Which Twin has the Tony?

[PairTheBoard]

Two girls are identical twins. One was born first so is technically the older of the two. One of the girls has a Tony haircut while the other does not. We do not know which girl has the Tony and have no reason to think one is more likely than the other to have the Tony. One girl is behind door #1 and the other is behind door #2 with a 50-50 chance for either to be behind either door.

Now, door #1 is opened to show that the twin behind it has the Tony haircut. What is the probabilty that the girl behind door #2 is the older twin?

PairTheBoard

[Tom1975]

I'll bite...um 50%?

[kyro]

Not enough information. What is a Tony haircut?

[Stephen H]

I have no idea what a Tony haircut is. That said, I don't see any reason why this wouldn't be 50%.

I ran some simulations using 2 doors, an index card that said "Tony Haircut", and my twin sisters, and they seemed to support the 50% theory.

[kyro]

Using an index card skews the results. You need to actually give one of your twin sisters the Tony haircut. Hey, don't look at me. I don't make the rules.

[BettyBoopAA]

50%, since age and the haircut are independent. only 4 possibilities in this problem and with the info only 2 choices remain, either Door 1 is older or Door 2 is older..

[MikeL05]

I'm going to be really disappointed if the answer is .5

[binions]

[ QUOTE ]
Two girls are identical twins. One was born first so is technically the older of the two. One of the girls has a Tony haircut while the other does not. We do not know which girl has the Tony and have no reason to think one is more likely than the other to have the Tony. One girl is behind door #1 and the other is behind door #2 with a 50-50 chance for either to be behind either door.

Now, door #1 is opened to show that the twin behind it has the Tony haircut. What is the probabilty that the girl behind door #2 is the older twin?

PairTheBoard

[/ QUOTE ]

50% unless you define "the twin" to mean the younger is "the twin" of the older, ie the older is the original, the younger is the twin.

In which case, when you say "the twin" has the Tony haircut, then the older girl must be behind Door #2.

[PairTheBoard]

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

[BettyBoopAA]

NO
There's only 4 combinations
D1 has tony and is older
D1 has tony and is younger
D1 no tony and is older
D1 no toney and is younger
once you take away 2 options, it's still 50-50.