Here's a review of Leonard Mlodinow's book The Drunkard's Walk. I will resist the temptation to review the review. (Although I've been meaning to write down what I think of the book. I might do so.)
For some difficult-to-explain reason it is illustrated with a couple images from Jessica Hagy's indexed.
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7 comments:
My review of The Drunkard's Walk is now only second from the top of my drafts pile. . . .
"(Even weirder, and I’m still not sure I believe this, the author demonstrates that the odds change again if we’re told that one of the girls is named Florida.)"
Can you explain this? I've not even a slight clue how this would effect the out come.
First, let's list the possibilities. We don't care what the boys are named, and a girl can either be named Florida or be named something else. So, the "sample space" of all possible combinations is as follows:
(boy, boy), (boy, Florida), (boy, Not-Florida), (Florida, boy), (not-Florida, boy), (Not-Florida, Florida), (Florida, Not-Florida), (Not-Florida, Not-Florida), (Florida, Florida).
The order in the pair just indicates which child was born first. If we're told that one of the children is a girl named Florida, then the only possible combinations from this list are the following:
(boy, Florida), (Florida, boy), (Not-Florida, Florida), (Florida, Not-Florida), (Florida, Florida).
Now, it's not terribly likely that a girl chosen at random has the name Florida; that probability might be, for the sake of argument, 1 in 1 million. The chances of two girls (in the same family, to boot) both being named Florida is so small it's not worth bothering with. So, we can neglect the (Florida, Florida) combination, leaving us with
(boy, Florida), (Florida, boy), (Not-Florida, Florida), (Florida, Not-Florida). These are, pretty much, equally likely. Two out of the four possibilities are families with two daughters, so the probability that the family has two daughters is 0.5.
Oh, and by the way, the word Florida sounds really !#%!#@$ weird when you say it to yourself that many times.
thanks blake
Wouldn't the same argument work if the girl had a common name, like Sarah? After all, no one ever gives two siblings the same name, so (Sarah, Sarah) is an impossible combination.
Aram,
you're right. The argument still works if Florida is replaced with a more common name, although the probability isn't quite as close to 0.5 as it is in the cases with rare names.
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