Re: Which Twin has the Tony?
 

[ QUOTE ]
To be clear on the experiment; The twin girls and their haircuts are fixed. One of them is older. One has the Tony haircut, we just don't know which. The repeatable, random part of the experiment involves the doors they stand behind. If the experiment is repeated, half the time the older twin will be behind door #1 and half the time she will be behind door #2.

Before any door is opened the probabilty that the older twin is behind door #2 is 50%. But now suppose door #1 is opened to reveal the twin with the Tony. We still don't know whether she is the older or younger twin. But those who say that the probabilty is still 50% that the older twin is behind door #2 are wrong.

Do you see why?

PairTheBoard

[/ QUOTE ]

The clarification, oddly enough, does not spell out the key facts given in the original problem; namely, that the Tony haircut being on the older twin isn't any more likely than the Tony haircut being on the younger twin (and, incidentally, there's no chance that both twins have the Tony haircut).

I'm also not sure what you mean by saying that the haircuts are fixed, but the door they are standing behind is not. Given the information we have, the Tony haircut being on the older or the younger is a 50/50 probability, nothing more, nothing less. If you repeat the experiment without possibility of moving the haircut, then the Tony location becomes known, and you aren't repeating the experiment, are you?

I don't see any reason why putting the sisters behind doors has changed the probability that the sister without the Tony is the older sister.

Re: Which Twin has the Tony?
 

[ QUOTE ]
[ QUOTE ]
To be clear on the experiment; The twin girls and their haircuts are fixed. One of them is older. One has the Tony haircut, we just don't know which. The repeatable, random part of the experiment involves the doors they stand behind. If the experiment is repeated, half the time the older twin will be behind door #1 and half the time she will be behind door #2.

Before any door is opened the probabilty that the older twin is behind door #2 is 50%. But now suppose door #1 is opened to reveal the twin with the Tony. We still don't know whether she is the older or younger twin. But those who say that the probabilty is still 50% that the older twin is behind door #2 are wrong.

Do you see why?

PairTheBoard

[/ QUOTE ]

The clarification, oddly enough, does not spell out the key facts given in the original problem; namely, that the Tony haircut being on the older twin isn't any more likely than the Tony haircut being on the younger twin (and, incidentally, there's no chance that both twins have the Tony haircut).

I'm also not sure what you mean by saying that the haircuts are fixed, but the door they are standing behind is not. Given the information we have, the Tony haircut being on the older or the younger is a 50/50 probability, nothing more, nothing less. If you repeat the experiment without possibility of moving the haircut, then the Tony location becomes known, and you aren't repeating the experiment, are you?

I don't see any reason why putting the sisters behind doors has changed the probability that the sister without the Tony is the older sister.

[/ QUOTE ]

I didn't say that the probabilty that the older twin has the Tony is 50%. Either she does or she doesn't. We just don't know. We do know that one and only one twin has the Tony.

Also, the experiment can be repeated by bringing in new observers each time. The same girls with the same haircuts get randomly shuffled behind the doors, and each time a new observer comes in and is asked for the probability that the older twin is behind door #2 after being shown the twin behind door #1. For those cases where the observer sees the twin with the Tony behind door #1, is it correct for him to say the probabilty is 50% that the older twin is behind door #2?

Or put another way, given the experiment as described, what is the conditional probabilty that the older twin is behind door #2 GIVEN that the twin with the Tony is behind door #1?

PairTheBoard

Re: Which Twin has the Tony?
 

[ QUOTE ]
[ QUOTE ]
To be clear on the experiment; The twin girls and their haircuts are fixed. One of them is older. One has the Tony haircut, we just don't know which. The repeatable, random part of the experiment involves the doors they stand behind. If the experiment is repeated, half the time the older twin will be behind door #1 and half the time she will be behind door #2.

Before any door is opened the probabilty that the older twin is behind door #2 is 50%. But now suppose door #1 is opened to reveal the twin with the Tony. We still don't know whether she is the older or younger twin. But those who say that the probabilty is still 50% that the older twin is behind door #2 are wrong.

Do you see why?

PairTheBoard

[/ QUOTE ]

The clarification, oddly enough, does not spell out the key facts given in the original problem; namely, that the Tony haircut being on the older twin isn't any more likely than the Tony haircut being on the younger twin (and, incidentally, there's no chance that both twins have the Tony haircut).

I'm also not sure what you mean by saying that the haircuts are fixed, but the door they are standing behind is not. Given the information we have, the Tony haircut being on the older or the younger is a 50/50 probability, nothing more, nothing less. If you repeat the experiment without possibility of moving the haircut, then the Tony location becomes known, and you aren't repeating the experiment, are you?

I don't see any reason why putting the sisters behind doors has changed the probability that the sister without the Tony is the older sister.

[/ QUOTE ]


this is the dumbest thing i have ever heard of. it is 50/50 or you haven't given enough information. end of story.

