Michael

I'm questioning the validity of those probability choices. Imagine instead if it were: Mon Tue Roll 1-5 1/3 0 Roll 6 1/3 1/3 Is it right to distribute...

You seem to be thinking of it as: 1. Sleeping Beauty picks tails. 2. We flip a coin. 3. If it's tails, we flip again. In that case; yes, it's more lik...

Getting to bet twice on tails doesn't mean that it's more likely to be tails. It just means she gets to bet twice on tails.

The probability that it's Monday given the fact that it's heads/tails.

It doesn't happen twice to her. It only happens once to her, given that it was only tossed once. She just wakes up to it twice.

Is that what I've done above? P(Tails and Monday) = P(Tails) * P(Monday|Tails) = 0.5 * 0.5 = 0.25 P(Heads and Monday) = P(Heads) * P(Monday|Heads) = 0...

Sure, but it doesn't mean that tails is twice as likely to occur as heads, which is why these betting examples miss the point. All the betting example...

Lewis has the same answer to me, but it looks like I got there a different way. His depends on a premise that Elga rejects whereas mine doesn't. I onl...

To better explain this, imagine I toss a coin. If it's heads then I give you a red ball, and if it's tails I toss again. If it's heads then I give you...

Adam Elga's reasoning from the Wikipedia article is this: But let's apply the general multiplication rule from above: P(Tails and Monday) = P(Tails) *...

Then I think you're wrong in suggesting that both are valid. The general multiplication rule, from here is: P(A and B) = P(A) * P(B|A) Where A is head...

This right here is the most succinct explanation.

And I seriously don't understand how you can't see the 50% argument; disagreeing with it is one thing but it has been explained to you at this point n...

How is this any different to awarding 1 point for successfully guessing heads and 0.5 points for successfully guessing tails? 1 point for each would a...

So, I ran 100,000 games and gave 1 point for successfully guessing heads and 0.5 points for successfully guessing tails (because you get two opportuni...

I still don't see how that makes it 33%. She knows that P(Heads) = 0.5 and that P(Monday|Heads) = 1. So she knows that P(Heads ? Monday) = 0.5. She kn...

A. Box with red ball B. Box with blue ball C. No box D. Box with black ball She wakes up and is given a box with a ball in it. What are the odds that ...

Assume she's woken on Monday if it's heads or Tuesday and Wednesday if it's tails. Do you agree that P(Monday|Awake) = 1/2?

Do you mean that if both people who are asked if it's tails correctly guess tails then that should only be counted as 1 success rather than 2?

I know, but it has a 50% chance of happening, which is exactly what I'm saying. 50% chance of red ball. 50% chance of Monday and heads. 50% chance of ...

No it doesn't. It's a blue ball on Tuesday and a black ball on Wednesday (if tails) and a red ball on Monday (if heads). If you're given a box then th...

These cases are different because being asked (again) provides you with additional information, whereas it doesn't in the original case. You're going ...

You're looking at it wrong; see the example with the balls in boxes.

That doesn't change the fact that P(H) = P(H & M) = 50%.

If it's heads then I'm given a box with a red ball on Monday. If it's tails then I'm given a box with a blue ball on Monday and a box with a black bal...

She already knows that it was a fair coin toss and that a fair coin toss has a 50% chance of landing heads. Nothing can change that.

I don't know what you mean by adding up to 33%. P(Heads) = 50% P(Monday|Heads) = 100% P(Heads & Monday) = 50% P(Tails) = 50% P(Monday|Tails) = 50% P(T...

They're not equally likely. Heads and Monday is 50%, because heads is 50% and heads guarantees Monday. P(H) = P(H & M).

Here's my variation: If it's heads then she's given a red ball. If it's tails then she's given a blue and black ball. What are the odds that she's giv...

Sorry, I thought you were arguing for the thirder answer.

But one of those awakenings is twice as likely as each of the other two, which is why the halfer answer is correct.

No, if there's a 50% chance that she is awakened on Tuesday and Wednesday then there's a 50% chance of Monday and heads.

What I'm saying is that there is no reason for her to have a greater belief that it was tails than heads. When she's asked what her belief is that it ...

So a 50% chance that it's tails and a 50% chance that it's heads.

Just pointing out that there's only one payout, not 99 in the case of tails. So if you were in her shoes, what would you bet? £1 on heads or £99 on ta...

The chance that on Monday the coin flip was tails is 50%, but that chance that any given waking day is Monday and that the coin flip was tails is 25%....

I think @"andrewk"'s example of betting is a good thing to consider. Let's say that you're woken up once if it's heads but 99 times if it's tails. You...

Why is P(A) 3/4? Given that she's awake (and knows it), P(A) is 1. She can dismiss P(S) as a possible outcome. And for the same reason P(A|H) should b...

Then she knows that there's a 50% chance that it landed heads. It doesn't matter if she's only woken once if it's heads but twice if it's tails; a fai...

As she's awake we have to dismiss Heads-Tuesday as an outcome. The only outcomes are Heads-Monday, Tails-Monday, and Tails-Tuesday. But is it right to...

She should flip a coin. If the original flip was heads then she’ll have a 50% chance of being right, but if it was tails then she’ll have a 75% chance...

False analogy. "Venus" is a proper noun that denotes a specific object, whereas "banana" isn't.

So a paradox is just a persuasive contradiction.

It just means that the axiom schema of unrestricted comprehension – ?y?x(x \in y ? P(x)) – is inconsistent, and so additional qualifications are requi...

I think he wife would disgree. She didn't know it was fake when it was reported.

S being a square circle isn't a paradox. It's just nonsense. R being a set that contains all sets that do not contain themselves isn't a paradox. It's...

Let S be a square triangle. How many sides does S have? Is this a paradox? If not, what makes Russell's set different? I say nothing. In both cases th...

He's saying that there cannot exist a barber who shaves all and only men who do not shave themselves. No barber is a "Russell barber". And so there ca...

What about 20? That's 1 in 9.5e-7, which is more than 3 times as rare as the 5-sigma confidence used in physics.

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