193,340 People Agree With Me, 85,660 Disagree 

ok

I liked

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First

??th

Yeah, it just seems like semantics. I depends on whose perspective you are using

Semantics, asking the wrong question, wrong definition, etc.

That's what makes Monty Hall problem so great - it's not about words, it's about the actual concept itself.

Yeah, "what was the probability that it came up heads?" vs "what is the probability that it came up heads?" can already make a difference to the answer. Only if you define questions properly can you answer them. I suppose that's why they were philosophy papers and not mathematics. In mathematics you need things to be defined unambiguously.

There is clearly a majority consensus on the entire thing with most people leaning towards the real world side instead of the fairytale book side. Why do you think they use a literal fairytale character to point this out? Math is 100% disconnected from reality. A concept. She's literally missing 25% of her ability to know what actually happened. She is at 75% comprehension of her reality since she can't tell the difference between waking up once or waking up twice. But the knowledge shown to her is letting her know, that she has two chances to respond on a tails flip, or once chance to respond on a heads flip. So she can take the chance of being right or wrong about a 50/50 chance twice in a row, or once. Her best chance of answering correctly on monday heads, monday tails, or tuesday tails is to realize that there is no tuesday heads and eliminate 25% of her ability to answer. Thus leaving 3 equal chance scenarios. Her real world probability is skewed by lack of information. Her fairytale probability is 1/2, because 1/2 is 1/2 and everyone knows 1/2 is 1/2.

Agreed, these are two different questions with different answers.

Yep, "whats the probability it was heads or tails" vs "What is the chance that today is tuesday" - or something along those lines.

This is a brilliant comment. Contrasts very well the difference that is muddled in the "what was the probability" question. The answer to, "what is the probability the coin was heads?" is objectively 50%. The answer to the question, "what is the probability that the coin was heads AND that your answer is correct?" is 1/3.

@Brad Banks What? So for the first question your answer doesnt need to be correct for it be... correct? The answer for "what is the probability of the coin to flip heads" is indeed 50%. But thats not the question, the question is "what is the probability the coin FLIPPED heads" with the given that if you are being asked that question you woke up. Similarly if someone flips a coin and it results in a Tail, it would be correct to say the probability of flipping tails in the past is still 50%, but wouldnt be correct to say the probability the coin that was flipped was tails was 50%, because you are clearly already seeing the result, and its 100%. Imagine if the SB only woke up if the coin was Tails and was asked "what is the probability the coin FLIPPED heads?" , it would be ridiculous for her to say the chance is 50% after being asked that question, because she knows she wouldnt be asked that question if it was Heads.

The probability that she guesses the side of the coin is ~1/6. ~1/2*1/3=1/6 But if you ask about the probability objectively, then of course ~0.707 It has no corelation to multiverse unless it exists (probability of Multiverse unknown)

​@Raymond' Remarkable Agenda stop dude you're talking to an anime pfp

@Raymond' Remarkable Agenda Honestly, that isn't just as justifying seeing that she could have done any other operation

​@roD Draft the general consensus is that your pfp doesn't affect your comment

Lol awesome analogy

There is no question to which the correct answer is 1/3. The whole thirder perspective is flawed because it treats the possible "states" as equally likely and independent, but they are not independent.

@nekekaminger The question would be, ‘What is the probability you were woken up by a flip of heads?’ I think the answer to the sleeping beauty question is 1/2 though because like the original comment said they are answering two different questions.

@Reuben Savage She's always woken up, otherwise you couldn't ask her. Prepending the question with the pseudo-condition of her being woken up doesn't actually change anything because it always happens. The question is fully equivalent for "What's the chance heads came up?" which is clearly 50%. I see what you are trying to do. You view each waking up event as an independent event and try to assign a probability to that event (just like Derek proposes in the video), but that approach is flawed since they are not independent. Monday Tails and Tuesday Tails cannot happen without the their also happening. Imagine you have a somewhat unusual coin that instead of heads has one dot on one side and instead of tails it has two dots on the other side. Each dot represents a waking up "event". After the toss pick one of the dots you see (which is either just one, in which case the choice is simple, or two, in which case you just randomly pick one, since SB can't remember being woken up before, the order does not matter) and ask yourself "What is the chance I see this particular dot because the coin came up with the single dotted side?". If two dots were up you answer the same question for the other dot. The experiment is exactly equivalent (if you don't agree, please explain). Do you still think the answer is 1/3?

