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Jan 4th, 2014
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  1. In the girl-named-Florida problem our information concerns not just the gender of the children, but also, for the girls, the name. Since our original sample space should be a list of all the possibilities, in this case it is a list of both gender and name. Denoting “girl-named-Florida” by girl-F and “girl-not-named-Florida” by girl-NF, we write the sample space this way: (boy, boy), (boy, girl-F), (boy, girl-NF), (girl-F, boy), (girl-NF, boy), (girl-NF, girl-F), (girl-F, girl-NF), (girl-NF, girl-NF), and (girl-F, girl-F).
  3. Now, the pruning. Since we know that one of the children is a girl named Florida, we can reduce the sample space to (boy, girl-F), (girl-F, boy), (girl-NF, girl-F), (girl-F, girl-NF), and (girl-F, girl-F). That brings us to another way in which this problem differs from the two-daughter problem. Here, because it is not equally probable that a girl’s name is or is not Florida, not all the elements of the sample space are equally probable.
  5. In 1935, the last year for which the Social Security Administration provided statistics on the name, about 1 in 30,000 girls were christened Florida. 5 Since the name has been dying out, for the sake of argument let’s say that today the probability of a girl’s being named Florida is 1 in 1 million. That means that if we learn that a particular girl’s name is not Florida, it’s no big deal, but if we learn that a particular girl’s name is Florida, in a sense we’ve hit the jackpot. The chances of both girls’ being named Florida (even if we ignore the fact that parents tend to shy away from giving their children identical names) are therefore so small we are justified in ignoring that possibility. That leaves us with just (boy, girl-F), (girl-F, boy), (girl-NF, girl-F), and (girl-F, girl-NF), which are, to a very good approximation, equally likely.
  7. Since 2 of the 4, or half, of the elements in the sample space are families with two girls, the answer is not 1 in 3—as it was in the two-daughter problem—but 1 in 2. The added information—your knowledge of the girl’s name—makes a difference.
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