You've misused the word "effect" 3 times now and have called others stupid. I'd just like to point that out.

Anyway, regarding this. Like I said, I can see the justification of the argument for 1/2 as well as the one for 1/3. When framed from beauty's POV, if you sim it, you will see it is 1/3. There was a guy who wrote a sim for this earlier. It's a conditional probability issue.

Those of you who scoff at the idea of simming it, just do it, and eat your words. If I have time today, I am gonna write a MATLAB script to sim this chit. We will settle this like men...with MATLAB!

Regardless of which day she wakes up on, a coin flip can only produce two outputs — a heads or a tails, each having equal probability of appearing.

The question is asking about the probability of a flip on heads, which, as explained above, is 1/2.

If it was as easy as siming it wouldn't be an ongoing debate would it? Thanks for correcting my grammar mistakes but I have some bad news for you. A simulation is only accurate if the variables and controls in the problem are entered correctly, aka it can't save you from being a retard

Original question is great. The order of operation question I understand why people get it wrong, but explanations in here are spot on.
This
Not this
This
Not this
This
This
Nope 7 days in a week, but you're still wrong. Not enough emphasis put on M or D and A or S instead of giving them an order.

I am a HS math teacher

How is this new info. She clearly knows before the experiment that it could be Tuesday when awoken to be interviewed. Particularly, she knows that tails might be flipped. Im not sure why you are bringing calculations, 1/3, etc into this, my post was just about the subject of new info.I was looking for a precise application of Baye's Theorem, all I'm seeing here is an attempt at a generic argument for 1/3. Someone might argue several points in the above calculation, for example you are saying P(Monday and heads) = P(Monday)*P(heads) = (2/3)*(1/2). Well P(A and B) = P(A)*P(B) in general when A and B are independent events....so I guess you are saying "it is Monday" and "heads was flipped" are independent....
(Edit: IronProdigy beat me to it ^^)

My true feelings on the problem are that it is not stated well, and depends strongly on a few items- particularly how we are interpreting Beauty's credence, and also to a lesser degree, how we are defining probablitly in general. I'm playing advocate for 1/2....but I do think, as the problem is stated, either side really has a claim.

In general, when you have no agreement amongst professionals and the larger community with problems of this type, it usually is because of a poorly stated problem. Surely if it was as easy, open and shut, as the 1/3 calculation made above, it wouldn't still be considered such an open problem in the puzzle community...

To the person flipping the coin, the answer is always 50/50.

To sleeping beauty, she should answer tails every time to be right 66% of the time.

Exactly. People aren't arguing as much the results of these sim trials. The question more is how they relate (or not relate) to concept of Beauty's credence. That is what the majority of the debate is about.

She doesn't know what the variable result entails that's the entire point of the experiment

Consider it 22 yo hubris but my answer is correct no matter who says otherwise. Idgaf if Albert Einstein ressurects to say some bs it can't be 1/3 because of the way the question is asked. No if ands or buts

So I wrote 2 sims. First sim defines the value of the coin flip, checks if it is heads or tails, and if it is heads, it awakens beauty on Monday, has her predict the flip randomly, keeps track of how often she was right, and then if it is tails, awakens her on Monday, has her predict the flip randomly, keeps track of how often she was right, and then has her awaken on Tuesday, predict the flip randomly, and keeps track of how often she was right. As expected, in this case, which corresponds to taking the pov of the experimenters, she is right 1/2 the time.

The other sim defines the value of the coin flip, and checks to see what happens if beauty always guesses heads. She is awoken on Monday. If the coin flip is heads, she guesses heads, and she is right, so it increases the tally of correct answers by 1. If the coin flip is tails, she guessed incorrectly so the tally of incorrect answers increases by 1. Then, if it was tails, she is again interviewed on Tuesday, and since she guesses heads, she is wrong, so it increases the tally of incorrect answers by 1. For this experiment, from the POV of beauty, she is right 1/3 of the time if she guesses heads, so she sound say she thinks the probability of the coin having been flipped being heads is 1/3. This is different from the POV of the experimenters, as I tried to argue earlier. There is a conditional probability change due to the knowledge that it has to be one of the days, and there are constraints on which day is more likely to occur and what happens for a given day.