@nekekaminger The part that I disagree with is that I'd argue they are independent events. She could be woken up on Monday Heads and be asked the question, or woken up on Monday Tails and be asked the question, or be woken up on Tuesday Tails and be asked a question. As others have stated, it really comes down to which question is asked of her. If she's asked "What do you believe is the probability that the coin came up heads?", then she should answer 1/2. Because the coin either came up heads, or it came up tails. It doesn't matter which day she woke up; the coin was either heads, or tails. If the question is "What do you believe is the probability that you were awoken on heads?", then she should answer 1/3. Because as I mentioned in my first paragraph, if she's asked this question on Monday Heads, she would be right. If she's asked on Monday Tails, she would be wrong. If she's asked on Tuesday Tails, then she would again be wrong. So it's a 1/3 chance of her being right about the 2nd question.

@Throw Away you haven’t tackled his point that these events are not independent. Monday tails and Tuesday tails are essentially the same event. For the example where she wakes up “a million times” it’s 1/2 chance that she’ll wake up a million times or 1/2 chance she wakes up once. Either way if she wakes up on the thousandth Tuesday and is asked “what’s the chance that you will wake up another thousand or so days”, its 1/2 as is “what’s the chance you only wake up today on the monday”. There’s not “more chance” of waking up in the millionth day like it’s compared to being in a simulation. It would be like saying the chance of you living in reality is 1/2, and the chance of you living in any of the millions of situations is also 1/2. 1/3 would be the answer to “what’s the probability today Is Tuesday” regarding the original question.

I've reasoned about this and I think it is correct to say 1/2. In my opinion 1/3 is simply wrong because it is not equally likely to be in any of the three cases. I'll copy here what I already said in other comments that are lost in the haystack. My opinion: When she is asked about the probability, the coin has already been flipped and its state is determined even if unknown to her. So here the word "probability" should be interpreted as her confidence that the coin landed heads. She is aware of the procedure and she knows that the coin is flipped one time at the beginning. Imagine she is asked the question immediately after the toss (of which she doesn't see the result) before being put to sleep. She would obviously answer 1/2. From now on there is no reason she should change her initial guess because the coin is tossed once for all and there is no subsequent event that could influence the output. It doesn't matter if it's the first or the millionth time she's being awakened: because she doesn't know what day it is she never gains new information and there's no reason she should update her initial guess. 1/3 is simply wrong because it assumes that the probability of being in one of the three cases is uniform while it is not. The probability is actually 1/2 of being Monday and it landed heads, 1/4 that is Monday and it landed tails and 1/4 that it is Tuesday and landed tails. The 1/3 argument moves from the wrong assumption that to the question "what day do you think it is today?" she should be 2/3 sure it is Monday. Actually she is instead 3/4 sure it is Monday to balance for the fact that there is no Tuesday/Heads combo. The probability it is Tuesday is in fact P(it landed tails) times P(it is Tuesday | it landed tails). I put video at 0.25x and he made a terrible error in his experiment. Look for yourself what he does. He simply writes a sign two times when the coin lands tails. He should have tossed the coin a second time to decide where to put ONE sign. If you do it right you get the expected 50-25-25 proportions. I wanna add something to make it more intuitive: in the case she is awakened 1 million times if it lands tails the probability that in any awakening that day is the first Monday is about 50% and not about 0%. Think of it this way: if she is asked "what day do you think it is today?" she is better off answering "The first Monday" because is much more likely to guess it landed heads and hence surely it is the first Monday than to guess it landed tails and then identify one of the million possible days.