Re: Which Twin has the Tony?
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
To be clear on the experiment; The twin girls and their haircuts are fixed. One of them is older. One has the Tony haircut, we just don't know which. The repeatable, random part of the experiment involves the doors they stand behind. If the experiment is repeated, half the time the older twin will be behind door #1 and half the time she will be behind door #2.

Before any door is opened the probabilty that the older twin is behind door #2 is 50%. But now suppose door #1 is opened to reveal the twin with the Tony. We still don't know whether she is the older or younger twin. But those who say that the probabilty is still 50% that the older twin is behind door #2 are wrong.

Do you see why?

PairTheBoard

[/ QUOTE ]

The clarification, oddly enough, does not spell out the key facts given in the original problem; namely, that the Tony haircut being on the older twin isn't any more likely than the Tony haircut being on the younger twin (and, incidentally, there's no chance that both twins have the Tony haircut).

I'm also not sure what you mean by saying that the haircuts are fixed, but the door they are standing behind is not. Given the information we have, the Tony haircut being on the older or the younger is a 50/50 probability, nothing more, nothing less. If you repeat the experiment without possibility of moving the haircut, then the Tony location becomes known, and you aren't repeating the experiment, are you?

I don't see any reason why putting the sisters behind doors has changed the probability that the sister without the Tony is the older sister.

[/ QUOTE ]


this is the dumbest thing i have ever heard of. it is 50/50 or you haven't given enough information. end of story.

[/ QUOTE ]

What's dumb is saying, "it is 50/50" and not knowing what you mean.

PairTheBoard

Re: Which Twin has the Tony?
 

Well, the probability is now either 100% or 0%, we just don't know which, since we don't know which twin is older.

Re: Which Twin has the Tony?
 

[ QUOTE ]
Well, the probability is now either 100% or 0%, we just don't know which, since we don't know which twin is older.

[/ QUOTE ]

Correct

PairTheBoard

Re: Which Twin has the Tony?
 

And therefore God exists and Jeebus will save us all.

Re: Which Twin has the Tony?
 

How is this not like saying: "I've flipped a coin, but I haven't looked down at it yet; the odds of it being heads is not 50:50, instead it's either 100% or 0% heads, I just don't know which". Because such a statement is, at best, a semantic argument, at worst a huge waste of our collective time.

Re: Which Twin has the Tony?
 

[ QUOTE ]
[ QUOTE ]
Well, the probability is now either 100% or 0%, we just don't know which, since we don't know which twin is older.

[/ QUOTE ]

Correct

PairTheBoard

[/ QUOTE ]

Sorry, no (with one condition, see (*) below.)

The question you asked was what is the probability the older twin is behind door #2.

The probability that the older twin has the Tony was 100% or 0%, but we don't know which, before we did the experiment. And this probability is still either 100% or 0% but we don't know which, after we do the experiment.

But, you placed the two twins randomly behind the two doors - so at the start of the experiment, the older twin had a 50% chance of being behind door #2 - and when you opened the door, you learned ABSOLUTELY NOTHING about the age of the girls. Whether neither, either, or both doors are open is completely irrelevant since you seeing a girl doesn't help you know which one she is. Posterior probabilities change only when additional information is gained.

The chance that the older twin is behind door #2 remains 50% from the time they are randomly positioned until the time you learn something new about how to tell the two of them apart.

(*) - You could, if you wanted, say "the probability was always 100% or 0%, as soon as the girls were placed behind the doors, and will forever remain so, since no amount of door-opening, questioning, or hair-cutting will cause them to physically move."

If you take that approach, however, you've basically chosen to regard probability theory in its entirety as meaningless - regarding your two hole cards as being best with probability 100% or 0% as soon as they are dealt, since the deck has already been shuffled and the identities of the flop turn and river are already fixed but unknown. True, in a vacuous way - but a useless attitude to take if you're interested in deciding whether to bet those cards or not.

Re: Which Twin has the Tony?
 

[ QUOTE ]
And therefore God exists and Jeebus will save us all.

[/ QUOTE ]

I wouldn't say that. But I think it does illustrate how incorrect it is when many people use the term "probability" in a haphazard way. In the repeatable experiment I describe above, if it were correct for the observers to say that the probability is 50% that the older twin is behind door #2 after seeing the twin with the Tony behind door #1, Then half the time the older twin would be shown to the observer behind door #2 and half the time the younger twin would be shown behind door #2. But this clearly does not happen. If the younger twin has the Tony then 100% of the time the repeating experiment will show the older twin behind door #2. If the older twin has the Tony then 0% of the time the repeating experiment will show the older twin behind door #2. Just because we don't know which it is doesn't make it 50-50.

When a nonexpert uses the "probability" term incorrectly it's understandable. But it irks me when David says things like, he estimates the probabilty that God exists to be about 1 in a Trillion - or whatever. As a recognized expert in probabilty his Misuse of the term amounts to an attempt to infuse his opinion with an authority it doesn't deserve. He can say he's 99.9999999999999999999% sure that God doesn't exist if he wants. That's fine. But delivering his opinion like it's an expert analysis of probability on the subject is just nonsense.

PairTheBoard