Spoiler!

Code is in above spoiler for MATLAB. This is why probability can be tricky because of language ambiguity. You have to be careful from what POV you compute the probabilities.

The only problem here is conditional probability issues have some sort of new condition, or new information, that is relevant to the probability in question. I'm still waiting for that new information.

In terms of creating the simulation, I would say save your time, it's pointless. Halfers are not arguing the result of that sim. They are arguing whether the sims are applicable to the problem of determining her credence.

I wrote 2 sims. One gave 1/2, and one gave 1/3. And I'm trying to explain why it matters which way you compute the probabilities. It is easier if you look at the code, and see the distinction between the two simulations. The frequency the coin was heads is given as headcount/(headcount+tailcount) and is always near 0.5. However, when she always guesses heads, she is only right 1/3 of the time. From her POV, it makes sense to guess tails. From the experimenters' POV, if she guesses randomly, she will be right half the time.

I've studied statistics

You were in primary school at the time, learning about vowels...

Ya are so unaware on PEMDAS troll thread
Also on the days of the week thread

Poser miscrs detected

Youre creating a new non existent condition; she guesses heads all three days. If you take a step back like the question asks, from her pov the odds are still 50/50 because the odds of her guessing heads is 50/50

What? What are you even saying? I simmed what happens if she guesses heads every day she is awoken from her POV. The answer is then that she is right 1/3 of the time. On the other hand, from the POV of the experimenters, as I explained, she is right half the time randomly guessing. There is no contradiction here because they are two different situations. See the code. There are only 2 days, btw, Monday and Tuesday.

Youre creating a condition that she guessed heads all 3 days, when in reality, there's only a 50% chance of that happening. You scoped in too hard and made the equation a completely new one. When you turn a variable into a constant, you **** up the equation

What do u mean 3 days dude there are only 2 days...she guesses heads on monday, and she is either right or wrong...if shes wrong on monday, she's also wrong on tuesday...

No.....no she's not.....

It's chance of correctness per interview, there's no forced recurring answer

I was saying if she guesses heads and is wrong on Monday, she is also going to be wrong on the corresponding Tuesday...

And I'm saying no......youre making up a rule. Try re reading the question

There's either

A. 2x of a 50/50 guess

Or

B. 1x of a 50/50 guess

There's no carry over answers or conditions, each day is a chance reset

You obviously aren't seeing what I am saying. The second sim was for the strategy of guessing heads every single time. If she does this, she is either right on Monday, or wrong on Monday and also she will be wrong on the following Tuesday. Not seeing the issue here.

This thing is still going? Can we just agree that there is no new information so it has to be 1/2

I simmed it and showed that in 1 interpretation it is 1/2, and in another, it is 1/3.

I'm the guy that wrote the sim. I'm thinking of making a simple neural network and asking it the same question.

Anyway, here's Beauty being asked the question 1000 timeshttps://codepen.io/TylerL-uxai/pen/Bwvrwv

I wrote one too. See my above post. My result was the same as yours for 1/3, but in a different context, it is 1/2.

Here's my MATLAB code

Spoiler!

Orlly??? Yea no **** but you don't realize you scoped in. Just because you can (look for key words here boyo) CREATE the condition to MAKE her guess heads all three days, does not mean that a RANDOMIZED guess over the span of 2 or 3 days is 33%

It's 50

But the 1/3 one assumes she picks heads every time which it doesn't say anywhere in the question

...The code demonstrates that if she guesses heads, she is right only 1/3 of the time, rather than the 1/2 you are saying. And there aren't 3 days. Where are you getting 3 phucking days? There are only 2 motherphucking days, Monday and Tuesday. WTF

I think that's giving her a random prediction rather than the case for always chosing heads vs always choosing tails. What would be *really* cool is if it was 1/3 for heads but something totally different for tails. Unfortunately it's just 2/3 I think. Looking for a browser JS library to run the sim on a neural network at the moment.

Also, good work on the code