Shocking take

The probability of the coin flip doesn't change with the way we want to measure it. If Sleeping Beauty was woken up a million times for a tails flip, it wouldn't make the coin flip any less likely to turn up heads. Being woken up two times instead of one doesn't make one outcome twice as likely as the other, as the thirder perspective implies. If we're asking about the probability of the coin flip alone, like the question in the video (1:04) very clearly is, then the answer cannot be anything other than 1/2. Now, if the question was anything like "For N times Sleeping Beauty was woken up, what is the probability of her being woken up because of a heads flip?", then it'd clearly be 1/3.

Let’s do a little thought experiment: I tell you: „I‘m about to flip a coin. If, and only if, the coin flips heads, I‘ll call you.“ The next day, I call you and say: „I flipped the coin now. What do you believe is the probability that the coin came up heads?“ What would be your answer?

I know it sounds counterintuitive,but the only correct answer for sleeping beauty is 1/3. When she wakes up, there are three possibilities: A: heads/monday, B: tails/monday, C: tails/tuesday. Obviously, A and B have the same probability, because it’s a fair coin flip, so if they would repeat the experiment every week, she would wake up every monday and the coin would have flipped each side 50% of the weeks. The probabilities of B and C must also be the same, because every week she wakes up on tails/monday, she also wakes up on tails/tuesday. So the probabilities of all three possible outcomes are the same. And the sum of the three possibilities must be 100%, because A, B and C are the only possible outcomes, and each time she wakes up, only one of them can be true. Thus, the probability of A: heads/monday is 1/3. P(A)+P(B)+P(C)=1 and P(A)=P(B)=P(C)=1/3

Stolen from Tom Scott. Doesn't bother me, but it is.

JPvid algo like that? It might get changed soon if it can be abused.

@Theeraphat Sunthornwit Pretty much all social media is optimised for controversy or moral outrage, because that's what drives the most interaction. I don't honestly have any idea about the YT algorithm, but we can be pretty sure it'll rank videos with a widely split opinion above a video that has just a high number of likes, especially if there are lots of comments too.

@Bryan Mahoney what video did Tom Scott do that abused the like count?

​@Bryan MahoneyThat would be the like and dislike number update The ideo of ratios was not stolen though

As a Brazilian I'm thankful for 4 out of 5... Canadian team is getting better and better (Brazilian team have been a lot better).

And there's a 100% chance of another balloon flying over Canada will be shot down by an F22. :D :D

As a Croatian, we beat you both, even though Brazil was better but unlucky against us. It was that 1/5 win for us 🙂 Good luck to Brazil!

@lukatore123 - I think it was more like 2/5. Croatia's got a great team (maybe the best one per capita - amongst Uruguay and Portugal). Brazilian team, of course, had better individual quality, but Croatia had a very interesting collective game. Afterall, i think it was very well deserved

@BillAnt 🤫🤫🤫

Correct.

No one here seems to understand conditional probability.

True

​@Stewart Holidaythe question has no condition about the day or your state "What do you belive is the probability that the coin came up head?"

@3lilougps The conditioning is on the fact you were woken.

VLR is still my favourite game to date even if it mostly hinges on the story and characters. The chills and thrills I got trying to figure out what was going on.

Correct.

It is a 50/50 chance on sleeping 1 day or a million. However, each time she wakes up its a 1/1000000 chance of being tails

@Josh POLLNITZ Each time she wakes up it's 50/50 chance she either exists in the heads sequence or the tails sequence. The sequence is one complete package. It doesn't matter how long the sequence is, it's still one package. The reason being that the conditional statement is the fair coin which only has two outcomes at 50% chance each.

You are confusing the probability of the coin coming up heads _before_ it was flipped with the probability that it _did_ comes up heads, after it was flipped and the observer has some amount of information pertaining to what the outcome was. These are two very different things. The answer to the first is always 50%, but the answer to the second is not necessarily 50%, depending on what information the observer has observed. This is the fundamental principle behind Bayesian probability.

Wow this actually made sense to me! Thank a lot for your explanation!

You can also think like this, there is 2/3 probability of getting the wrong door, and 1/3 probability of getting the right door. When you have chosen your door and host has also opened another wrong door, its always right to switch to the new door because the probability that you have chosen the wrong door is 2/3, so there is a probability of 2/3 of getting the right door if you switch to the only door left.

