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

read a book *******

1/3 does not make any sense at all, you genuinely have to be autistic or severely retarded to come to that conclusion. A coin flip is not biased, its chances of landing heads or tails are the same. When she wakes up should not be a factor considered when determining a probability of how often it lands heads.

If I say yes to this, and I assume you are looking for the answer it is more likely to be Monday, it does not mean it's new information- it would have been known before the experiment. To see why, I will ask how Beauty would know it's more likely to be Monday after waking. If it's because of any sort of logical deduction, then she could have made this deduction before the experiment and the info is not new. If it's the physical act of waking up somehow instilling in her this knowledge...that doesn't make any sense to me.

In the paper, W is picked to be the event "Beauty wakes a least once during the experiment" for a very particular reason, namely it encompasses every scenario matching our given info that Beauty awakes. The interesting point about W here is that P(~W) is nonzero if c<1 and in in general depends on c.

Where exactly does he say P(H)P(W|H) = 1/2? I'm not finding this.

no, beauty wakes at least once treats tails Monday and tails Tuesday as the same event. the day matters because it's what differentiates the coin flip outcomes.

the very act of waking up instils in her knowledge that it is definitely not tuesday and that heads was flipped; she could not have known that wouldn't be the outcome before the experiment.

you are confusing posterior probability and prior probability.

fuuuuuuuuuuk i get what youre saying brah

She would say 50/50... but only because she is a dumb biitch and the actual answer is 1/3

Lol at the twinks agreeing with Snow White, even after rational explanation. Seriously just...

lol go back to reddit or your Mom's basement, or wherever you came from

You are misunderstanding why he is utilizing W here. It's got nothing to do with differentiating days, it's simply a defined event: that she wakes up at least once during the experiment. And I see no errors in terms of how he is utilizing W in his calculations (if you find any, please point them out specifically). I also am still not seeing where you said he started off with P(H)P(W|H) = 1/2. Bottom line is, this article is the closest thing I've seen to a sound mathematical argument for 1/2. He's not even using philosophical hoops like I've seen in some of the 1/3 arguments- it's literally just a calculation.

Edit 1: More precisely, to see why he is choosing W to be the event (Beauty wakes up at least once during the experiment), consider three options:

1. Beauty never wakes during the experiment.
2. Beauty wakes exactly once during the experiment.
3. Beauty wakes at least once during the experiment.

These 3 are saying different things. The only one we knowfor surefrom the given info is statement 3. That is why he is choosing W to be statement 3.

Edit 2: Regarding Beauty waking up and realizing it's not Tuesday and heads- ridiculous even arguing this at this point, but let me list two statements. Can you tell me if they are both true? Only one true? None true?

- After Beauty is awoken, she knows it's not both Tuesday and heads was flipped.
- Before the experiment begins, Beauty knows that if she is awoken, that it will not be both Tuesday and heads flipped.

This entire premise is negated by the fact that she's intentionally unaware as the question states nor does it address that multiple guesses are made after separate memory resets that have a constant change of 50/50 regardless of number of days guessed on because the flip is a single event with a constant answer, like I said odds can only exponentially increase if the question is "how often is beauty correct" not "will she be correct"

Lol. This.

Well I just proved that it's better to pick tailshttps://codepen.io/TylerL-uxai/pen/Bwvrwv

It is new information. The fact that she woke up, and she is being interviewed means it is either Monday or Tuesday, so we can look at what conditions occur given that it is Monday or Tuesday. That's where you get the 1/3. It's conditional probability.

I can see both arguments honestly. I'd imagine if you simmed this, you'd find 1/3 to be the answer.

Can you explain how "it is either Monday or Tuesday" is information added? Your post leaves that out.

Basically because just because she doesn't know if it is Monday or Tuesday doesn't mean that she doesn't know which one is more likely. It is obviously more likely that it is Monday. There are 2 ways Monday happens, and only 1 way Tuesday happens with equal probability. Similarly, there is only 1 way heads happens, but 2 ways that tails happens with equal probability.

This is not new information. Surely she knew before initially being put to sleep, that when she is awoken to be interviewed, that it would either be Monday or Tuesday. It is simply the given info, known before experiment.

It has to be 1/3. How can it be 1/2?

take a stats class my man just fking lol

If sleeping beauty considers what day it is, at all, when figuring out the odds, she should get 1/3 - basically. The fact that she is awake tells her that it could be Tuesday.

What a detailed, sound response there brah

So since you are a stats guy....can you please explain how exactly you are using Bayesian inference, which you linked above, to get from Probability(Monday|Beauty awakes), to Probability(Heads|Beauty awakes)?

If it's an unsolved debate with professionals, fawk dat shyte, tl;dr.

Nah bro you can't give up, we got this!

Something to think about if you dislike the 1/3 rational is that if the question was: "What side do you think the coin landed on?" - You would be outright wrong to say heads. If there was a "prize" to be won by guessing correctly you would win 2/3 of the times you wake up by guessing tails. So how could you wake up and believe there was equal chance the coin landed heads as tails?

in simple english,

given that beauty is awake, what is the probability it is monday? she is awake for sure on monday (H & T) and awake with 50% probability on tuesday (T only) so 2/3 (2 out of the 3 possible circumstances are monday)
probability that it is monday and it was heads? 2/3 * 1/2 + probability that it is tuesday and it was heads 0 (she would be asleep) = P (H | beauty awakes) = 1/3

lol, just lol.

So you are saying if we simulated a coin flip in excel, we would find that the coin lands on heads only 1/3 of the time?

Let me just flesh this out a little more to make sure that I understand you:

If we program an application on excel to generate 1,000 truly random selections between only to numbers -- 1 and 2 (1 representing heads and 2 representing tails)--you are saying that the random number generator would select 1 only 333 times and it would select 2 666 times? Or in other words, are you suggesting that excel would defy 1st-grade probability fundamentals?

That does not effect the probability of the flip, it could only effect her response except for the fact that the controlled factor in the experiment is her not knowing how often she's interviewed is connected to the flip. How stupid are you people

How often she is awake doesn't effect her answer nor does it pertain to the question. Seriously how stupid are y'all

You need to use proper notation. Are you saying
P(Monday | Awake) = 1 ?
If so, that's not correct. P(Awake | Monday) = 1 but
P(Monday | Awake) = 2/3
Also, P(A | B) = P(AB) / P(B) but it seems like you took the sum of independent intersections for the formula, which is wrong and by the way you can't assume are independent.

What's the explanation behind 1/2 ?

Your formula application is wrong because her being awake or asleep on whatever day doesn't effect her probability of being correct

wut? Can you explain which formula is wrong? Also, the formula I used has no relationship to the credence of head. He altered his formula to probability values that suit 1/3. I believe the answer to the original question is 1/2.

Youre measuring the probability of her being awake which has 0 effect on the probability of her being correct, which is the question. Y'all aren't combining your math skills with scientific method properly. If you disregard control factors (her unawareness of coin flip prior, resulting effect on days awake as a result of flip) while calculating probability you get the question wrong. The fact that y'all are trying to use statistical method on an algebra 1 problem is a result of reading comprehension issues. Re read the question, determine the variable, result of variable answers, and controlled factors. It's actually less than 2 steps to solve