because PART OF THE TIME you'll select a box with gold but you get a silver box and these results ARE THROWN OUT.
This is where the extra odds are effected. WHEN YOU THROW OUT THE RESULTS when you select silver from the 50/50 box.
Once you've selected gold it's 50/50.
kek

>>15198188
To get to a situation where I've selected a box at random, and the first ball I picked was gold, I have to select a box at random and pick balls until the first ball I picked was gold. There's no other way to get to that scenario.
So, "running the experiment" includes the setup necessary to get to the midpoint. There is literally no other way to get to the "middle" while staying consistent with the parameters set in the question.

>>15198195
it is IF

>>15198196
The odds are skewed when you start from the beginning because 50% of the time you select the one silver/one gold box you THROW OUT THE DATA.

But once you have a gold ball in hand, you are now keeping all the data.

>>15198200
if you did this, and you happened to have a gold ball, not knowing which box you picked, chances are you're in the first box.
same concept as monty hall

>>15198200
Yeah, that's what I did in the simulation. I ONLY looked at situations where the first ball picked was gold, from a randomly selected box. Like it says in the original question. 2/3.

>>15198209
But that includes the first round of evidence.
That includes that you threw out box two repeatedly.

>>15198218
Yeah. Are you saying that someone could pick a box randomly, select a ball without seeing inside (like the question says how the experiment was set up), and if the box happened to be 2, they pick gold with 100% certainty? Again, this is under the conditions, specified by the question, that you can't see inside the box.

It's given that you got gold, but you have to get gold under the conditions specified by the question, which includes the fact that you had randomly selected the box, and randomly pulled out a ball.

>>15198235
this

>>15198235
At the beginning, if you just pick a box and take out a ball, the odds that it will be gold are 1/2 since there are 3 gold balls and 6 total balls..

Once you've picked the gold ball, the odds of the second ball in the box being gold is 1/2. The one remaining ball can be one of two colors.

The odds at the beginning of picking a gold ball twice in a row is 1/2 * 1/2 = 1/4

>>15198329
Bruh. Once you pick a box you're stuck with it. The odds of picking gg at the beginning is 1/3

>>15198356
How many balls remain in the box you're stuck with? 1
How many colors could it be? 2
1/2

>>15198165
>You just keep insisting it's random from the start.
What are you talking about? Is not random, choosing the good ball greatly increases the chance you chose from the all gold box. You keep ignoring this. You keep arguing they are equally likely with no reason. You lost.

>>15198385
>1/2
Doesn't follow. It's twice as likely the box you're in is the all gold box, since the other box is only half gold. You just keep ignoring this fact and repeating the same non sequiturs.

>>15198329
>Once you've picked the gold ball, the odds of the second ball in the box being gold is 1/2.
Wrong.

>The one remaining ball can be one of two colors.
And? That doesn't mean the two colors are equally likely.

>>15198514
>>15198520
At the beginning there are 4 scenarios that can happen as you pick your 2 balls.

red then red
red then gold
gold then red
gold then gold

Before any picking starts the odds of the gold then gold scenario is 1 in 4.

After you've picked the first ball and it's gold, there are only 2 scenarios remaining.

red
gold

>And? That doesn't mean the two colors are equally likely.
Yes it does.

>>15198534
>At the beginning there are 4 scenarios that can happen as you pick your 2 balls.
They are not equally likely.

>red then red - 1/3
>red then gold - 1/6
>gold then red - 1/6
>gold then gold - 1/3

>Before any picking starts the odds of the gold then gold scenario is 1 in 4.
Wrong.

>After you've picked the first ball and it's gold, there are only 2 scenarios remaining.
Correct.

>gold then red - 1/3
>gold then gold - 2/3

>Yes it does.
Wrong.

>>15198553
Yeah, the first part is wrong, but the fact remains that once you've picked the gold ball there are only two remaining scenarios that are equally likely.