Yeah I agree, it's more about semantic than statistic. Derek just found a nice trick to get tons of likes and views with a question that is more intellectual masturbation than anything else.

@En théo exactly. And I love Derek and his content but this video just felt like a gotchya. And the worst part is I can't even express this to him by downvoting the video

Maybe it's a social experiment on how much influence his opinion has

Exactly

I agree it's a trick question, but it's not two different questions. It's just one invalid question. The tail scenarios cannot be viewed as two separate outcomes: informationally they are identical to sleeping beauty, and therefore the same outcome. The question just arbitrarily labeled the tail scenarios as two outcomes, not with any kind logic compatible with reality, but with memory erasing magic.

Correct.

There are other false linkages here. For example, (Monday) and (Monday and Tuesday) are two event chains, "misrepresented" (for logic fun reasons) as three events. The number of times Sleeping Beauty wakes up is the wrong way to define the events. Instead, there objectively are two event chains whose content is irrelevant because which chain happens depends only on a binary independent precursor event (the coin toss). Defining subsequent events the wrong way leads to the conclusion that a fair coin has a one-third chance of being heads, which itself should be clear evidence of wrongness, but which maybe some people find intriguing. 🙃🙂 I'm no mathematician but maybe it matters that the two sets (All Mondays) and ((All Mondays Plus All Tuesdays) OR (All Mondays Plus Maybe The Next Bijillion Calendar Days Or Whatever)) are all, or are all tantamount to, countable infinities. If I understand Cantor correctly, all countable infinities are the same size which might suggest that the two event chains indeed are apples to apples.

Throwing in the Monty Hall problem is an impressive misdirection 🙂 but it is another false linkage. The Monty Hall problem is a three way choice at its initial stage, and is not a coin toss (a binary choice) as the Sleeping Beauty problem is. The reason it is optimal to switch doors in Monty Hall is that it is only not optimal to switch doors if your initial choice of one door among three was right, which means at the second stage the odds of being wrong at the first stage, two in three, become merged into the remaining closed door which thus becomes preferred.

Then take them both to the consideration and calculate the average. That would be the real solution to this dilemma.

@Or Ka no, these are not two approaches to the same question, they are two different questions. Averaging them is kind of meaningless. Estimating the distribution is not the same as minimizing expected error.

@John Morrell I think you hit the nail on the head - those who agree with him are answering a different question than those who do not.

funny, but no: the imbalance of the heads and tails here is only due to a deliberate mistake in sampling; because of a sampling error you record "tails" twice when a single "tails" event occurs, but only a single "heads" event is recorded for "heads" events. The dataset is seriously screwed up; when presented with a new "instance", the "thirder's classifier" will have its probability estimates wrong: it will be predicting "tails" with prob. 0.66 but it will only be "tails" with prob. 0.5.

@Or Ka here we have the engeneer

Okay.... Let's say it this way... Imagine I tell you that I will eat an ice-cream if the coin lands tails, and refrain from doing so if it lands heads... Now you see me eating an ice-cream and I ask you- "What is the probability that the coin came up heads?" Although it's a fair coin, you would not answer 50% Right?

@Rajiv Kumar since I already see you eating ice cream I know its tails. But this is not what the sleeping beauty is about. Sleeping beauty has no way of knowing what day it is

A random number of 4 digits coinciding with a given number is always 1/10.000, why would the odds decrease just because it happens to you? Makes no sense at all. If anything the odds are higher because you ignored all the other significant numbers it could have been (for example it could have been the year you were born, and that would have been surprising to you but equally likely), making the odds much more like 1/500 or so

@Fresh Rock Papa-E I think it's because if you have a sort of main character syndrome where you think that you're the only person on Earth, then even 1:10000 probability seems "astronomical". I.e. if you're only randomly assigned a PIN once or a handful of times in your life, you expect it never to match to your SSN. So you come away with the conclusion that this should not happen to you over your lifetime. This conclusion is ignoring the fact that millions of SSNs are issued, and so the thousands of failures (no match to PIN) that you'd expect to occur DID occur: just to other people. By the same logic as this original commenter, no one should win the lottery, right? Rare things do occur, and they can occur frequently if given enough random trials.

