Children

i supposed next we'll be discussing the "let's make a deal" question....here it is for anyone that hasn't heard it yet:

3 doors. a, b, and c. only one prize behind one door, you obviously don't know which has the prize.
you choose door a.
the host shows you door b, which is NOT the winning door. then he asks you if you want to switch to door c.
do you switch?

[lorinda]

See thread on here titled "Does it matter" for this debate,also thread titled "The game show" on internet gambling (though the one on here, predictably, is better)
It also has several new twists on this forum

Depends on the nature of the utterance.

If someone asks the question to a person who has two children “Is one of your children a boy?” Then, of the people who answer “Yes, one of my children is a boy”, there is a 1 in 3 chance that the other child is a boy.

If someone asks the question to a person who has two children: “Tell me the gender of one of your children”. Then of the people who answer “One of my children is a boy”, there is a 1 in 2 chance that the other child is a boy.


Detailed argument for each follows.

For the first case, start with 1000 people that two children and ask them the question “Is one of your children a boy”. On average, 250 people will have 2 girls and say “No, none of my children is a boy”. On average 500 people will have a boy and a girl and say “Yes, one of my children is a boy”. On average, 250 people will have 2 boys and say “Yes, one of my children is a boy”.

Thus 750 people will say “Yes, one of my children is a boy” and out of those 750, in 250 cases will the other child be a boy. Thus 1 in 3.

For the second case, start with 1000 people that two children and ask them the question “Tell me the gender of one of your children”. On average, 250 people will have 2 girls and all will say “One of my children is a girl”. On average 500 people will have a boy and a girl and on average 250 of those will say “One of my children is a boy”. On average, 250 people will have 2 boys and all 250 will say “One of my children is a boy”.

Thus on aveage 500 people will say “One of my children is a boy” and out of those 500, in 250 cases will the other child be a boy. Thus 1 in 2.

Realized I didn't really complete my thought and didn't bother to register so I could edit...so here is the rest.

So of the two scenarios which should one assume matches the original question that Lorinda posed. This is more subjective question. But the key to me is whether or not the friend was "free" to say "One of my friends children is a girl" even if one was a boy. Since no restrictions were given on what she possibly could have said, if I must bet solely on the information given, I would go with the assumption that the 1 in 2 scenario matches most closely.