Re: The Language Guy:

"Three reporters from Arizona, on the condition of anonymity, also let me in on another incident involving McCain's intemperateness."

Three anonymous reporters? I can see it if he was sourcing three former campaign staffers or something, but three anonymous reporters? It's not like they're revealing national security secrets. Here's their chance to be famous, why hide?

Would you believe it if three anonymous reporters claimed Michelle Obama used the word 'Whitey'? Of course not! Why the double standard?

Another smile for JoAnn:

http://news.bbc.co.uk/1/hi/world/americas/7441941.stm

Group hug, everybody.

lol

Thanks Zaphod ;)

Senator Clinton's speech was outstanding. In my mind, it was almost an A+. My only wish was that she would have spoken a bit more than she did about the "glass ceiling" as concerns African Americans. But other than that, her speech, at moments, brought me to tears.

Well done.

Re: You buying it?

To them I say, all right, you want to know what it is? The appeal, the pull, the ethereal and magical thing that seems to enthrall millions of people from all over the world, that keeps opening up and firing into new channels of the culture normally completely unaffected by politics?

Well, in the later stages of her campaign, Hillary Clinton also has this certain ethereal and magical pull with roughly 50 percent of Democrats.

I'm still pulling for the so-called "Dream Ticket". I think that Barack and HIllary together would be unbelievably inspiring.

About tossing a coin up in the air: what is the probability it will come to rest on head (or tail)? 50%, or one chance out of two? No. i thought it was, like everybody, but—and this is a true story—i once threw a coin to decide some outcome with a friend, and the coin came to rest on its edge! Since this rare occurence is bound to happen once in a while, the chance to get head or tail is surely less than 50%. That's what i concluded anyway. (If i'm wrong, i'll be happy to be corrected.)

i once threw a coin to decide some outcome with a friend, and the coin came to rest on its edge!

You lived a twilight zone episode.

re: probability (I will pick up the book). But, someone help me out here, because I'm a little confused.

If a woman has two children and one is a girl, the chance that the other child is also female has to be 50-50, right? But it’s not. Cardano again: The possibilities are girl-girl, girl-boy and boy-girl. So the chance that both children are girls is 33 percent. Once we are told that one child is female, this extra information constrains the odds. (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.)

If the permutations represent birth order, and we already know the first child was a girl, then boy-girl is not an option, only girl-girl and girl-boy. Therefore, the odds of having another girl or a boy are the same, 50%. If the permutations do not represent birth order, then boy-girl and girl-boy are the same combination, and so redundant.

(Note that this is different then the coin case for which the reversables heads-tails, tails-heads is legitimate because neither coin has been flipped).

Perhaps someone who knows more about probability can help me out?

I totally believe the Florida bit, though.

Dammit, I misread. We don't know the first was a girl, we just know that one child is a girl.

At any rate, I still don't see how boy-girl or girl-boy represent distinct possibilities, rather than exactly the same possibility.

Indeed it is 1 in 3

Here is some additional discussion of the problem from the book.

The effect on the probability of an event will occur if or given that other events occur is what Bayes theory is all about. To see in detail how it works, we'll turn to another problem, one that is related to the two daughter problem we encountered in Chapter 3. Let us now suppose that a distant cousin has two children. Recall that in the two daughter problem you know that one or both are girls, and you are trying to remember which it is --- one or both? In a family with two children, what are the chances if one of the children is a girl, that both children are girls? We didn't discuss the question in those terms in Chapter 3, but the effort makes this a problem in conditional probability. If that if clause were not present the chances that both children were girls would be 1 in 4, the four possible birth orders the (boy, boy), (boy, girl), (girl, boy), and (girl, girl). But given the additional information of the family has a girl, the chances are one in three. That is because if one of the children is a girl, there are just three possible scenarios for this family --- (boy, girl), girl, boy), and (girl, girl --- and exactly one of the three corresponds to the outcome that both children are girls. That's probably the simplest way to look at base ideas -- they're just a matter of accounting. First write down the sample space and -- that is, the list of all the possibilities -- along with the probabilities if they are not all equal (that is actually a good idea in analyzing any confusing probability if you). Next, cross off the possibilities that the condition (in this case, "at least one girl") eliminates. What is left are the remaining possibilities and their relative probabilities.