Agree.

I like the way you explained this. His statement “Something changed” was important because it matters that an event occurred between observations.

But if sleeping beauty doesn't remember any times she's been woken up, every time is her first. So to her it's always 50/50. Any other wake-up (Tuesday) in _her_ existence never actually happened

I think there should be a distinction between asking "What is the probability A coin came up heads?" and "What is the probability THE coin came up heads?" The question is about THE coin, and given she is awake, the answer is the probability of her being awake.

AKA take the red pill or the blue pill 💊

Split the difference!

@Professional Tiresome They divvied up the hadrons amongst themselves and Erwin got a new cat.

Ahh I dont have enough neurons in my brain to understand this, someone please do the honors.

@bluzter it is a reference to Shrodinger’s Cat

@bluzter The cat referenced above, plus they're saying that they flipped the coin and it landed on neither heads nor tails, landing instead on its edge and therefore she will never awaken. It's the hidden third result.

Yes, the question from her perspective is not, "what is the probability of each sequence", but what is the probability that you're in a particular sequence where heads came up.

Correct.

Yes and there is also a bias toward agreeing with who is presenting the information, especially if they are a source one presumes to be trustworthy. There additionally might even be people who watched so little of the video that they didn't know about the meaning of the likes and dislikes and just chose to like or dislike, but that is probably negligible.

Best way to start a Monday

That's why I pick heads everytime

Some people prefer waking up with tail.

By Veritasium? I'd only want it to be from Sleeping Beauty. If not, I'd pass

bruh

The formulation of the question directly tells you to consider it from sleeping beauty's perspective.

In other words, if we repeat the experiment every week for the rest of eternity, is she trying to be right most on *days* or right on most *weeks* ?

I really like how you worded this. And you're 100% percent correct. I personally believe that because of the way that the question was asked that it should be answered from sleeping beauty's perspective just as @rantingrodent416 stated, but the way you acknowledged both points of view without hating on either one I very much respect.

Flip heads, put one green bean in the bowl. Flip tails, put two red beans in the bowl. You pick a bean, what are the odds it is green?

@rantingrodent416 Well she has no way of telling if she was awaken or not, so her only guiding point would be her understanding of the fact that a coin has only two outcomes, so it would be 50%. If someone flips a coin and ask you what are the pobability of it being heads, with no previous context (as sleeping beauty didnt remember if she had been awaken) you would answer 50%, because there is no way for you to say how many times you have been asked that question.

Not exactly equivalent, your question is more straightforward and has no mental trap. But the answer is the same 1 in 2.

EXACTLY, probability? heads, obviously, what you think the result for this run was? tails, obviously

My thoughts exactly! Was looking for this argument. What is the probability of coin came heads - 1/2, because that is the fact. What is the probability that we woke you because coin came heads - 1/3 and is very different question.

What I was about to type.

but she wasn't asked what is the probability a toss of a coin comes out heads. She was asked what is the probability the coin did come out heads. There is a big difference in asking about the probability of an event that has not occured vs the probability that a specific event has happened in the past so long as you gain knowledge when transition from that past point to the present. One view the point when asked what is the probability of A. Which is 50% What is the probability of A|B (A given B in statistics). The probability of A given I have information B modifies the probability of A having occurred. This is not an independent probability but a dependent one.

i agree with this because fundamentally she can't remember if she been woke up before (according to the experiment) so the fact that she is awake now can't be used to bias the answer dose 50/50 should be the right answer. correlation does not equal causation.

agree with this, but would say I'm a halfer in this instance because the exact question asked is 'what do you believe the probability of the coin being heads?' not 'what do you believe the probability of being woken up by the coin being heads?' subtle difference, but to one question I'm a halfer, the other a thirder.

