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.
|