That might all seem obvious. Feeling cocky, you may think you could have figured it out without the help of a dear Reverend Bayes and vow to grab a different book to read the next time you step into the bathtub. So before we proceed, let's try a slight variant on the two daughter problem, one whose resolution may be a bit more shocking.

The variant is this: in a family with two children, one of the chances, if one of the children is a girl named Florida, to both children are girls? Yes, I set a girl named Florida. The name might sound random, but it is not, or in addition to being the name of a state known for Cuban immigrants, oranges, and old people who traded their large homes up north to the joys of palm trees and organize beagle, it is a real name. In fact it was in the top 1000 e-mail American names for the first 30 or so years of the last century. I picked it rather carefully, because part of the riddle is the question, what, if anything, about the name Florida affects the odds? But I'm getting ahead of myself. Before we move on, please consider this question: can a girl named Florida problem, are the chances of two girls still one in three (as they are in the two daughter problem)? I will shortly show that the answer is no. The fact that one of the girls is named Florida changes the chances to one in two: don't worry if that is difficult to imagine. The key to understanding randomness in all of mathematics is not being able to intuit the answers to every problem immediately and merely having the tools to figure out the answer.

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 sound 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), (girlNF, girl-F), (girl-F, girl-NF), (girl NF, girl-NF), and (girl-F, girl-F).

Now, the pruning. Since we know that one of the children is a girl named Florida, we can reduce a 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 the 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.

in 1935, the last year for which the Social Security Administration provides statistics on the name, about one in 30,000 girls were christened Florida. 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 one 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, boy), girl-NF, girl-F), and (girl-F, girl-NF) which are, to a very good approximation, equally likely.

Since two of the four, or half, of the elements in the sample space are families with two girls, the answer is not one in three --- as it was in the two daughter problem --- but one in two. The added information --- your knowledge of the girls name --- makes a difference.

the four possible birth orders the (boy, boy), (boy, girl), (girl, boy), and (girl, girl). But given the additional information of the family has a girl, the chances are one in three. That is because if one of the children is a girl, there are just three possible scenarios for this family --- (boy, girl), girl, boy), and (girl, girl ---

(Emphasis added).

This helps me ask my question in a sharper way. Obviously, boy-boy can't be the case because we know there's at least one girl. My problem was that both "girl" and "boy" in the "girl-boy" and "boy-girl" variations are the same boy and girl in both syntactical permutations, and so not distinct possibilities in terms of gender/sibling pairings, only of birth order. I do not see the relevence of birth-order for determining the probable gender of the other sibling if we already know one of the children is a girl. That is, if all that is in question is the probability of whether the other sibling is a boy or a girl, the order in which the siblings were born is irrelevent, and 'boy-girl' and 'girl-boy' represent one and only one possibility: namely, the two siblings being of different genders.

In other words, the expressions 'boy-girl' and 'girl-boy' are systematically ambiguous, depending on whether the relevent criterion is birth order (first or second?) or gender (male or female?). If it is birth order, 'boy-girl' and 'girl-boy' each represents a distinct possibility, either with the boy coming first or the girl, so the possibility represented by the term 'boy-girl' would exclude the one represented by the term 'girl-boy' and vice versa. If each term is merely a representation of a possible gender pairing of siblings, 'boy-girl' and 'girl-boy' represent exactly the same possiblity: for to say there is one boy and one girl in a family is the same as saying there is one girl and one boy. Same difference.

I can give formulas to explain more clearly what I don't see, but I'll see if that clarification helps.