Danm

@superkeefo This. That question sounds to me like question that would be asked in a hospital to check if my brain functions correctly like what's the date, who is current president etc. It made me 1/2er just because of semantics but I understood what he meant and in that context I'm 1/3er, so I don't know whether I should like or dislike

@0Ne but if you're saying there is context then you are essentially adding it and rephrasing the question given to you to be the second question. That's the point momo was making, the implied context makes you think you need to answer the second question. But really the question should be asked with that context or else it's 50/50

This! 100% this! The problem is that the language being used isn't precise enough.

Which paper was ist?

@Lp Gx I don't recall, but there is a lot posted now about the frequentist vs. Bayesian perspective of probability.

Apparently you believe the perceived probabilities of two different observers must sum to 1.

@Stewart Holiday Indeed; I think so. I would rephrase: the respective probabilities of two opposed rational observers having "their side win" while "the other side loses" should add up to 1. Those probabilities are both opposed (X + Y = 1) and the same (X = Y) as the protocol is completely symmetrical, therefore the probabilities are both 1/2 (X = Y = 1/2)

​@Florian Jourda You're going to have to define what you mean by "win". What is the game, what decides the result of the game, how many games are decided per experiment? And I assume based on your claim that your game won't permit both to "win" simultaneously?

I agree

Knowing Derek, The like/dislike options is a study in of it's self. We'll get another video where the like is the wroner answer and then a later video examining the results.

@Brandon Francey That makes a lot of sense. I'd bet that is the actual purpose of this video.

I liked this question as a vote to the proposition that people expressing enjoying the video will have a massive distortive effect on any attempt at polling. (Edit: Wait don't use comments as polls! Dislikes just bury the poll itself!)

I have liked your comment because I agree with it.

I am pretty sure he knows enough scientific methodology to know this liking/disliking thing is complete bs. It helps increase interaction so I guess it's a smart trick

"what is the question being asked?" is not a dilemma. The question is clearly about "the probability that the coin came up Heads". Answer to that question is 50%. And I agree with you that those who answer 1/3 are answering the wrong question.

that is so perfect an answer. how did you make it so easy,, in that, what is your background?

@Jonathan Lavoie what is the challenge being set, then. Is it to answer correctly on what the coin toss was, or something else? That's the dilemma here - not what is the correct answer, but what is being asked of her in the first place.

If the challenge was « guess the outcome and I give you 1$ » she would answer Tails, not because the probability is 2/3 but because the reward is twice. Just like I give you 1$ if you guess Heads right, and 2$ if you guess Tails right. You would answer Tails not because the probability is higher. It remains 50%. In the SB experiment, the question is the probability it came un Heads.

@uRealReals Thank you. You're the first person who reply to me so kindly! A short anecdote about me: In my programming course there was an exam in probability and statistics. Three of the questions were about the same problem. In a basket containing 9 blue balls and 11 red balls, what are the probabilities of A) draw 2 blue balls. B) 2 red balls. C) 2 balls not the same color. Questions A and B are very easy. But for question C I knew that the teacher wanted us to use a complicated formula learned by heart. I didn't want to use this formula because 1- The formula is complicated and I'm lazy, 2- I don't like to use a ready-made formula that I don't fully understand and 3- I wasn't sure if the formula really applied to the situation. So, I solved question C by following this simple reasoning: Probability of 2 blue balls + probability of 2 red + probabilities of 2 different = 100%. Total must be 100% because there is no other possibility. As expected, the teacher's formula answer was not the same as my answer, and I had to argue to get the point, but he had no choice but to acknowledge that his formula didn't apply to the situation, and that my answer was correct. I argued my point in front of the review board, not because I needed the point (my average was already 98%) but because I like the truth. That's who I am...

Correct.

You throw a coin once and see that it landed heads. What is the probability that it landed heads?

"The way i see it, a coin was thrown once. It does not matter if "tails" meant shed be awakened a hundred times - the coin was still thrown ONCE = so i vote 50/50 😊 Love your channel 😊" Correct.

Yeah, one of the confusions is that "what's the probability that the coin came up heads" can mean different things. Halfers think it's a question about the behaviour of coins. Thirders think it's a question about your on-the-spot beliefs about past events.

