
Posted by: stak
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Posted on: 20090307 16:32:34
So I came across the "girl named Florida" problem today on somebody's blog. (Part 1, 2, 3). The problem is taken from the book "The Drunkard's Walk" by Leonard Mlodinow and is easily googleable. Here's the problem:
Suppose that a family have two children.
1. What is the probability that both of them are girls?
2. Suppose you know that at least one of the children is a girl. Now what is the probability that both children are girls?
3. Suppose you know that at least one of the children is a girl, and her name is Florida. Now what is the probability that both children are girls?
The answers provided are 1/4, 1/3, and 1/2, respectively (I'm not sure if these answers are actually in the book, but I assume they are based on what everybody is parroting). You can follow the supposed logic in the part 2 link above, or in question 3 here.
The thing is, the solutions given make no sense intuitively. And therefore, I don't think they're right. Knowing the name of one of the girls shouldn't change a thing, because you can assume that the girl is named "x" and the exact same reasoning would apply. Therefore the answers to question 2 and question 3 must be the same.
My answers are 1/4, 1/2, and 1/2. For the second question, there are really four possibilities with equal probability: BG, GB, GG, and GG. And half of them have two girls. Another way of looking it is to simply discount the child you know is a girl. Since the two children are independent events, the second child has a 50% chance of being a girl, and therefore there is a 50% chance that they are both girls.
I'm convinced my solution is right. As a consequence I'm also convinced that everybody else must be stupid, starting with the author of the book (assuming the book says 1/3). Somebody please prove me wrong.


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