Let me see if I can straighten things out a little bit. I’ve read most of your posts, Wissdock, and I’ve learned a lot, even though you’re a little hard to decode.

Say I discover a town that has 100 families, and each family has 2 children. I decide I want to make a little bit of money, so every mother I run into I ask if she has a daughter. If she says yes, I bet her a $100 that I can guess her other kid’s gender. Of course I’m going to be right 2/3 of the time when I guess boy, because I’ve weeded out the moms who only have boys. (This is in line with Cecil’s answer). Over time, I begin to see a profit.

This is when I start getting greedy. I decide if I can rip off the parents, I can rip the kids off too. I know that if I see a girl on the street, she can’t belong to a family will all boys, so the odds of winning my bet should be the same. So I start to bet every girl I run into that I can guess whether she has a brother or a sister, and subsequently guess brother. To my dismay, I’m not making any money as it appears the odds are now 50/50.

I ask myself, “what’s changed?” I then read a math article that wissdock linked.

http://64.233.161.104/search?q=cache:b2FuesRPPL8J:mathforum.org/library/drmath/view/52186.html+as+1/3+for+it+being+a+boy+and+2/3+for+being+a+girl.+&hl=en&lr=lang_en&ie=UTF-8)

Essentially, the chance of the sister having another sister is doubled because I have an equal chance of picking either sister in the girl/girl family.

After I realize my mistake I decide to go back to only making bets with the mothers.

On one occasion, before I have the chance to ask the mother whether she has a girl, her daughter walks into the room. What’s just happened? I know that the mother has a daughter now, so if I guess her other kid is the opposite I should have 2/3 chance of winning. But if I bet the daughter she has a brother I should only have 50/50 chance of winning. Is this some kind of paradox?

This leads me to conclude that probability means NOTHING in isolated cases. Probability only means ANYTHING when the experiment is repeatable. Saying I have a 2/3 chance or a 50/50 chance of being right only means something in the context of how I repeat the experiment.

In other words: *ANY PROBABILITY VALUE I ASSIGN TO MY CHANCES OF BEING RIGHT IS ARBITRARY, THEREFORE THE ORIGINAL QUESTION IS MEANINGLESS WITHOUT MORE INFORMATION. *

Let me ask a question: how would you repeat the original experiment?

Let me ask another question: After you met the girl in the last meeting of my story, if the mother said “This is my oldest and tallest girl, and the one I love the most, and I think she will be President someday,” would that change your odds of winning the bet with the mother? (OF COURSE NOT). I only mention that because some people seem to think that once you know the girl as a specific, it changes the odds. That doesn’t even make sense to me. The odds will only change in relation to who you’re betting against.

Someone earlier, (in the other thread) stated that how the information is obtained should not affect how the probability is calculated. I could not disagree more.

It took me hours to think of this, and I’m no genius or mathematican, so if anyone would like to rebut, I’d love to hear why I’m wrong.