@Meamer I agree. Thirders actually think that the question is, "what are the chances that you were woken up once before?"

yup, like nearly all things, the readers interpretation is what truly matters... and yet the world doesnt care

@Words of Cheresie No, thirders are answering the exact question asked. Sleeping Beauty wasn't asked "did the coin come up heads?" She was asked, "what are the *chances* that the coin came up heads?" In the soccer analogy @veritasium used, he talked about this difference without actually pointing it out. About ten billion humans have been born. So the odds of you being born as you is one in 10 billion. So when I ask if you are you, what is your response? If I ask what were the *chances* that you would be born exactly as you are, what is your answer? The questions are different and so the answers are as well.

The best way to explain it is the way he already did. Let's Make a Deal gives you 3 doors, with only one valid prize, heads. The other two have tails behind them. Then they take away a confirmed wrong door, giving your probability of choosing heads an increase. That's why you always switch the door you choose after the removal of a tails door. This method is simply presenting you with two possible doors but then adding a 3rd confirmed possible door. Your safest bet is to be realistic and realize that the original two doors always had a 1/3 chance of having heads no matter what door you chose. Changing doors still results in a 1/3 chance of choosing the heads door.

👍

+ It's this bloody simple. Counting tails twice doesn't change the chance.

Yep. Think about the marble example. Its not pulling one marble out of a bag of 1 million black marbles and one white marble. It should be stated - flip a fair coin then if its heads pull a marble from a bag of 1 white marble and if its tails pull a marble from a bag of 1 million black marbles. Whats the probability of a white marble? 50%

@rakino close. If it's tails, grab all the black marbles. Now you have a lot of black marbles and only one white marble. The chance to end up with that many black marbles is still 50%, but that analogy more closely resembles the mess that is this probability discussion :')

Exactly, what that test is saying is that 1 heads = 1 heads, while 1 tails = 2 tails. The latter is then saying 1 = 2, which cannot be.

If the sweets could not see the wrapper color but felt movement, what color should they guess they are?

Dislikes, likes, youtube counts them both as engagement

@Joel Cook Right. "The algorithm" will often give you things that make you angry on purpose. Thats why republicans are always filled with outrage - because they engage these things. Their feeds are filled with things that make them angry.

the opposite, the aim of the video is to increase engagement and also shows the counter in the video title. perfect for the algorithm

I just think it's his curiosity for the answer of this question that he used likes and dislikes as voting poles. I mean scientists can go as far as to put there life on the line sometimes just to prove or experiment something.

Agreed. It is the perspective.

"Came" is the keyword. It's past tense. When an event has already occurred, any information you can access regarding that event changes the probability that it occurred one way or another. What's the probability that the card I pulled out of the deck is the ace of spades? 1/52. But now you draw a card. It's not the ace of spades. Since you've removed that card from the list of possible cards I might have, the probability that the card I pulled at the beginning was the ace of spades is now 1/51. Since it's a past event, new information about it changes the probability. I draw another card. Now it's a 2/51 probability that I have the ace of spades. You draw another. One less possible card I could have, so now it's a 2/50 probability that I have the ace. And so on and so on until all the cards have been drawn and the probability becomes 1/1 whether I have the ace or not.

I do think at least for those fully understanding it that it's about how we value information. Thirders are incorporating the fact she lacks information. Halfers are assuming lacking information is irrelevant. For the sake of Halfers it's important we define the problem of her guess in one single instance based on the rules. There is inaruguably three states in the state space. She's awake on a Monday with tails, she's awake on Tuesday with tails and she's awake on Monday with heads. I actually think it's Halfers that have one extra step of justification. (unless you completely missed this is about the shared information that she lacks information.. it's not a matter of perspective). That extra step is say even though she knows there's three states in the state space there's ultimately only two that matter. The third being she doesn't know it's not Tuesday and heads so the question is like saying it's 50-50 on Monday or Tuesday.

It's pretty clear that he asked the first question, it's explicitly written on the screen. So thirders are just wrong.

I agree. And as a halfer I have to point that the question is "What is the probability that the coin was heads"

It's more important to read the question.