>>15196068
I just Googled it, and this is some bullshit ass "thought experiment" that was literally made up by some quack "philosopher". Complete schizo non-sense, and the entire premise of this though experiment is retarded and doesn't make sense because sleeping beauty is literally a fictional character. Philosophy is not science or math. It is pseudointellectual schizo babble masquerading as real knowledge. Next time, post this shit on >>>/x/ or >>>/pol/.

>>15198592

Let's say there are 10,002 boxes.
10,000 boxes have nothing but red balls.
1 box has a red and a green ball.
1 box has two green balls.
You draw and draw and draw boxes pulling out red ball after red ball. Then at some point, you draw a box and pull out a green ball. What are the odds that the next ball you pull out of the box is red?

>>15198592
>once you've picked the gold ball there are only two remaining scenarios that are equally likely.
Wrong. It's twice as likely you chose from the all gold box, because the other box is only half gold. You're talking out off your ass.

>>15198720
what about this?>>15198708
Wouldn't it be a 1/2 chance of the second ball being red?

>>15198806
No, it's 1/3. It's twice as likely your green ball came from the all green box rather than the box that's only half green.

Me watching this thread
God, I'm convinced about half of the population or so is just cognitively impaired
inb4:
>adhom
Yes, it is.

>>15197274
>>15197308
ChatGPT is often wrong. Ask it this question:
If it takes two trucks 4 hours to travel between city A and city B, how long will it take four trucks?

>>15197834
She gets information before the experiment begins because she doesn't know what day it is. Which means that tails results are weighted as twice what heads results are because whenever its tails she gets to answer two times but when it's heads she only gets to answer once. Ergo, when she wakes up, it could be monday and heads, it could be monday and tails, or it could be tuesday and tails.

Plot twist: the dark witchbitch stabs her with a massive needle should she answer wrong.

What should she answer?

>>15196068
seems like an exercise in trying to separate truth from experience.

>>15197362
>then the probability it landed on heads is 1, not 1/2
Exactly you doofus. Which is why the correct answer for OP is 1/2.

>>15199472
How so? You're saying the information that it is not Tuesday after heads doesn't affect the probability that the coin landed on heads. But you admit information affects the probabilities of past events. Make up your mind.

>>15196068
I didn't even understand the question

>>15199493
Prior probabilities:

The coin landed heads and it is Monday - 1/4
The coin landed heads and it is Tuesday - 1/4
The coin landed tails and it is Monday - 1/4
The coin landed tails and it is Tuesday - 1/4

When Sleeping Beauty is awakened she knows it is not the Tuesday after heads, so the remaining possibilities have their probabilities increased proportionally:

The coin landed heads and it is Monday - 1/3
The coin landed tails and it is Monday - 1/3
The coin landed tails and it is Tuesday - 1/3

Therefore the probability the coin landed on heads is 1/3.

>>15196071
I feel like 1/3rd, but I'm not convinced by changing the question to waking up 1,000,000 times if it comes up tails. It's 50% she's woken up once, or 50% she's woken up 1,000,000 times. It differs from the Monty Hall problem because in that riddle, with 1,000,000 doors, you're choosing BEFORE anything is opened, so it literally becomes 1 out of 1,000,000 you'll pick the correct door the first time, and 999,999 out of 1,000,000 if you switch. In short, shit if i know the answer. I'm leaning toward 50/50 now.

Suppose 100 men decide by a coin toss if they have two children (with different women) or one child. The end result will be 300 kids, 200 from the other toss, 100 from the other.

If you ask these children whetever they're from from the 200 or 100 bunch, the obvious answer is to guess the 200 group. If you ask an outside what are the odds of one of these men choosing either option, it's 50%.

QUESTION SOLVED. Anyone still debating this is an actual midwit arguing semantics

>>15200070
Think about running this game many times. She will be woken up millions of times more after tails than after heads. So she should always guess that the coin landed tails, because she will almost always be right. From her perspective, all possible awakenings are equally likely regardless of whether they come after heads or tails. You are using an outsider's perspective to answer a question from her perspective.