Which Twin has the Tony?

[Stephen H]

[ 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.